International Economics II: Parity Conditions, Exchange-Rate Models and Trade Policy

Branch: Economics & Corporate Completions (Finance-Plus Ring) · Node EC1.04 · ~20 focused hours · Standard gate ≥ 85%

A dealer in Mumbai shows you 84.4800 / 84.5200 for the dollar. A dealer in Frankfurt shows 1.0840 / 1.0845 for the euro. A third dealer, who has not looked closely at either screen this morning, offers to buy euros from you against rupees at 91.8000. Buy your euros the long way round, rupees into dollars into euros, and each one costs you 91.661940 rupees. Sell them to the third dealer at 91.8000 and you have made 13.8060 paise a euro. On ₹10 crore that is ₹150,619, earned in the four seconds it takes three messages to leave a keyboard, with no overnight position and no view about anything.

That trade is the smallest and hardest member of a family. Everything in international economics that carries the word parity is a claim that some price is pinned by an arbitrage of this kind, and the family sorts itself by how hard the pin holds. Triangular arbitrage is enforced in milliseconds by machines, so it barely exists. Covered interest parity is enforced by a fully hedged funding trade, so it holds to a few basis points and the residual has a name. Uncovered interest parity is enforced by nothing at all, because it is a statement about expectations, and it fails so reliably that a whole industry has been built on the failure. Purchasing power parity is enforced by shipping containers, over decades, badly.

Read the family in that order and the confusion clears. An analyst who says "parity implies the rupee will weaken 2.3% next year" has collapsed an arbitrage identity that must hold into a forecast that usually does not, and the collapse is worth real money to whoever is on the other side. When flows rather than arbitrage set the price you need a model of the flows, which is where Mundell-Fleming, the monetary approach and the portfolio-balance approach come in, each answering a different question and each wrong outside its own question. When a government changes the price of traded goods on purpose you need surplus arithmetic, which turns "the tariff protects jobs" into a number with a currency sign on it.

Two habits get built here. The first is notational: you will be able to read any quoted pair under either convention in circulation and say, out loud and correctly, which currency just got more expensive. That sounds trivial until you notice that the market's convention and the CFA curriculum's convention write the same number with the two currencies in opposite order, and that getting it backwards inverts every conclusion downstream. The second is arithmetical, because every relation here is solvable and checkable by a second route, and the check is what separates an analyst from someone repeating a sentence they read.

One trap is worth naming before you meet it. Most of the numbers here come from central banks and statistical offices reporting under a manual that was revised in 2009 and adopted at different dates in different countries. A confident assistant will classify a patent sale, a debt forgiveness or a migrant's transfer into the wrong account with total fluency, because the older manual put some of them elsewhere and the training text is full of both. The accounts are exactly the kind of fact that cannot be checked from first principles.

This Ring is additive institutional and CFA breadth. It presents the toolkit and the plumbing alongside, not in place of, the programme's process-over-P&L, concentration-over-diversification philosophy. Nothing here asks you to run a carry trade. It hands you the machinery so that when a broker note, a central-bank bulletin or a trade-policy submission uses this vocabulary precisely, you are reading rather than guessing.

Learning objectives

By the end you can:

1. Convert between the two live quote conventions (the market's base/quote pair and the CFA's price-currency/base-currency form), read any quoted rate correctly under either, and compute the asymmetry between one currency's appreciation and the other's depreciation exactly rather than approximately.
2. Build a cross rate from two-way quotes with the bid and offer on the correct side, and test a third dealer's quote for triangular arbitrage, reporting a profit or a loss after the spread rather than before it.
3. Derive and solve all five parity conditions (covered interest parity, uncovered interest parity, absolute and relative purchasing power parity, the Fisher effect and the international Fisher effect) from a single set of spot, interest and inflation inputs, and reconcile the forward premium against the purchasing-power drift through the real-rate wedge.
4. Price a forward two ways, from covered interest parity and from quoted forward points, read the gap as an implied funding basis rather than an arbitrage, and state what forward-rate unbiasedness claims, how the regression tests it, and why the forward-premium puzzle and the carry trade are one fact rather than two.
5. Classify any cross-border transaction into the current, capital or financial account under the sixth edition of the balance-of-payments manual, apply the sign convention, and make the identity close with a stated errors-and-omissions residual.
6. Solve the Mundell-Fleming system for monetary and fiscal shocks under fixed and floating rates at high and low capital mobility, and state the exchange-rate prediction and the crowding-out mechanism in each cell.
7. Trace a Dornbusch overshoot from a money-supply shock through the impact jump, the walk-back and the long-run level, and say precisely which assumption produces the overshoot.
8. Decompose an interest differential into expected depreciation and a currency risk premium, explain how a rising stock of government debt moves the premium and therefore the spot rate under floating, and cost a sterilised intervention, which reaches the exchange rate through that same imperfect-substitutes channel.
9. Test the Marshall-Lerner condition on stated elasticities, tabulate the J-curve path, and compute the consumer loss, producer gain, revenue or rent and both deadweight triangles for a tariff, a quota, a voluntary export restraint and an export subsidy.
10. Rank a trade agreement on the free-trade-area to economic-union ladder, separate trade creation from trade diversion with the resource-cost arithmetic, and score an emerging market against a currency-crisis checklist from primary data, saying what would have to change for the verdict to flip.

Prerequisites & connections

Builds on. M7.06 gave you the FX market's plumbing: what an exchange rate is, the five forces that move one, covered interest parity with the arbitrage that enforces it, the carry trade, the impossible trinity, and the dollar system with its eurodollar and swap-line machinery. This node assembles those pieces into a single solvable system and extends them; it does not re-derive the trilemma or re-explain the eurodollar. M7.03 supplies the real-versus-nominal distinction and the Fisher decomposition that the international Fisher effect exports across a border. DV1.01 owns forward and futures pricing mechanics, including the cost-of-carry logic that makes the covered forward a no-arbitrage price rather than a forecast, and this node uses that result as given. MS1.04 owns the FX swap, the non-deliverable forward and the cross-currency basis as funding instruments, which is why the basis appears here only as a number to interpret. EC1.01 owns consumer and producer surplus, the choke price, deadweight loss and the elasticity machinery; the trade-policy arithmetic below is that toolkit applied at a border and adds no new welfare theory.

Deliberate non-overlaps. We do not re-teach the quote conventions from scratch, the CIP arbitrage narrative, the carry trade's risk profile, the impossible trinity, comparative advantage and the distributional debate around it, or the global financial cycle and sudden-stop mechanism; all of those are M7.06's, and it gains the two-notation box as a section fix. Nor do we re-teach forward pricing mechanics (DV1.01), the cross-currency basis as a funding instrument (MS1.04), or the derivation of surplus and deadweight loss (EC1.01). Where those own a concept, this node cites and moves on. The balance-of-payments treatment here is the exception that is not an exception: M7.06 gives the two-halves identity and the quality-of-financing lens, and gains the manual-edition box as a section fix, while the three-account separation and the classification drill live here.

Feeds forward. EC1.05 takes the trade-policy machinery into regulation and geopolitics. AA1.04's capital-market expectations need the parity relations as the arithmetic that turns an inflation forecast into a currency forecast, and needs the honest warning about how badly that arithmetic forecasts. FI1.06 and FI1.07 hedge and trade the rate differentials measured here. PW1.01's private-client policy statements inherit the currency-hedging decision that the forward premium prices. The quant-code region is where the parity system, the Fama regression and the crisis scorecard get vectorised into a monitored pipeline; the assistant callouts below name the hand-off.

Core teaching content

2. Two-way quotes, cross rates and triangular arbitrage

A dealer does not show one price. A dealer shows a bid, the price at which the dealer will buy the base currency from you, and an offer (or ask), the price at which the dealer will sell it to you. The offer is always the higher number, the difference is the spread, and the spread is the dealer's compensation for standing there.

