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Resources › International economics map › Exchange rate regimes and the trilemma
International economics · Balance of payments and exchange rates

Exchange rate regimes and the impossible trinity

Who sets a currency’s price, the market or the government? The answer decides what the central bank can do, and the impossible trinity is the sharpest statement of what it cannot. This page goes from the menu of regimes, through the history that produced them, to a lab that breaks a peg, the central bank’s balance sheet under sterilisation, and a proof of the trilemma. 22 past-paper questions at the end.

A question to hold on to
Which one of these combinations of policies is NOT possible? Free capital mobility with an independent monetary policy and a floating rate; the same with a fixed rate; free capital mobility with no independent policy and a fixed rate; or restricted capital with independent policy and a fixed rate.
GATE 2026Solved at the end ↓
In this guide
Guide · about 45 minutes
  1. The menu of regimes
  2. From gold to floating
  3. Defending a peg, and where it breaks
  4. Sterilisation
  5. The impossible trinity
  6. What each regime does to policy
  7. The rupee
  8. The mistakes examiners are fishing for
  9. The opening question, solved
  10. The page on one screen
  11. Check yourself
  12. Past papers, by level
  13. Sources
  14. Quick answers
01
The idea

The menu of regimes

An exchange rate regime is the rule that decides how a currency’s price is set. Pick a regime below and look at three things: who sets the rate, what the central bank does, and what is left of its monetary policy.

Market decidesGovernment decides
Who sets the rate
The market, but the central bank leans against sharp moves.
What the central bank does
Buys foreign currency when the home currency is rising too fast and sells it when it is falling too fast. Holds reserves for this.
Monetary policy, with free capital
Mostly free. The central bank gives up some freedom to smooth the rate.
Where you meet it
India: the rate is market-determined, and the RBI intervenes to curb excess volatility.

Some vocabulary, because examiners reuse it. A rate set by the market with no central bank intervention is flexible, also called floating. UOH 2014 asks which name fits a system with no intervention, and the key is that either does. A rate the government holds at a stated parity is fixed or pegged. When the government changes the parity it is a devaluation (the home currency is made cheaper) or a revaluation; when a market rate moves it is a depreciation or appreciation. A crawling peg is an automatic system for revising the rate in small steps, which UOH 2021 sets against a system of long constant periods punctuated by sharp devaluations. A currency union removes the rate between members altogether.

Even without a rate between them, two members of a currency union can have different real exchange rates, since the real rate depends on price levels as well as the nominal rate (JNU 2013). A regional inflation gap is a real appreciation for the dearer region, and it has no devaluation to undo it.

02
History

From gold to floating

The regimes in use today are the result of three systems that broke. The timeline is short, and each step is the answer to at least one past-paper question.

  1. Before 1914

    Gold standard

    Each currency is defined as a weight of gold, so every rate between two currencies is fixed through gold. JNU 2013: countries linked the value of their money to a specific weight of gold.

  2. July 1944

    Bretton Woods

    Forty-four countries sign the IMF's Articles of Agreement. The dollar is worth one thirty-fifth of an ounce of gold, and every other currency is pegged to the dollar. The dollar becomes the reserve currency.

  3. 1969

    The SDR

    The IMF creates the Special Drawing Right, an asset of its own that countries can hold as reserves. At first it was defined as a fraction of gold equal to one US dollar. UOH 2013 calls it paper gold.

  4. 1971 to early 1973

    The par-value system ends

    In August 1971 the United States stops exchanging officially held dollars for gold. The Smithsonian realignment of December 1971 does not hold, and by early 1973 the major currencies float.

  5. 1976 and 1978

    Jamaica and the Second Amendment

    The Jamaica Agreement of January 1976 lets members choose their own regime, and the Second Amendment to the IMF's Articles of 1978 writes that into law. Managed floating, since 1973, is the result (CUET 2020).

  6. Since 1999

    The euro

    Maastricht (in force November 1993) set the road to a single currency. The euro began on 1 January 1999, with notes and coins from 2002.

Two of the questions are on how reserves were held. Under the gold exchange standard, foreign exchange reserves consist of gold plus convertible currencies (UOH 2013), which is what the Bretton Woods system did with the dollar. And between 1944 and 1971 the exchange rate between any two currencies was fixed within narrow boundaries (UOH 2015), unlike the period after, in which managed exchange rates have supported some restriction on fluctuations without fixing them (CUET 2020).

