The IS–LM–BP model explained: the BP curve, capital mobility and all 16 policy cases

A closed economy has two markets to keep in balance: goods (the IS curve) and money (the LM curve). Open it to the rest of the world and two things cross the border. Goods do: exports X and imports M, so spending on home output now includes net exports, NX = X − M. And money does: savers can buy foreign bonds and foreigners can buy ours, so capital flows in or out depending on whose interest rate is higher.

Both kinds of flow show up in the balance of payments (BoP), the record of a country’s transactions with the rest of the world:

• the current account is mainly net exports. It worsens when income rises, because people buy more imports, and improves when the currency depreciates, because exports get cheaper for foreigners;
• the capital account records capital flows. It improves when the domestic interest rate rises above the world rate r*, because capital flows in.

The two together must add up to zero unless the central bank’s reserves change. When their sum is positive the country has a surplus: more foreign currency is coming in than going out. When it is negative, a deficit.

Throughout this guide the economy is small (it takes r* as given), prices are fixed, and the exchange rate e is the price of foreign currency in rupees, so a rise in e is a depreciation of the rupee. If IS–LM itself is new to you, start with the IS–LM lessons.

The BP curve is every combination of income Y and the interest rate r at which the balance of payments is exactly in balance. It goes on the same diagram as IS and LM, with income across and the interest rate up.

Why it slopes up. Start at a point where payments balance, and raise income. Imports rise, so the current account worsens. To stay in balance, more capital has to come in, and capital comes in only if the domestic interest rate rises. So a higher income needs a higher interest rate: BP slopes up.

Off the curve. At any point above BP (or to its left) the interest rate is higher, or income lower, than balance needs: capital inflows are larger or the import bill smaller, so there is a surplus. At any point below BP (or to its right) there is a deficit.

What shifts it. A depreciation raises net exports at every income, so the same interest rate now balances payments at a higher income: BP shifts right. An appreciation shifts it left. A rise in the world interest rate shifts it up.

Capital mobility, K in the formula, says how strongly money flows across the border when interest rates differ. It decides how steep BP is, because BP’s slope is m/K.

• Perfect capital mobility. Economically: the smallest gap between our interest rate and the world rate would bring in, or send out, unlimited capital, so the domestic rate can never differ from r*. Graphically: BP is a horizontal line at r* (JNU 2018). This is the Mundell–Fleming case.
• Imperfect capital mobility. Economically: capital responds to interest differences, but only so much, because of controls, risk or transaction costs. Graphically: BP slopes up. The more mobile capital is, the flatter BP. Textbooks split this into high mobility (BP flatter than LM) and low mobility (BP steeper than LM), and that comparison with LM is what decides the cases, not the level of K on its own. A high propensity to import makes BP steep even with mobile capital.
• Zero capital mobility. Economically: no capital crosses the border, so only trade matters, and payments balance at just one level of income, where exports pay for imports. Graphically: BP is vertical at that income.

A policy moves IS or LM. If the new point is off BP, the balance of payments is in surplus or deficit, and something has to move until all three curves meet again. The exchange-rate regime decides what moves.

Fixed exchange rate. The central bank promises to buy or sell its currency at a fixed price. A surplus means foreigners want more rupees than are on offer, so the central bank sells rupees for dollars: new rupees enter the economy and the money supply rises. A deficit means it must buy rupees back with its reserves, and the money supply falls. Under a fixed rate the money supply stops being the central bank’s choice.

Flexible (floating) exchange rate. The central bank leaves the currency market alone and the price moves. A surplus pushes the rupee up (appreciation), a deficit pushes it down (depreciation). The money supply stays wherever the central bank put it.

These are the cases most exams ask about, and the clearest place to see the three steps. With BP flat at r*, any policy that moves the interest rate at all causes a surplus (rate above r*) or a deficit (rate below).

Once BP slopes up, a policy no longer has to cause an imbalance of a known sign. The question is whether the new point lies above or below BP.