You always transact on the side that is worse for you. Buying dollars against rupees, you pay the offer, 84.5200. Selling dollars, you receive the bid, 84.4800.

The 4.0000-paise spread is what a round trip costs before anything moves.

Building a cross rate from two quoted pairs is the same discipline applied twice. To construct the rupee price of a euro from USD/INR and EUR/USD, notice that buying a euro means buying dollars first and then buying euros with them, so both legs hit the offer:

EUR/INR offer = USD/INR offer × EUR/USD offer = 84.5200 × 1.0845 = 91.661940

Selling a euro reverses both legs and both hit the bid:

EUR/INR bid = USD/INR bid × EUR/USD bid = 84.4800 × 1.0840 = 91.576320

The synthetic spread is 0.085620 rupees, or 9.3452 basis points of the mid, which is wider than either component spread because a cross rate crosses two of them. That is the general rule and it explains why liquidity in a cross is worse than in its legs.

Those two numbers define a no-arbitrage band. Any dealer whose euro-rupee quote sits entirely inside 91.576320 to 91.661940 is offering you nothing, however generous the quote looks against the mid of 91.619130. A quote that pokes out of the band is free money for whoever notices first, and Worked Example 2 runs both cases leg by leg on ₹10 crore.

Report the spread-inclusive number or do not report one. What an arbitrage computed on mid rates actually shows you is a spread you have not yet paid. The discipline of crossing every spread the trade touches, every time, is what stops a screen full of apparent opportunities from becoming a screen full of losses.

5. The balance of payments under BPM6

The balance of payments is a double-entry record of every transaction between residents of one economy and the rest of the world over a period. Because it is double-entry, it balances by construction, and the interesting question is never whether it balances but which account absorbed what.

The sixth edition of the IMF's Balance of Payments and International Investment Position Manual, published in 2009 and phased in by national compilers over the following decade, sets the current classification. Three accounts, and the second one is where most errors live.

The current account records transactions in goods, services and income. Four components:

• Goods, the merchandise trade balance, exports minus imports on a change-of-ownership basis.
• Services, covering transport, travel, software and business services, insurance, financial services, and charges for the use of intellectual property. A royalty paid for a licensed patent is a service.
• Primary income, the return to factors of production supplied across a border: compensation of employees, and investment income in the form of interest, dividends and reinvested earnings.
• Secondary income, formerly "current transfers", where nothing is received in return. Workers' remittances are the large item for many economies, along with grants and taxes.

The capital account is small, specific and constantly misclassified. Under this manual it contains exactly two things:

• Capital transfers, meaning transfers of ownership of a fixed asset, forgiveness of a liability by mutual agreement without a quid pro quo, investment grants, and non-life insurance claims arising from a catastrophe. Debt forgiveness sits here. Migrants' transfers do not, and this is the trap: the fifth edition booked a migrant's accumulated assets as a capital transfer on the change of residence, and the sixth removed the category, because nothing passes between two parties when somebody moves. The assets are reclassified in the international investment position instead, and no balance-of-payments transaction is recorded at all.
• Acquisition and disposal of non-produced, non-financial assets: the outright sale of a patent, a trademark, a copyright, a lease or a natural-resource extraction right. Note the word outright. Selling the patent is a capital-account entry; licensing it and collecting a royalty is a current-account service.

If you learned an older vocabulary in which "the capital account" meant everything that was not the current account, unlearn it now. Under the fifth edition, the financial flows sat inside a "capital and financial account", and a great deal of secondary literature still uses the old sense. Both usages are in print, and a number lifted from one framing into a sentence written in the other will be wrong by the entire financial account.

The financial account records net acquisition of financial assets against net incurrence of liabilities, in five functional categories: direct investment (a lasting interest, conventionally a 10% or greater voting stake), portfolio investment (tradable equity and debt without control), financial derivatives, other investment (loans, currency and deposits, trade credit), and reserve assets.

The sign convention changed with the manual and is the second common error. This edition presents the financial account as net lending (positive) or net borrowing (negative), computed as assets acquired minus liabilities incurred. Under that presentation the identity is:

Current account + Capital account − Financial account + Net errors and omissions = 0

Worked Example 7 builds a full synthetic set of accounts and closes the identity. Two readings of that table matter more than its arithmetic. The first is composition on the current side, where a merchandise deficit of 7.128205% of GDP is covered 63.309353% by a services surplus and a further 43.165468% by remittances, which is how an economy imports far more goods than it exports and still lands at a current account of −0.871795% of GDP. The second is composition on the financing side, where net direct investment covers 82.352941% of that deficit and net portfolio flows cover 29.411765%. Direct investment cannot be sold on a Tuesday. Portfolio investment can, and the same deficit financed the other way round is a different country.

Errors and omissions deserve one sentence of respect. A small residual against gross flows in the hundreds is ordinary. A residual that grows steadily in one direction over several quarters is usually unrecorded capital flight, and it has preceded more than one currency crisis.

6. The flow approach to the exchange rate, and where it runs out

The oldest model of the exchange rate treats it as the price that clears a flow market. Exporters earn foreign currency and sell it; importers need foreign currency and buy it; the rate moves until the flows match. A current-account deficit is excess demand for foreign currency, so the home currency must fall until the deficit closes.

The model has the great virtue of being about something real, and it delivers one durable prediction: a currency cannot run a large real overvaluation indefinitely while the trade account bleeds, because the financing has to come from somewhere. Every currency crisis in the historical record involved a trade or current account that had been signalling for years.

It also has a fatal defect at short horizons, which is arithmetic rather than theory. Trade flows are small relative to financial flows, and not slightly.

The Bank for International Settlements triennial survey put global foreign-exchange turnover at about $7.5 trillion a day in April 2022 (check against the most recent triennial survey, which supersedes this figure). World exports of goods and services ran about $31 trillion in 2022 (check against the WTO's annual statistics). That is $84.93 billion of trade a day against 7,500 billion of turnover, a ratio of about 88 to 1. Put the other way, four and a bit days of foreign-exchange turnover would settle a full year of world trade.

A model in which trade flows set the price is therefore a model in which one percent of the volume sets the price for the other ninety-nine. It can be true over decades, when the financial flows have to be serviced out of trade flows in the end.

Over a quarter it is noise.

What replaced it is a family of asset-market models, and they all share one move: treat the exchange rate as the relative price of two stocks of assets rather than two flows of goods, and let it jump when new information arrives, the way any asset price does. The next three sections are three members of that family, distinguished by what they assume about prices and about how substitutable domestic and foreign bonds are.

15. Working with an assistant on this material

The material in this node has an unusual risk profile for machine assistance. Some of it is pure arithmetic that an assistant does faster and more accurately than you do, and some of it is institutional classification where a confident answer drawn from the older manual is wrong in a way that leaves no trace.

Sort the tasks before you delegate them. Solving the parity system, running a Fama regression, tabulating a J-curve and computing surplus areas are arithmetic, and the check is a recomputation plus an identity that must close. Classifying a transaction under the current manual, reading a country's reserve or debt data, and stating a capital-control limit are institutional facts, and the only check is the primary source with a date on it.