Pause and predict
Under the Bretton Woods system, which currency did the other members peg to, and which acted as the international reserve currency?
03
Interactive

Defending a peg, and where it breaks

Suppose a currency is overvalued at its peg: at the fixed rate, people want to buy more foreign currency than others want to sell. The central bank has to fill the gap or the peg goes. The order of events is a UGC NET question, and the logic is a chain:

  1. The fixed rate is lower than the market-clearing rate (the home currency is overvalued).
  2. So the demand for foreign currency exceeds its supply.
  3. The central bank sells foreign currency from its stock of reserves.
  4. That closes the gap between supply and demand at the fixed rate.
  5. But the bank’s stock of foreign currency is depleted.

That is B, A, E, C, D in the question, UGC NET Dec 2023. The last step is the weak point. If the pressure is temporary the bank can wait it out. If it persists, the reserves run down and the peg falls. Try it. The market is the one used on the exchange-rates page, where the rate clears at ₹80, and each year the demand for dollars grows by a little more.

Rate in year 10₹87.5
Reserves left0
Dollars sold in all100
Peg breaksyear 6
123456789107678808284868890Year₹ per $1234567891020406080100YearReserves
Rate in forceRate the market would set (dotted)Reserves
What it shows

The central bank sells dollars every year, and the sales grow because the gap grows. In year 6 the reserves are gone and the rate jumps to the market's ₹84.5. A shock that persists defeats any peg, and the fall comes in one step.

With a shock of 6 a year and reserves of 100, the fixed rate holds until year 6, then jumps to ₹84.5. A float never runs out of anything, because it moves at once: ₹87.5 by year 10. A band is in between. The rate floats until it touches ₹84, and then the bank has to defend that edge, so by year 10 it has sold 80 and holds 20 (try 300 for reserves to see a defence that lasts).

Two lessons. A peg is only as strong as the reserves behind it relative to the pressure, and a shock that keeps growing beats any reserves. And the pain is not avoided by a peg; it is postponed, and arrives all at once. The speed of the fall is why governments dread a peg breaking.

04
Interactive

Sterilisation

The mirror image of defending a peg is holding one down during a capital inflow. Foreigners want the home currency, so it would rise. To stop it, the central bank buys foreign currency and pays in newly created home money. Look at the bank’s balance sheet. Its assets are net foreign assets (reserves) and domestic assets (bonds and loans); its liability is the monetary base. Buying foreign currency raises the first, and the base rises with it, so the money supply grows and the interest rate falls.

Sterilisation nullifies that effect on the money supply. The bank sells domestic bonds of the same value, which takes the new money back out. In the lab below, try both ends.

Capital is flooding in and the central bank is holding the rate. To stop the home currency rising it buys the foreign currency on offer, and pays for it with newly created home money.

Net foreign assets200 to 260
Domestic assets300 to 300
Monetary base500 to 560

Before

Net foreign assets200
Domestic assets300
Monetary base500

After

Net foreign assets260
Domestic assets300
Monetary base560
What it shows

Unsterilised: the base money rises by 60, the same as the foreign currency bought. More money pushes the home interest rate down, which is how a fixed rate with free capital pulls policy toward the world rate.

Unsterilised, buying 60 takes the base from 500 to 560. Fully sterilised, net foreign assets rise to 260, domestic assets fall to 240, and the base stays at 500. CUET 2023 asks for exactly this change: a rise in net foreign assets and a decline in domestic assets. A second CUET question tests the statement form. In an open economy, (A) sterilisation implies nullifying the impact of foreign-exchange transactions on the domestic money supply, and (B) in a sterilised intervention a purchase of foreign assets should be matched by a sale of domestic assets. Both are true. (C) is false, since a fixed rate with perfect capital mobility leaves no independent monetary policy, and (E) is false, since the real rate also moves with prices. So the key is A and B only.

Sterilisation is limited. It lets the bank keep its interest rate away from the world rate for a while, but it needs a supply of bonds to sell, it costs the bank the gap between what the bonds pay and what its foreign assets earn, and by keeping the home rate high it keeps attracting the inflow it is trying to stop.