• A monetary expansion always causes a deficit. Income rises, so imports rise; the interest rate falls, so capital leaves. Both push the same way.
• A fiscal expansion can go either way. Income rises (imports up, bad for payments) and so does the interest rate (capital in, good for payments). The new point lies on the old LM, so the question is whether moving up LM takes you above or below BP. If BP is flatter than LM, you end up above BP: a surplus. If BP is steeper than LM, below it: a deficit.

Fiscal policy is where imperfect mobility changes the answers. The same comparison, BP against LM, decides whether an expansion brings money in or drains it out under a fixed rate, and whether the rupee rises or falls under a flexible one. Read cases 3 and 11 together (BP flatter), then 5 and 13 (BP steeper): the regime turns the same surplus or deficit into opposite results.

Monetary policy is simpler, because a monetary expansion always causes a deficit. Under a fixed rate the deficit drains the money back out, whatever the slope of BP. Under a flexible rate the deficit depreciates the rupee, which adds to the expansion.

The remaining four cases, with zero capital mobility, follow the same rules and are worked in the appendix.

Every thumbnail is drawn from the same model, starting from the same point, with the same size of policy: government spending up by 20 or the money supply up by 20. Colours compare the final rise in output with what plain IS–LM gives before the balance of payments adjusts. Tap a case to step through it in the graph underneath, or move the capital-mobility slider to see how one case turns into the next.

Every case in one table, with the numbers from the diagrams. The last column compares the final rise in output with plain IS–LM, the rise before the balance of payments adjusts (+23.5 here). Mobility runs perfect (BP flat), high (BP flatter than LM), low (BP steeper than LM), zero (BP vertical). Tap a case number to jump to its diagrams.

The same results in the four-by-four layout most textbooks use:

The table comes down to four facts:

1. Fixed rate, monetary policy: always useless. The central bank can’t choose the money supply and the exchange rate at once (unless it sterilises, below).
2. Fixed rate, fiscal policy: better the more mobile capital is. Mobile capital means the expansion brings a surplus, and the surplus adds money.
3. Floating rate, fiscal policy: worse the more mobile capital is. Mobile capital means a surplus, and the surplus appreciates the rupee, which crowds out net exports. Fiscal policy under the two regimes runs in opposite directions down the table.
4. Floating rate, monetary policy: always works, best with mobile capital. The deficit always depreciates the rupee, which helps.

The knife-edge. If BP and LM are equally steep, a fiscal expansion moves the economy along both: payments stay in balance, nothing adjusts, and the result is plain IS–LM under either regime. Try it in the graph with the mobility slider.

Sterilisation. A central bank with a fixed rate can offset the money its interventions create or destroy, by selling or buying government bonds (CUET 2023). Sterilised, a fiscal expansion behaves like plain IS–LM, and a monetary expansion keeps working, but only as long as the reserves last: a sterilised deficit drains reserves every period.

Other shocks follow the same three steps:

• A devaluation under a fixed rate raises net exports: IS and BP shift right, a surplus follows, money flows in, and output rises.
• A rise in the world interest rate shifts BP up. Under a fixed rate with perfect mobility, money flows out and output falls; under a floating rate the rupee depreciates and output rises (CUET 2023).
• A rise in foreign income raises exports. Under a floating rate with perfect mobility, the rupee appreciates until net exports are back where they were, and output is unchanged (DSE 2006).

The impossible trinity. Cases 2, 4, 6 and 8 are the general rule: a country cannot have a fixed exchange rate, free capital movement and an independent monetary policy all at once (GATE 2026; JNU 2020).

With no capital flows, BP is vertical at the one income where trade balances, and only the current account matters. Any policy that raises income raises imports and causes a deficit. Under a fixed rate that deficit always drains money until income is back at the BP line, so neither policy can move output. Under a flexible rate the rupee depreciates until trade balances again, which makes both policies work.