{
  "skill": "Solving and reconciling the five parity conditions from one input set",
  "use": "Have an assistant write code that takes spot, two interest rates and two inflation forecasts and returns the covered forward, the forward points, the uncovered and relative-PPP expected spots, both exact real rates and the reconciliation wedge, with assertions that force the identities to close before anything is printed.",
  "tools": ["Chat assistants with code execution", "Python: plain arithmetic, plus statsmodels or NumPy for the Fama regression", "A spreadsheet for the side-by-side reconciliation"],
  "prompt": "Given spot 84.50 INR per USD, one-year rates of 6.75 percent INR and 4.35 percent USD, and expected inflation of 4.60 percent India and 2.40 percent US, compute: (a) the covered interest parity forward and the forward points in paise, (b) the uncovered interest parity expected spot, (c) the relative PPP expected spot, (d) exact Fisher real rates for both countries, and (e) the multiplicative wedge between the forward premium and the PPP drift. Then assert that (1 + forward premium) / (1 + PPP drift) equals (1 + r_domestic) / (1 + r_foreign) to within 1e-12, and assert that the uncovered expected spot equals the covered forward exactly. Use exact ratios throughout, never the additive approximation. Print every intermediate at nine decimals.",
  "verify": "Recompute the forward and one real rate by hand and confirm they match to the sixth decimal. Then break the code deliberately: feed it an additive approximation for one real rate and confirm the wedge assertion actually fires, because an assertion that never fails on bad input is decoration. Trace the two interest rates to a named primary source with a date, since a stale policy rate propagates into every one of the five outputs. Confirm the code has not silently swapped the price and base currencies, which is the error that leaves every number plausible and every sign wrong: the quickest test is that a higher domestic rate must produce a forward above spot when spot is quoted as domestic currency per unit of foreign.",
  "diy": "You must be able to produce the covered forward, both exact real rates and the reconciliation wedge with a calculator, because the gate tests exactly that and because the wedge is the identity that tells you whether an assistant's five outputs are mutually consistent or five independent guesses. Worked Example 1 is the drill.",
  "market": "IN"
}

{
  "skill": "Classifying balance-of-payments entries and scoring a crisis checklist from primary data",
  "use": "Use an assistant to turn a central bank's published balance-of-payments release into a structured table and to generate the identity checks and threshold tests you then run yourself, keeping the classification judgement and the source tracing in your own hands.",
  "tools": ["Document AI grounded on the release you already hold", "Chat assistants with code execution for the identity checks", "The IMF manual, the country's central bank statistics pages and the joint external debt database as primary sources"],
  "prompt": "From this balance-of-payments release, extract into a table: goods balance, services balance, primary income, secondary income, capital account, and each functional category of the financial account including reserve assets, with the units and the sign convention the publication uses stated explicitly. Then list every arithmetic relationship among those rows that I can verify independently, compute the errors-and-omissions residual implied by the identity current account plus capital account minus financial account plus errors equals zero, and flag any row whose sign convention you inferred rather than read.",
  "verify": "Do not accept the extracted table. Trace every row back to the published release yourself, because table extraction transposes columns in dense statistical annexes and a transposed sign is invisible downstream. Confirm which edition of the manual the publication follows and which sign convention it uses for the financial account, since the presentation changed and both are in circulation. For any classification question, meaning whether an item belongs in the capital account or the current account, go to the manual itself rather than to the model's recollection: debt forgiveness and outright sales of patents are capital-account items and royalties on the same patent are current-account services, and an assistant trained on older text will place them by the previous convention with complete confidence. Recompute the residual by hand and check it against the published errors-and-omissions line; a mismatch means you have misread a sign, not that the statisticians did.",
  "diy": "You must be able to classify a transaction into the three accounts and close the identity without help, because the classification is the analysis and the arithmetic is the easy part. You must also be able to say which reserve test binds in a rollover crisis and why import cover is the wrong one, which is judgement no extraction step supplies.",
  "market": "IN"
}

Common mistakes & how experts think differently

1. Reading a parity relation as a forecast. The most expensive error in the section. Covered interest parity is an arbitrage identity that holds because a trade enforces it; uncovered interest parity is a hypothesis that has been rejected in every long sample anyone has run. They produce the same number on the same inputs, ₹86.443460 here, which is exactly why the confusion survives. An expert states the enforcement mechanism before quoting the number, and if there is no enforcement mechanism, calls the output a null hypothesis rather than an expectation.

1. Using the additive approximation and then compounding on it. The interest differential of 2.40 percentage points overstates the true forward premium of 2.299952% by 10 basis points. On a one-year forward that is a rounding error. Carried into a five-year cross-currency valuation, or a real-rate comparison where the whole quantity of interest is 15 basis points wide, it is the answer. Experts use ratios everywhere and reserve the subtraction for mental arithmetic they will not act on.

1. Netting an arbitrage on mid rates. A triangular opportunity that shows a profit on mids and a loss after crossing two spreads has nothing left in it at all, marginal or otherwise. The synthetic euro-rupee spread of 9.3452 basis points is wider than either leg's spread, and a cross rate always is. The habit that fixes this is computing the no-arbitrage band first and only then looking at the third quote.

1. Confusing appreciation with the reciprocal of depreciation. The dollar rose 4.142012% against the rupee; the rupee fell 3.977273% against the dollar. Both are correct, neither is the other's negative, and the gap widens with the size of the move. Analysts get caught by this when they compute a return in one currency and a hedging cost in the other, then add them.

1. Putting a patent sale, or debt forgiveness, in the wrong account. Under the current manual the outright sale of a non-produced, non-financial asset and the forgiveness of a liability are capital-account items, while a royalty on the same patent is a current-account service. Under the previous manual the vocabulary was different and much published commentary still uses it. When a number does not tie, check the manual edition before checking your arithmetic.

1. Quoting import cover when the binding constraint is rollover. Adaria has 6.5625 months of import cover, which passes, and reserves covering only 0.8235 of short-term external debt, which fails. Both are reserve adequacy measures and they answer different questions. In a sudden stop the country is not trying to buy goods, it is trying to refinance maturities, so the second one binds. The ministry will quote the first.

1. Judging a devaluation at the trough of the J-curve. Three quarters of a widening deficit after a devaluation is consistent with the policy working exactly as the elasticities predict. It is also consistent with the policy failing. Distinguishing them requires the elasticity path, not the balance, and an expert asks "what elasticity sum does this quarter's number imply?" rather than "is the deficit smaller yet?"

1. Treating a quota as a tariff. They deliver an identical price and an identical quantity, and they differ by $1,125 million a year in this example, entirely because of who receives the rent. A voluntary export restraint hands that rent to the exporting country, which is why exporters accept one and why the importing country's welfare loss is 3.571429 times the tariff's. Whenever someone compares protection instruments on price effects alone, the missing question is where the rent went.

1. Applying the high-mobility Mundell-Fleming answer to an economy with capital controls. Fiscal expansion appreciates a floating currency when capital is mobile and depreciates it when it is not, because import leakage outruns the capital inflow. The sign reverses. An analyst who has memorised the four-cell table without the mobility dimension will get emerging-market fiscal shocks backwards.

1. Calling an overshoot irrational. The Dornbusch jump of 11.064344% against a long-run move of 10.00% is the unique path consistent with rational expectations and sticky goods prices. Exchange-rate volatility far in excess of fundamentals volatility is what the model predicts, so observing it is not evidence of anything going wrong. Experts reserve the word "excessive" for moves that fail the interest-parity path test, which is a computation rather than an impression.

Worked examples

Ground rules for all eight. Every input is stated. Every answer is verified by a second, independent route wherever one exists. Every closing note says what the number does not mean, because that is where the errors live. Work each one before reading its solution.

Worked example 1: The five parity conditions, solved and reconciled (India, ₹)

Spot is ₹84.5000 per US dollar. The one-year rupee rate is 6.75% and the one-year dollar rate is 4.35%. Expected one-year inflation is 4.60% in India and 2.40% in the United States. Solve all five parity relations, price the one-year forward two ways, and reconcile the forward premium against the purchasing-power drift.

Solution. Step 1, covered interest parity. F = 84.5000 × 1.0675 / 1.0435 = ₹86.443460. The forward premium on the dollar is 86.443460 / 84.5000 − 1 = 2.299952%, quoted as 194.3460 paise of forward points. The additive approximation gives 2.40%, which is 0.100048 percentage points too high.

Step 2, the same forward from market points. Suppose the one-year points are quoted at 196.00 paise, so the market forward is ₹86.460000. That sits 1.654049 paise above the parity forward, a gap of 1.913446 basis points. Solving i_INR_implied = (1 + 0.0435) × 86.460000 / 84.5000 − 1 gives 6.770426%, which is 2.042604 basis points above the quoted rupee rate. The gap is a funding basis, meaning the market is paying slightly more than parity to obtain dollars through the swap market, and it is not an arbitrage unless it exceeds the transaction costs and balance-sheet charges of running the trade.