05
Derivation

The impossible trinity

Three goals look attractive together. A fixed exchange rate gives traders certainty. Free capital movement lets savings find the best use anywhere. An independent monetary policy lets the central bank fight home recessions and inflation. The trilemma says a country can hold any two, never all three. The proof is short, and it rests on the uncovered interest parity of the parity page.

Derive it

Why you cannot have all three

We want to show
A country cannot at once fix its exchange rate, let capital move freely, and set its own interest rate. With the first two, i=i∗: the home rate is the world rate.
  1. 1
    Start from what investors compare.

    An investor with one rupee can hold a home bond paying i, or change it into foreign currency, hold a foreign bond paying i∗, and change back. The second route also earns or loses whatever the exchange rate does. With Δee/e the expected rise in the price of foreign currency, the two routes give the same return only if

    i=i∗+eΔee​

    This is uncovered interest parity, from the parity page. If the two sides differ and capital is free, money moves until they match.

  2. 2
    Now fix the exchange rate.

    If the government fixes the rate and people believe it, nobody expects it to move: Δee/e=0. The condition becomes

    i=i∗

    The home interest rate is the world interest rate. It is no longer a choice.

  3. 3
    See what happens if the central bank tries anyway.

    Say the world rate is 5% and the central bank wants 8%. Every rupee now earns 3 points more at home, so investors bring money in and sell foreign currency. To hold the rate, the central bank has to buy that foreign currency, and the rupees it pays out are new money, which pushes the home rate down toward 5%. It can offset this by selling bonds (sterilising), which mops the money up and keeps 8%, but then the inflow carries on, reserves swell, and the bonds to sell run out. The rate cannot be held at 8%.

  4. 4
    Give one up, and the equation has room again.

    Let the rate float, and Δee/e can be anything, so the home rate can differ from the world rate: at 8% against 5%, investors are content if they expect the rupee to lose 3% a year. Or restrict capital, and the equation does not bind because money cannot move to enforce it. Or accept i=i∗ and give up the independent policy. Each side of the triangle is one of these.

Step 1 of 4
So
The trilemma is uncovered parity read in reverse. A fixed rate removes the expected depreciation, free capital enforces the equation, and the home interest rate has nothing left to be independent of. JNU 2020, DSE 2008 and GATE 2026 each test which three goals clash, and UGC NET 2023 tests the reason: perfect capital mobility aligns the domestic rate with the world rate.
The link that does the work
i=i∗+eΔee​ fixed rate ​i=i∗
Δeᵉ/e is the expected rise in the home-currency price of foreign currency. A credible peg makes it zero.
Each side of the triangle is a regime

Fixed rate and free capital: the interest rate is not yours (a euro-area member). Fixed rate and independent policy: capital must be controlled (Bretton Woods). Free capital and independent policy: the rate must float (the large floaters).

06
Consequences

What each regime does to policy

The trilemma shows up in the effectiveness of policy. With free capital, the result of the Mundell-Fleming model (see the IS-LM-BP page) is a mirror:

Policy effectiveness with perfect capital mobility
Fixed rateFloating rate
Monetary policyCompletely ineffective (UOH 2021)Effective, and autonomous (UOH 2018)
Fiscal policyEffective: the central bank accommodates itIneffective: the exchange rate crowds out the gain

Why does a floating rate help with monetary policy? Lower home rates cause a capital outflow, which depreciates the currency, which boosts exports. Under a fixed rate the same outflow forces the central bank to sell reserves and shrink the money supply back, undoing the cut.

Related, and asked twice by JNU, is the conflict of internal and external balance. Under a fixed rate, the goals can conflict: expansionary policy to cut unemployment lifts income, which raises imports and can open a trade deficit and a balance of payments problem (statements A and C of JNU 2019 are true; B is false). Greater flexibility eases that conflict, and means a recession abroad does not have contractionary effects at home, since the exchange rate absorbs it (JNU 2021, A and C). A more stable environment for trade and investment (B) is an argument for fixed rates, not flexible.

What a country gives up by sharing a currency, and when that is worth it, is the subject of the optimum currency area section of the integration page.

✓✓Fixed rateFree capitalIndependent monetary policy
Possible: you give up an independent monetary policy. The home interest rate is whatever the anchor country's is. This is the position of a euro-area member or a currency board.
07
India

The rupee

India’s own path, from a controlled rate to a market-determined one, is a short list of dates that the RBI records:

  1. July 1991

    The rupee is devalued in two steps, about 18% against the dollar in all, in the balance of payments crisis.

  2. March 1992

    A dual exchange rate system, the Liberalised Exchange Rate Management System, is introduced as a step toward a market-determined rate.

  3. March 1993

    The exchange rate is unified: one rate, determined by demand and supply.

  4. August 1994

    India accepts Article VIII of the IMF's Articles, making the rupee convertible on the current account. Capital account convertibility stays partial.

UOH 2015 asks what the rupee is. The answer, since August 1994, is fully convertible on the current account but not on capital account transactions. Current account convertibility means no restriction on buying foreign currency to pay for imports, services, travel or interest; capital account convertibility would mean the same for buying foreign assets. India has opened its capital account only part of the way. The rate itself is market-determined, with the RBI intervening, which is the managed float of the menu.

08
Exam focus

The mistakes examiners are fishing for

Watch out for

The mistakes examiners are fishing for

  • Putting the balance of payments in the trilemma. The three are a fixed rate, free capital movement and independent monetary policy. Balance in the balance of payments (JNU 2020, option E) is not one of them.
  • Writing “floating” into the trilemma pair. UOH 2010 offers incompatibility among independent monetary policy, free capital and a floating rate. They are compatible. The key is none of the above.
  • Saying a central bank intervenes under a float. A pure float has no intervention. A managed float does, and the label matters.
  • Thinking sterilisation is free. It swaps interest-bearing home bonds for lower-yielding foreign assets and runs out of bonds.
  • Mixing devaluation and depreciation. One is a government decision under a peg, the other a market movement under a float.
  • Believing fiscal policy is weak under a peg. With free capital and a fixed rate, it is monetary policy that is lost, and fiscal policy that is strong.
09
Back to the puzzle

The opening question, solved

GATE 2026 · moderate
Which combination of simultaneous policy actions is NOT possible?
  1. 1
    Name the three goals
    Free capital mobility, independent monetary policy, and a fixed rate.
  2. 2
    Test each option
    A has free capital, independent policy and a float: two goals plus a float, possible. C has free capital, no independent policy, and a fixed rate: possible. D has restricted capital with independent policy and a fixed rate: possible, because controls break the link. B has all three.
Answer
B: full capital mobility, independent monetary policy and a fixed rate cannot be held together.
UGC NET 2023 · hard
A central bank fixes the exchange rate and its currency is overvalued. Put in order the steps of the intervention.
  1. 1
    Start with the cause
    (B) the fixed rate is lower than the market-clearing rate, so (A) demand for foreign currency exceeds supply.
  2. 2
    Then the action
    (E) the bank sells foreign currency from reserves, which (C) equalises the gap.
  3. 3
    End with the cost
    (D) its stock of foreign currency is depleted.
Answer
B, A, E, C, D.
10
Revision

The page on one screen

The lesson on one screen
Regimes
Float, managed float, crawling peg or band, fixed peg, currency union: from the market to the government deciding.
History
Gold standard, then Bretton Woods (1944, dollar and gold at $35), then collapse in 1971 to 1973 and managed floating.
Defending a peg
An overvalued currency means excess demand for foreign currency, so the bank sells reserves until they run out.
Sterilisation
Offset a purchase of foreign currency by selling bonds: net foreign assets up, domestic assets down, base unchanged.
Trilemma
Fixed rate, free capital, independent monetary policy: any two. Parity gives i = i* under a peg.
Policy
Fixed with free capital: monetary policy ineffective, fiscal effective. Floating: the reverse.
India
Unified market-determined rate in 1993, current account convertible since August 1994, capital account partly open.
11
Practice

Check yourself

0 of 10 correct so far

Numbers

The foreign-exchange market of the exchange-rates page: the rate that clears it is ₹80 per dollar before any shock.