Step 3, uncovered interest parity. Expected rupee depreciation is 2.299952% and the expected spot in one year is ₹86.443460, identical to the forward to fourteen decimal places, because both are the same ratio applied to the same spot.

Step 4, relative purchasing power parity. 1.0460 / 1.0240 − 1 = 2.148438%, giving an expected spot of ₹86.315430. The additive version gives 2.20%.

Step 5, absolute purchasing power parity. An identical basket at ₹4,200 and $58.00 implies ₹72.413793 per dollar. The market rate sits 16.690476% above it, so the rupee is 14.303203% undervalued against the basket.

Step 6, the Fisher effects. Exact real rates are 1.0675 / 1.0460 − 1 = 2.055449% in India and 1.0435 / 1.0240 − 1 = 1.904297% in the United States, a gap of 0.151152 percentage points. The international Fisher effect predicts the nominal differential of 2.40 points would be entirely an inflation differential; the inflation differential is 2.20 points, so the effect does not hold here and 0.20 points is real.

Step 7, verify by two independent routes. Route one: (1 + 0.02299952) / (1 + 0.02148438) − 1 = 0.148328%. Route two: (1 + 0.02055449) / (1 + 0.01904297) − 1 = 0.148328%. The residual is 0.000e+00. The forward premium is the purchasing-power drift multiplied by the real-rate wedge, and the two routes agreeing exactly is the check that no input was mistyped.

Read it. The 12.803-paise gap between the covered forward and the purchasing-power path is not a trading signal and not an error. It is the real-rate differential, stated as a currency number. Nothing in this table forecasts the rupee. The first row is a price you can transact at today, the second is a hypothesis, the third is a decades-long tendency, and the fourth is a level comparison that a middle-income currency will fail permanently for reasons that have nothing to do with mispricing.

Worked example 2: A cross rate, a live arbitrage, and one that dies in the spread (India, ₹ / US, $ / euro area, €)

A Mumbai dealer quotes USD/INR at 84.4800 / 84.5200. A Frankfurt dealer quotes EUR/USD at 1.0840 / 1.0845. Construct the synthetic euro-rupee two-way price. Then test two third-dealer quotes for arbitrage on ₹10 crore: dealer A at 91.8000 / 91.8500, and dealer B at 91.6000 / 91.7000. Report the profit or loss after the spread.

Solution. Step 1, the synthetic band. Buying a euro means paying the offer on both legs: 84.5200 × 1.0845 = 91.661940. Selling a euro means receiving the bid on both: 84.4800 × 1.0840 = 91.576320. The synthetic spread is 0.085620 rupees, or 9.3452 basis points, wider than either leg.

Step 2, dealer A, leg by leg. Start with ₹100,000,000. Buy dollars at 84.5200: $1,183,151.916706. Buy euros at 1.0845: €1,090,965.345049. Sell those euros to dealer A at its bid of 91.8000: ₹100,150,618.675538.

Step 3, the profit. ₹150,618.68 on ₹10 crore, which is 15.0619 basis points and 0.138060 rupees per euro. Cross-check by the one-step route: 100,000,000 / 91.661940 = €1,090,965.345049, agreeing with the leg-by-leg figure to within 2.3e-10, which confirms both legs were taken on the correct side.

Step 4, dealer B. Its quote sits inside the band. Buying synthetically at 91.661940 and selling at 91.6000 loses 0.061940 rupees a euro, ₹67,574.39 on the notional. Buying from dealer B at 91.7000 and selling synthetically at 91.576320 loses 0.123680 rupees a euro, ₹134,874.59. Both routes lose, so there is no trade.

Read it. The arbitrage against dealer A is real and it is also nearly extinct in liquid pairs, because the same calculation runs continuously in machines. What survives is the discipline: any claimed cross-currency opportunity must be quoted after crossing every spread it touches, and the number of spreads is the number of legs. Dealer B's quote looks generous against the mid of 91.619130 and is worthless, which is the normal case.

Worked example 3: A US tariff, then the same protection as a quota (US, $)

A synthetic US market for an industrial input has domestic demand Qd = 1,200 − 20P and domestic supply Qs = 100 + 15P, with quantities in millions of units a year and prices in dollars. The world price is $20 and the country is small. Compute the welfare effects of a $5 tariff. Then impose an import quota that delivers the same domestic price, with the licences held by foreign exporters, and compare.

Solution. Step 1, free trade. At $20, Qd = 800, Qs = 400, imports = 400.

Step 2, the tariff. At $25, Qd = 700, Qs = 475, imports = 225, a 43.75% compression.

Step 3, the four areas. Consumer surplus loss = (800 + 700)/2 × 5 = $3,750.00m. Producer surplus gain = (400 + 475)/2 × 5 = $2,187.50m. Government revenue = 5 × 225 = $1,125.00m. Production distortion = ½ × 75 × 5 = $187.50m. Consumption distortion = ½ × 100 × 5 = $250.00m.

Step 4, verify the deadweight loss two ways. By residual: 3,750.00 − 2,187.50 − 1,125.00 = $437.50m. By triangles: 187.50 + 250.00 = $437.50m. Residual 0.000e+00.

Step 5, the quota that matches. Set the quota at 225. Solving (1,200 − 20P) − (100 + 15P) = 225 gives 35P = 875, so P = $25.000000, identical to the tariff price. Consumer loss and producer gain are unchanged. The $1,125.00m that was tariff revenue becomes quota rent.

Step 6, who holds the licence. Auctioned domestically, the rent stays home and the national loss is $437.50m. Held by foreign exporters, which is what a voluntary export restraint does, the rent leaves and the national loss is 437.50 + 1,125.00 = $1,562.50m.

Step 7, the ratios. The restraint costs 3.571429 times the tariff, an extra $1,125.00m a year, which is 7.031250% of free-trade consumer spending of $16,000.00m on the good, and takes the total national loss to 9.765625% of it. Consumers pay $1.714286 for each dollar reaching producers, and the extra 75 million units of domestic output cost consumers $50.00 each against a world price of $20.00.

Read it. Nothing here says protection is never worth it. It says what protection costs, and it says that the cheapest way to deliver a given amount of protection is the one that keeps the rent at home. The number that should never survive contact with this table is "a voluntary restraint is gentler than a tariff." It is the same restriction with the revenue given away.

Worked example 4: Mundell-Fleming, four cells from one system (US, $)

Use the system from the teaching section: C = 100 + 0.75(Y − 400), I = 300 − 20i, NX = 110 − 0.10Y + 15q, M/P = 0.5Y − 25i with M/P = 800, G = 500, and perfect capital mobility at i* = 4. Solve the base case, then a fiscal expansion of 60 and a monetary expansion of 50, under both floating and fixed rates.

Solution. Step 1, the base. The money market alone gives 800 = 0.5Y − 100, so Y = 1,800. Then C = 1,150, I = 220, G = 500, and the goods identity forces NX = −70 with q = 0. Identity residual 0.000e+00.

Step 2, floating with fiscal expansion. The money market is untouched and the interest rate is pinned, so Y stays at 1,800. Solving the goods market with G = 560 gives q = −4.000000% and NX = −130, a fall of exactly 60. Crowding-out ratio −1.000000.

Step 3, floating with monetary expansion. 850 = 0.5Y − 100 gives Y = 1,900, a rise of 100 on an injection of 50, a multiplier of 2.000000. The goods market then gives q = +2.333333% and NX = −45, an improvement of 25.

Step 4, fixed with fiscal expansion. Now q is pinned at 0 and Y is free. Solving Y = [100 + 0.75(Y − 400)] + 220 + 560 + [110 − 0.10Y] gives 0.35Y = 690, so Y = 1,971.428571, a rise of 171.428571 and a multiplier of 2.857143 = 1/0.35. The money stock required is 0.5 × 1,971.428571 − 100 = 885.714286, so reserves rise 85.714286, a 10.714286% money-supply expansion. Identity residual 2.274e-13.

Step 5, fixed with monetary expansion. The injection pushes the domestic rate below 4, capital leaves, and the bank must sell 50 of reserves, 6.25% of the money stock, to restore the parity. Y ends at 1,800, unchanged.

Read it. The table is a statement about signs and mechanisms, and the magnitudes belong to this particular parameterisation and to nothing else. What travels is the pattern: monetary policy is powerful under floating and unavailable under a credible peg, fiscal policy is the reverse, and the exchange rate is the channel in both directions. What does not travel is 171.428571, which depends entirely on a marginal propensity to consume of 0.75 and an import propensity of 0.10 that were assumed rather than estimated.

Worked example 5: A Dornbusch overshoot, traced through four dates (India, ₹)

Spot is ₹84.5000. The central bank permanently raises the money supply 10%. Goods prices are sticky and adjust over a year; asset prices are not. On impact the rupee rate falls from 6.75% to 3.35% while the dollar rate stays at 4.35%. Trace the spot rate from impact to the long run, and show the real exchange rate at each date.

Solution. Step 1, the long run. Purchasing power parity holds eventually and the money shock is permanent, so the long-run rate is 84.5000 × 1.10 = ₹92.950000 and the long-run domestic price index is 110.000000.

Step 2, what uncovered interest parity requires on impact. With the rupee rate 100 basis points below the dollar rate, rupee assets are only held if the rupee is expected to appreciate. Exactly: (1.0335 / 1.0435) − 1 = −0.958313% over the year.

Step 3, solve for the jump. The rate must sit high enough today that appreciating 0.958313% over the year lands it on 92.950000: S_impact = 92.950000 / (1 − 0.00958313) = ₹93.849371.

Step 4, the size of the overshoot. The impact move is 93.849371 / 84.500000 − 1 = 11.064344% against a long-run move of 10.000000%, so the rate overshoots by 1.064344 percentage points, sitting 0.967586% above its eventual level.

Step 5, the path. On a constant-rate geometric path the six-month rate is 93.849371 × (92.950000/93.849371)^0.5 = ₹93.398603, and the annualised appreciation along it is −0.958313%, matching the interest differential exactly. Path check: 93.849371 × (1 − 0.00958313) − 92.950000 = 0.000e+00.

Step 6, sensitivity. Halve the shock to 5% with the rupee rate falling only to 3.95%. The required appreciation is 0.383325%, the impact rate is ₹89.066414, the move is 5.404040%, and the overshoot is 0.404040 percentage points. The overshoot scales with how far the interest rate is allowed to fall.

Read it. The overshoot is a model result and it depends on the interest-rate response, which the model does not observe. A central bank that resists the rate decline gets a smaller jump; one that lets rates collapse gets a larger one. What the example does establish, and this part holds whatever the parameters, is that a nominal shock produces a temporary real depreciation which then unwinds completely. Any story that attributes a permanent competitiveness gain to a monetary devaluation has to explain why the price level did not follow.

Worked example 6: Marshall-Lerner and the J-curve, tabulated (India, ₹)

Trade is initially balanced with exports and imports of ₹100 billion each. The rupee devalues 15% in real terms. Export demand and import demand elasticities start small and grow over eight quarters as stated below. Test the Marshall-Lerner condition, tabulate the trade balance path, and find where it crosses zero. Then repeat the test on an unbalanced account.

Solution. Step 1, the condition. With export prices sticky in rupees and import prices sticky in dollars, ΔTB = X₀ × d × (η_X + η_M − 1). The balance improves if and only if η_X + η_M > 1.

Step 2, the failing case. At η_X = 0.45 and η_M = 0.40 the sum is 0.85, so ΔTB = 100 × 0.15 × (−0.15) = −₹2.25 billion. The devaluation makes the deficit worse, permanently, at those elasticities.

Step 3, the path. With elasticities rising quarter by quarter:

Step 4, the trough and the crossing. The worst point is −₹11.25 billion in quarter 1, which is 11.25% of pre-devaluation exports. Interpolating the elasticity sum linearly between quarter 3 at 0.90 and quarter 4 at 1.15, it reaches 1.00 at quarter 3.400000.

Step 5, verify at the endpoint by the closed form. At quarter 8, 100 × 0.15 × (1.80 − 1) = ₹12.000000 billion, matching the table.

Step 6, the unbalanced case. With exports of ₹90 billion and imports of ₹120 billion, the change per unit of devaluation is 90 × 0.45 + 120 × 0.40 − 120 = −31.500000, so a 15% devaluation gives −₹4.725 billion. Break-even requires 90 η_X + 120 η_M = 120, so with η_M held at 0.40 the export elasticity has to reach 0.800000 and the sum 1.200000, against 1.00 on balanced trade. Move η_M instead, holding η_X at 0.45, and break-even arrives at η_M = 0.662500 and a sum of only 1.112500, which is why the bare sum stops being the whole condition once trade is unbalanced.

Read it. The J-curve says a correct devaluation looks like a failing one for three quarters. It does not say every failing devaluation is a J-curve, and the difference is testable: back out the implied elasticity sum from each quarter's number and check whether it is rising. A path where the sum stays flat below 1 shows a country whose trade does not respond to prices at all, and no amount of patience fixes that.

Worked example 7: Reading a balance of payments under the current manual (India-like, $bn, synthetic)

A synthetic large emerging economy reports, in US dollar billions: goods exports 448.00, goods imports 726.00, services exports 372.00, services imports 196.00, primary income credits 32.00 and debits 84.00, secondary income credits 128.00 and debits 8.00. Separately it records debt forgiveness received of 1.40, an outright sale of a patent to a non-resident of 2.60, and an investment grant received from a foreign government of 0.50. On the financial side, residents acquired 18.00 of direct investment abroad, 12.00 of portfolio assets and 11.00 of other investment, the central bank added 20.00 to reserves, and non-residents supplied 46.00 of inward direct investment, 22.00 of portfolio inflows and 20.00 of other investment. GDP is 3,900.00. Classify, compute each balance, and close the identity.

Solution. Step 1, the current account. Goods −278.00, services +176.00, primary income 32.00 − 84.00 = −52.00, secondary income 128.00 − 8.00 = +120.00. Current account = −34.00.

Step 2, the capital account. All three of the separately recorded items belong here: debt forgiveness and the investment grant are capital transfers, and the outright patent sale is a disposal of a non-produced non-financial asset. Capital account = +4.50. Note what is not here: a royalty on that patent would have been a current-account service, and interest on external borrowing is primary income.

Step 3, the financing need. −34.00 + 4.50 = −29.50.

Step 4, the financial account. Assets acquired = 18.00 + 12.00 + 11.00 + 20.00 = 61.00. Liabilities incurred = 46.00 + 22.00 + 20.00 = 88.00. Financial account, on the net-lending presentation = 61.00 − 88.00 = −27.00, meaning net borrowing of 27.00.

Step 5, close the identity. CA + KA − FA + NEO = 0 gives NEO = FA − CA − KA = −27.00 + 34.00 − 4.50 = +2.50. Check: −34.00 + 4.50 − (−27.00) + 2.50 = 0.000e+00.

Step 6, read the composition. The merchandise deficit is 7.128205% of GDP. The services surplus covers 63.309353% of it and secondary income covers a further 43.165468%, which is why the current account lands at only −0.871795% of GDP. On the financing side, net direct investment of +28.00 covers 82.352941% of the deficit while net portfolio flows of +10.00 cover 29.411765%. A closing reserve stock of 660.00 is 8.590022 months of goods and services imports and 16.923077% of GDP.