How long a peg lasts
The rate is fixed at ₹80. Each year demand for dollars rises by 6 more than the year before (6 in year 1, 12 in year 2, and so on) and the central bank sells whatever is needed. It starts with reserves of 100. In which year do the reserves run out?
A band
The central rate is ₹80 and the band is ±5%. What is the highest rate the central bank will allow, in rupees per dollar?
A crawl
A crawling peg starts at ₹80 and rises 1% a year. What is the central rate after three years? (₹, to two decimals)
Sterilisation
A central bank holds net foreign assets of 200 and domestic assets of 300. It buys 60 of foreign currency to stop its currency rising, and fully sterilises. What are its domestic assets afterwards?
The home rate under a peg
Capital is free and a peg is fully credible. The world interest rate is 5%. What interest rate must the home economy have, in per cent?

Concepts

1Which three can an economy NOT achieve at the same time?
2Under perfect capital mobility and a fixed exchange rate, monetary policy is
3Under a floating rate, following an increase in the money supply, the monetary authorities
4A fully sterilised purchase of foreign currency, during a capital inflow, leads to
5The currency of a country in a currency union can have a real exchange rate that differs from its partners’. This is because
12
Past papers

Past papers, by level

Foundation

Definitions, directions and one-step sums. Most CUET, UGC NET and Hyderabad questions sit here.

5 questionsPractise →

Standard

Classification traps, multi-step numericals and statement questions, up to the hardest JNU, JAM and GATE items.

17 questionsPractise →

Delhi School level

The Delhi School entrance asks this topic harder than any other exam. These questions are kept apart from the ordinary sets.

1 questionTry it →
All 22 past-paper questions on exchange rate regimes and the impossible trinity, easiest first: practise the full set →

✦These are questions from the TestStop bank. A free account answers 10 a day, each with its worked solution; All-Access opens every set with no daily limit.

13
Checked against

Sources

Facts on this page were read against these sources on 6 October 2026. India’s dates: the RBI chronology for 1991 to 2000 (July 1991 devaluation of about 18% against the dollar, LERMS in March 1992, a unified rate in March 1993, and rupee convertibility on the current account with acceptance of Article VIII in August 1994). Bretton Woods: Federal Reserve History (forty-four nations, $35 an ounce, lasted until 1971). The end of the par-value system in early 1973 and the Second Amendment: the IMF’s History 1972 to 1978. The SDR, created in 1969: IMF fact sheet. The euro: EU history, 1990 to 99. The first price of the model, ₹80 per dollar, is a stylised number, not a quotation.

14
Quick answers

Quick answers

What is the impossible trinity?

The impossible trinity, or trilemma, says a country cannot have all three of a fixed exchange rate, free movement of capital, and an independent monetary policy. Any two can be had together. The reason is interest parity: with a credible fixed rate and free capital, the home interest rate must equal the world rate, so the central bank has no rate of its own to choose.

What is the difference between a fixed and a floating exchange rate?

Under a fixed rate the government sets the rate and the central bank buys or sells foreign currency in any amount to hold it, using its reserves. Under a floating rate the market sets the rate through demand and supply and the central bank does not intervene. A managed float sits between, with intervention to smooth sharp moves.

What is sterilised intervention?

Sterilised intervention is a central bank purchase or sale of foreign currency that is offset by an opposite trade in domestic assets, so the money supply does not change. If it buys foreign currency during a capital inflow, it sells domestic bonds of the same value: its net foreign assets rise, its domestic assets fall by the same amount, and the monetary base is unchanged.

What is a crawling peg?

A crawling peg is an exchange rate fixed to a currency or basket but revised in small steps, by a rule, usually to follow the inflation gap. It avoids the large, sudden devaluations of an ordinary peg, which UOH 2021 contrasts with a system of long constant periods broken by sharp devaluations.

Is the Indian rupee fully convertible?

No. The rupee has been convertible on the current account since August 1994, when India accepted Article VIII of the IMF's Articles of Agreement, but the capital account is only partly open. Anyone can buy foreign currency to pay for imports, travel or interest, but investment flows are still governed by limits.

What happened to the gold standard and Bretton Woods?

Under the gold standard each currency was defined as a weight of gold. Bretton Woods, agreed in July 1944, pegged every currency to the dollar and the dollar to gold at $35 an ounce. The United States ended dollar-to-gold convertibility in August 1971, and by early 1973 the major currencies floated. The Jamaica Agreement of 1976 and the Second Amendment of 1978 accepted this.

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