Read it. The headline current-account number is the least informative row in the table. Two economies with an identical −0.87% deficit are in completely different positions if one is financed by direct investment and the other by portfolio inflows, because the first cannot leave in a week and the second can. And the errors-and-omissions line of +2.50 is unremarkable at this scale; what would not be unremarkable is the same sign, growing, for six consecutive quarters, which historically means unrecorded outflows that the official accounts have not yet found.

Worked example 8: Trade creation and trade diversion on the same agreement (India, ₹)

A country imports a component. Producing it domestically costs ₹100 a unit. A prospective free-trade-area partner produces it for ₹88. A non-member produces it for ₹80. Annual consumption is 5 million units. Evaluate the agreement twice: once when the pre-existing tariff on everyone is 30%, and once when it is 12%.

Solution. Step 1, the 30% case, before. Domestic ₹100.00, partner 88 × 1.30 = ₹114.40, non-member 80 × 1.30 = ₹104.00. The country supplies itself at ₹100.00 and collects no tariff revenue.

Step 2, the 30% case, after. The partner's tariff goes to zero, so the partner lands at ₹88.00 against the non-member's unchanged ₹104.00 and domestic ₹100.00. Imports begin from the partner. Consumers save ₹12.00 a unit, no revenue is lost because none was being collected, and the real resource cost of supply falls from ₹100.00 to ₹88.00. Net national gain = ₹12.00 a unit, ₹60,000,000 a year. This is trade creation.

Step 3, the 12% case, before. Domestic ₹100.00, partner 88 × 1.12 = ₹98.56, non-member 80 × 1.12 = ₹89.60. The country imports from the non-member at ₹89.60 and the treasury collects ₹9.60 a unit.

Step 4, the 12% case, after. The partner lands at ₹88.00, beating the non-member's ₹89.60. Trade switches to the partner. Consumers save ₹1.60 a unit. The treasury loses the full ₹9.60. The real resource cost of supply rises from ₹80.00 to ₹88.00.

Step 5, net it. 1.60 − 9.60 = −₹8.00 a unit, which equals −(88.00 − 80.00) exactly, confirming that the national loss is the resource-cost increase and nothing else. On 5 million units the country is ₹40,000,000 worse off a year, with consumers ₹8,000,000 better off and the treasury ₹48,000,000 poorer. This is trade diversion.

Read it. The same agreement, the same three producers, opposite verdicts, and the only thing that changed was the tariff that existed beforehand. Consumers gain in both cases, which is why consumer prices are a useless test. The test is whether the real resource cost of supply fell, and computing it requires knowing the pre-tariff costs, which is exactly the number a lobbying submission will not contain.

Verify block

Every figure printed above, restated at full precision, for reproduction:

Practice set

Work each problem before reading its solution. A calculator is assumed. Unless a problem says otherwise, use exact ratios rather than additive approximations, and treat an answer as correct if it matches to the precision printed. Problems P1 to P3 carry scaffolding; the rest are bare. P1 (guided). Read three quotes correctly. A screen shows USD/INR = 84.5000, EUR/USD = 1.0840 and USD/JPY = 151.20. (a) State what each number means in words, with units. (b) USD/INR moves to 88.0000. By what percentage did the dollar appreciate, and by what percentage did the rupee depreciate? (c) Show that the two answers satisfy the exact relationship between them.

Solution. (a) 84.5000 rupees per dollar; 1.0840 dollars per euro; 151.20 yen per dollar. In every case the first-named currency is the one you get exactly one of. (b) The dollar appreciated 88.0000/84.5000 − 1 = 4.142012%. The rupee depreciated 84.5000/88.0000 − 1 = −3.977273%. (c) If one appreciates by x, the other depreciates by x/(1+x): 0.041420118 / 1.041420118 = 0.039772727, matching the rupee's move to nine decimals. The two moves are never equal in magnitude, and the gap grows with the size of the move.

P2 (guided). Build a cross rate and test a quote. USD/JPY is quoted 151.20 / 151.26 and EUR/USD is quoted 1.0838 / 1.0842. (a) Construct the synthetic EUR/JPY bid and offer. (b) A dealer quotes EUR/JPY at 163.95 / 164.02. Is there an arbitrage? (c) A different dealer quotes 164.10 / 164.16. Is there an arbitrage, and how much on €10 million?

Solution. (a) Buying a euro hits both offers: 151.26 × 1.0842 = 163.996092. Selling hits both bids: 151.20 × 1.0838 = 163.870560. (b) The first dealer sits inside the band. Buying synthetically at 163.996092 and selling at 163.95 loses 0.046092 yen a euro; buying from the dealer at 164.02 and selling synthetically at 163.870560 loses 0.149440 yen a euro. No arbitrage; the better of two losses is −¥460,920 on €10 million, −2.810555 basis points. (c) The second dealer's bid of 164.10 is above the synthetic offer. Buy synthetically at 163.996092, sell at 164.10, and earn 0.103908 yen a euro, ¥1,039,080 on €10 million, 6.336005 basis points. The reverse route still loses 0.289440, so only one direction trades.

P3 (guided). Run the CIP arbitrage. Spot is ₹84.5000, the rupee rate is 6.75%, the dollar rate is 4.35%, and a dealer quotes the one-year forward at ₹85.9000. Show the trade on a $1,000,000 borrowing and compute the riskless profit.

Solution. Borrow $1,000,000 at 4.35%, owing $1,043,500 in a year. Convert at spot to ₹84,500,000. Invest at 6.75% to hold ₹90,203,750. Today, buy $1,043,500 forward at 85.9000 for ₹89,636,650. Profit = 90,203,750 − 89,636,650 = ₹567,100, which is 0.671124% of the rupees invested, locked at inception with no open currency position. The no-arbitrage forward is ₹86.443460, and the dealer's quote is 54.3460 paise below it.

P4. Reconcile the parity system. Spot is ₹84.5000, rates are 6.75% and 4.35%, expected inflation is 4.60% and 2.40%. Compute the forward premium, the relative purchasing power parity drift, both exact real rates, and show that the forward premium reconciles to the drift through the real-rate wedge.

Solution. Forward premium 2.299952%; relative PPP drift 1.0460/1.0240 − 1 = 2.148438%; real rates 1.0675/1.0460 − 1 = 2.055449% and 1.0435/1.0240 − 1 = 1.904297%. Wedge from the currency side: 1.02299952/1.02148438 − 1 = 0.148328%. Wedge from the rate side: 1.02055449/1.01904297 − 1 = 0.148328%. Residual 0.000e+00. The arithmetic gap between the forward and the purchasing-power path is the real-rate differential and nothing else.

P5. Compute a carry return two ways. Borrow $1,000,000 at 4.35%, convert at ₹84.5000, invest at 6.75%, and unwind at a realised spot of ₹85.4295. Compute the profit in dollars and state the return on both a notional-borrowed and a funding-leg basis. Then compute what the profit would have been fully hedged at ₹86.443460.

Solution. Rupees at maturity 84,500,000 × 1.0675 = ₹90,203,750, converted at 85.4295 to $1,055,885.26, against a repayment of $1,043,500.00. Profit $12,385.26. On the notional borrowed that is 1.238526%; on the grossed-up funding leg it is (1.0675)/((1.0435)(1.0110)) − 1 = 1.186896%. Both are correct and they differ by the denominator, so name it. Hedged, the ₹90,203,750 sells forward at 86.443460 for exactly $1,043,500.00, giving a profit of $0.00. The entire carry return is payment for holding the currency risk.

P6. Test forward-rate unbiasedness. On the eight-year panel in the teaching text, the fitted slope is −0.922621 with a standard error of 0.853631 and an R-squared of 0.163. (a) What does unbiasedness predict for the slope? (b) Compute the t-statistic against that null and state whether it rejects at 5%. (c) What is the average carry excess return and its standard deviation?

Solution. (a) Unbiasedness predicts a slope of exactly 1 and an intercept of 0. (b) t = (−0.922621 − 1)/0.853631 = −2.252285, against a two-tailed 5% critical value of 2.446912 at six degrees of freedom, so it does not reject. Eight observations are far too few, and the same regression on decades of monthly data across many pairs is what produces the literature's rejection. (c) Mean +0.943750 percentage points a year, standard deviation 1.877201, information ratio 0.502743, six positive years out of eight, worst year −1.600000.

P7. Classify ten transactions. Assign each to the current, capital or financial account under the current manual, naming the component. One of the ten is not a balance-of-payments transaction at all under that manual, so say which and why. (i) Software services exported. (ii) A royalty received for licensing a patent abroad. (iii) The outright sale of that patent to a non-resident. (iv) A worker's remittance received from abroad. (v) Interest paid on an external commercial borrowing. (vi) A foreign fund buying a 3% listed equity stake. (vii) A foreign firm buying a 15% stake with board representation. (viii) Debt forgiveness granted by a foreign government. (ix) The central bank buying dollars in the spot market. (x) A migrant's accumulated assets transferred on changing residence.

Solution. (i) Current, services. (ii) Current, services, charges for the use of intellectual property. (iii) Capital, disposal of a non-produced non-financial asset. (iv) Current, secondary income. (v) Current, primary income. (vi) Financial, portfolio investment, since it is below the 10% direct-investment threshold. (vii) Financial, direct investment. (viii) Capital, capital transfer. (ix) Financial, reserve assets. (x) Neither, under the current manual: a change of residence passes nothing between two parties, so the assets are reclassified in the international investment position and no transaction is recorded. The previous manual booked it as a capital transfer, which is why most secondary sources and most assistants still put it in the capital account. Items (iii) and (viii) are the two genuine capital-account entries, and (ii) against (iii) is the pair worth memorising.

P8. Close a balance-of-payments identity. A country reports a current account of −32.00, a capital account of +1.50 and a financial account of −22.00 on the net-lending presentation, all in US dollar billions. Compute net errors and omissions and verify the identity.

Solution. CA + KA − FA + NEO = 0, so NEO = FA − CA − KA = −22.00 + 32.00 − 1.50 = +8.50. Check: −32.00 + 1.50 + 22.00 + 8.50 = 0.000e+00. A residual of 8.50 against a current account of 32.00 is large, more than a quarter of the deficit, and it is the kind of number that deserves a footnote about unrecorded flows rather than a shrug.

P9. Solve two Mundell-Fleming cells. Using the system C = 100 + 0.75(Y − 400), I = 300 − 20i, NX = 110 − 0.10Y + 15q, M/P = 0.5Y − 25i and i* = 4: (a) with a float, what happens to output and the exchange rate if the real money supply is cut from 800 to 760? (b) With a fixed rate and perfect capital mobility, what happens to output if the money supply is cut instead?

Solution. (a) 760 = 0.5Y − 100 gives Y = 1,720, a fall of 80. Solving the goods market: q = −1.866667%, a real appreciation, and NX = −90, a deterioration of 20. Monetary contraction under a float cuts output and strengthens the currency, which then makes the contraction worse through net exports. (b) Under a fixed rate the contraction pushes the domestic rate above the world rate, capital flows in, and the bank must buy foreign currency and issue domestic currency to hold the parity, restoring the money supply to 800. Output ends at 1,800, unchanged, and the bank has accumulated reserves for nothing.

P10. Back out a currency risk premium and price its effect. The rupee rate is 6.75%, the dollar rate 4.35%, and a survey puts expected rupee depreciation at 1.20%. (a) Compute the exact currency risk premium and compare it with the subtraction answer. (b) The premium then rises 56 basis points while the expected level of the rupee in one year stays at ₹85.5140. Compute the new spot and the immediate move.

Solution. (a) (1.0675)/((1.0435)(1.0120)) − 1 = 1.086909%. Subtraction gives 2.40 − 1.20 = 1.200000 percentage points, overstating by 0.113091 points, an error of roughly a tenth of the quantity. (b) New premium 1.646909%, so expected depreciation must fall to (1.0675)/((1.0435)(1.01646909)) − 1 = 0.642462%. With the endpoint anchored at 85.5140, S = 85.5140/1.00642462 = ₹84.968112, an immediate depreciation of 0.553979%, or 46.81 paise. Nothing about interest rates, inflation or trade changed; the required return did.

P11. Price a tariff and its quota twin. Domestic demand is Qd = 800 − 10P, domestic supply is Qs = 40 + 10P, and the world price is $30. Impose a $4 tariff. Compute the consumer loss, producer gain, revenue and deadweight loss, and verify by two routes. Then state the national loss if the same restriction were imposed as a voluntary export restraint.

Solution. Free trade at $30: Qd = 500, Qs = 340, imports 160. With the tariff at $34: Qd = 460, Qs = 380, imports 80. Consumer loss (500+460)/2 × 4 = $1,920.00m. Producer gain (340+380)/2 × 4 = $1,440.00m. Revenue 4 × 80 = $320.00m. Deadweight loss by residual 1,920 − 1,440 − 320 = $160.00m; by triangles ½(40)(4) + ½(40)(4) = 80 + 80 = $160.00m. Residual 0.000e+00. As a voluntary export restraint the $320.00m of rent leaves the country, so the national loss becomes $480.00m, three times the tariff's.

P12. Sort creation from diversion. A country's domestic cost is ₹100, a partner's is ₹88, and a non-member's is ₹80. (a) With a pre-existing tariff of 30% on all sources, does a free trade area with the partner create or divert trade, and by how much per unit? (b) With a pre-existing tariff of 12%, same question. (c) State the general rule connecting the pre-existing tariff to the likely verdict.

Solution. (a) Before: home 100.00, partner 114.40, non-member 104.00, so the country supplies itself at 100.00. After: partner 88.00. Resource cost falls 100.00 to 88.00, a gain of ₹12.00 a unit, trade creation. (b) Before: home 100.00, partner 98.56, non-member 89.60, so the country imports from the non-member at 89.60 with 9.60 of revenue. After: partner 88.00. Consumers save 1.60, the treasury loses 9.60, and the resource cost rises 80.00 to 88.00, a loss of ₹8.00 a unit, trade diversion. (c) High pre-existing tariffs mean a member was probably supplying itself, so an agreement is likely to create trade; low pre-existing tariffs mean it was probably already buying from the cheapest global source, so an agreement is likely to divert it.

P13. Convert a real appreciation into a required devaluation. Over a decade the nominal exchange rate did not move. Domestic prices rose 5.5% a year and foreign prices 2.1% a year. (a) By how much did the home currency appreciate in real terms? (b) What nominal depreciation would restore the starting real rate?

Solution. (a) Domestic prices reach 1.055^10 = 170.814446 on a base of 100; foreign prices reach 1.021^10 = 123.099821. The real appreciation is 1 − 123.099821/170.814446 = 27.933601%. (b) Restoring the original real rate requires a nominal depreciation of 170.814446/123.099821 − 1 = 38.760922%, which is larger than the real appreciation for exactly the asymmetry reason in P1. A currency whose nominal rate has been stable for a decade under a 3.4-point inflation gap is not stable; it is 28% more expensive and the adjustment has been deferred, not avoided.

Applied mini-project

Score one emerging market against the currency-crisis checklist, from primary data, and write the note.

Pick a single emerging-market economy that is not India and not one you already follow closely, and build a nine-indicator scorecard from published primary sources. Four artefacts, each with a numbered test it must pass before it counts. Every figure traces to a named publication with the date you retrieved it. Where a source disagrees with another, both get recorded and the disagreement gets a sentence.

Artefact 1, the data sheet (2 tests). One table, one row per indicator, with the value, the source publication, the reference date of the data and the date you read it. Reserves, short-term external debt on a residual-maturity basis, monthly imports, the current account, GDP, the real effective exchange rate index and its own ten-year average, private credit growth, nominal GDP growth, broad money, the foreign-currency share of external debt, the fiscal deficit and export growth. Test 1: every row names a publication and two dates, and no row is sourced to a data aggregator without the underlying publication also named. Test 2: the current account you record and the GDP you record produce a ratio that matches the ratio the central bank itself publishes, to within 0.2 percentage points, or you explain the difference (a different GDP vintage is the usual answer, and finding that out is the exercise).

Artefact 2, the scorecard (2 tests). Apply the nine thresholds. Report which fire and which do not, with the value and the threshold side by side. Test 3: the reserve adequacy row is computed both ways, months of import cover and cover of short-term external debt, and the note says which one binds in a rollover scenario and why they can disagree. Test 4: the real exchange rate row states which index you used, whose weights it carries and what its base period is, because a REER deviation is meaningless without those three.

Artefact 3, the balance-sheet stress (1 test). Take the foreign-currency share of external debt and compute what a 25% devaluation does to the local-currency value of that debt, expressed as a percentage of GDP. Test 5: the calculation is shown, and the note states explicitly whether the country can use exchange-rate adjustment to fix its flow problem without creating a stock problem.

Artefact 4, the flip analysis (1 test). For each firing indicator, compute what would have to change for it to stop firing, in the units the country actually controls: how many billions of reserves, how many percentage points of current-account improvement, how much real depreciation. Test 6: each flip number is a quantity, not an adjective, and each is compared with something that makes it interpretable, such as a year of net foreign direct investment or a quarter of export earnings.

Deliverable. A two-page note carrying the scorecard table, the stress calculation, the flip analysis, a named list of every assumption and threshold you used, and a closing paragraph on the single indicator whose data you trust least and what you would do about it. State a verdict in one sentence at the top, before the evidence, and make it falsifiable.

Rubric (20 points; pass at 16 with no zero on any row).

Score each row 0 to 3 and take the total. Any artefact whose test fails scores zero on that row whatever the prose around it looks like, because a scorecard built on an undated number is a scorecard about last year, and the whole value of this exercise is that it is about now.

Reading & resources

Treat each of these as an anchor to verify against, never as a source to lift a number from without tracing it yourself.

The primary manuals and rulebooks:

• IMF, Balance of Payments and International Investment Position Manual, sixth edition (2009). The definitive classification of every transaction in this node, including the two-item capital account that trips everyone. Read the chapter on the capital account once, in full; it is short. [Free] [Intermediate]
• IMF, Institutional View on the Liberalization and Management of Capital Flows and its subsequent reviews. The current official position on when capital-flow management measures are legitimate. [Free] [Intermediate]
• WTO, Understanding the WTO and the regional-trade-agreements database. The ladder from free trade area to customs union in its own legal vocabulary, with the current inventory of agreements in force. [Free] [Beginner]
• RBI Master Directions on the Liberalised Remittance Scheme and on External Commercial Borrowings (current versions). The India-side limits and eligibility rules, amended by circular, so record the date you read them. [Free] [Intermediate]

The theory, at source:

• Rudiger Dornbusch, "Expectations and Exchange Rate Dynamics", Journal of Political Economy, 1976. The overshooting result in fourteen pages, and still the clearest statement of why one sticky price produces a jump in another. [Paid] [Advanced]
• Eugene F. Fama, "Forward and Spot Exchange Rates", Journal of Monetary Economics, 1984. The unbiasedness regression run above, with the finding that started the forward-premium literature. [Paid] [Advanced]
• Jacob Viner, The Customs Union Issue, 1950. Where trade creation and trade diversion come from, and a corrective to anyone who assumes a trade agreement is good by construction. [Paid] [Intermediate]
• Paul Krugman, Maurice Obstfeld and Marc Melitz, International Economics: Theory and Policy. The standard graduate-adjacent treatment of every model here, with the tariff and quota diagrams done properly. [Paid] [Intermediate to Advanced]
• Maurice Obstfeld and Kenneth Rogoff, Foundations of International Macroeconomics. The rigorous version, for anyone who wants the models derived rather than asserted. [Paid] [Advanced]

Data you will actually use:

• BIS Triennial Central Bank Survey of foreign exchange and OTC derivatives markets. The turnover figures, by currency pair and instrument, that put the flow approach in its place. [Free] [Intermediate]
• BIS effective exchange rate indices, both nominal and real, for most economies, with the weights and base period documented. The right source for a REER deviation. [Free] [Beginner]
• RBI's Handbook of Statistics on the Indian Economy and its monthly bulletin's balance-of-payments tables. The India-side primary source for every balance-of-payments account taught here. [Free] [Beginner to Advanced]
• Joint External Debt Hub (BIS, IMF, OECD and World Bank) and the World Bank's international debt statistics. Short-term external debt by residual maturity, which is the number the reserve-adequacy test needs and the one that is hardest to find. [Free] [Intermediate]
• IMF International Financial Statistics and the Article IV consultation reports. The consultation reports are the fastest route to a country's own reserve-adequacy assessment, and they show their working. [Free] [Intermediate]

Do the following rather than only reading. Take one month of your own country's balance-of-payments release and re-derive the errors-and-omissions line from the other rows. It will not tie on the first attempt, and finding out why teaches more about the sign convention than reading the manual's chapter on it. Then take a single quoted currency pair, pull the one-year forward points and the two one-year interest rates from the same afternoon, and compute the basis. Do that once a week for a month and you will have a feel for how wide the basis runs in calm conditions, which is the only way to recognise a stressed one.

Teach it back & journal

Feynman prompt. Sit a colleague down who knows what an interest rate is and nothing else about currencies, and get them to the point where they can tell you, unprompted, why a currency paying 240 basis points more than the dollar trades at a forward discount of almost exactly 240 basis points. Start with the trade, not the formula: borrow a million dollars, convert, invest, sell the proceeds forward, and show them that the profit is zero at ₹86.443460 and ₹567,100 at ₹85.9000. Make them tell you who would do that trade and how large they would do it. Only after they have said "so the forward has to move" should the formula appear, and then it is a name for something they already worked out.

Then break it for them. Take the forward away and ask what is left. They should arrive at the answer themselves: the number is the same, and nothing enforces it any more. If they can say out loud that covered interest parity is a price and uncovered interest parity is a guess wearing the same number, they have the single most useful distinction in this material.

Finish on the trade-policy side with one question and no diagram. A quota and a tariff produce the same price and the same import volume, and one of them costs the country three and a half times as much. Ask them why. If they reach for elasticities, redirect them to the rent, and do not accept "the government loses revenue" as a complete answer until they can say who receives it instead and why the exporting country prefers that arrangement.

Journal prompt. For two weeks, every time you meet a currency forecast, in a broker note, a budget document, a corporate hedging policy or a newspaper, write down three things before you use it.

• Which relation the forecast implicitly invokes: a forward, a purchasing-power drift, a model output, or a view held by a person.
• What enforces it, and whether the author admits the answer when the answer is nothing.
• What would have to be true for it to be wrong by 10%.

Then, at the end of the two weeks, answer these in writing.

• How many of the forecasts you collected were forwards being reported as expectations?
• How many purchasing-power comparisons named the basket?
• How many balance-of-payments numbers named the manual edition or the sign convention?
• Where you could not tell, what did you do, and what should you have done instead?

Close with a paragraph on the habit this material is actually trying to install. These relations are all exactly solvable and almost none of them forecast. That combination is uncomfortable, because the arithmetic feels like knowledge and the forecast feels like the point. Write down which of the four checks you are most likely to skip when you are in a hurry: the second route on a deadweight loss, the identity close on a balance of payments, the spread on an arbitrage, or the date on a perishable figure. Then write what specifically goes wrong when you skip it, and one thing you will change this month to make skipping harder than doing.

This module's flashcards and mastery quiz are wired into the app: see the node's Quiz and Reviews.