Macroeconomics: Income, Consumption, Investment, Money, Inflation and IS–LM

This chapter answers "Section XH1.2: Macroeconomics" of the Humanities and Social Sciences (XH) paper. It is part of Section XH1.2 of XH1 Economics, one of the six optional sections of XH, chosen at the time of application. It teaches national-income accounting for closed and open economies, the classical and Keynesian determination of output and employment, the theories of consumption (absolute, relative, life-cycle, permanent-income and Hall's random walk), investment (Jorgenson's neoclassical theory, Tobin's q and the accelerator) with the autonomous multiplier, the demand and supply of money with the liquidity trap and the money multiplier, central and commercial banking and monetary-policy instruments, theories of inflation and the expectations-augmented Phillips curve, adaptive and rational expectations and real business cycles, and the closed-economy IS–LM and Mundell–Fleming models with the impossible trinity. The numericals are the expenditure multiplier, the money multiplier, an IS–LM solution and consumption-function arithmetic.

1. National income accounting: closed and open economy

National income is measured three ways that must agree: the product (value-added) method sums value added across firms, the income method sums wages, rent, interest and profit, and the expenditure method sums final spending. For a closed economy the expenditure identity is Y = C + I + G; for an open economy it is Y = C + I + G + (X − M), where (X − M) is net exports. The aggregates nest: GDP is output produced within the borders; GNP = GDP + net factor income from abroad (NFIA); NNP = GNP − depreciation; and national income is NNP at factor cost.

Nominal GDP values output at current prices; real GDP values it at base-year prices, stripping out inflation. The GDP deflator = (nominal GDP ÷ real GDP) × 100 is the broadest price index. Open-economy measurement adds the balance of payments: the current account records trade and factor income, the capital and financial account records asset flows. A country's GDP can exceed its GNP (net payments abroad) or fall short of it (net receipts).

⚠️ GDP is within borders, GNP is by residents
GDP counts output produced inside the country regardless of who owns the factors; GNP counts output earned by the country's residents wherever produced. The bridge between them is net factor income from abroad, and confusing the two is the commonest accounting slip.

2. Output and employment: classical and Keynesian frameworks

The classical model assumes flexible wages and prices and rests on Say's law: supply creates its own demand, so there can be no lasting general glut. The labour market clears at full employment, output is set by the production function, and the interest rate equates saving and investment. Money is neutral: the quantity theory MV = PY fixes the price level but not real output (the classical dichotomy). Unemployment can only be voluntary or frictional.

Keynes rejected Say's law and made effective demand the driver. With sticky money wages, aggregate demand (C + I + G) can settle output at an underemployment equilibrium: there is no automatic force to full employment. Saving and investment are brought into line by changes in income, not only by the interest rate, which Keynes derived instead from liquidity preference. The paradox of thrift follows: an attempt by all to save more lowers income and can leave saving unchanged. This opens the door to active demand management.

3. Theories of consumption

  • Absolute income hypothesis (Keynes): consumption depends on current absolute income, C = a + bY, with 0 < b < 1 (the fundamental psychological law). The average propensity to consume APC = a/Y + b falls as income rises and stays above the marginal propensity b, which fits budget studies but not long-run constancy.
  • Relative income hypothesis (Duesenberry): consumption depends on income relative to others (the demonstration effect) and on past peak income (the ratchet effect), so people resist cutting consumption when income falls. APC is roughly constant in the long run.
  • Life-cycle hypothesis (Modigliani): people smooth consumption over a lifetime, borrowing when young, saving in working years and dissaving in retirement, so consumption depends on lifetime resources and wealth, not current income alone.
  • Permanent income hypothesis (Friedman): consumption tracks permanent (expected long-run) income; measured income = permanent + transitory. The MPC out of permanent income is high but out of transitory income is near zero. Hall's random walk model adds rational expectations to the PIH: consumption then follows a random walk, so only unanticipated news changes it and future changes are unpredictable.
🎯 Why the later theories were needed
Kuznets found that over long spans APC is roughly constant, while cross-section budgets show a falling APC. The relative, life-cycle and permanent-income hypotheses each reconcile the two by making consumption depend on something steadier than this year's income.

4. Investment, the accelerator and the multiplier

Keynes made investment depend on the marginal efficiency of capital (in its investment-schedule form, the marginal efficiency of investment, MEI) against the interest rate: a project is undertaken while its expected yield exceeds the cost of funds. Jorgenson's neoclassical theory derives a desired capital stock where the marginal product of capital equals the user cost of capital (the price of capital times the sum of the interest rate r and the depreciation rate δ), and net investment closes the gap toward that desired stock. Tobin's q restates the rule through asset markets: q = market value of installed capital ÷ its replacement cost, and firms invest when q > 1 and disinvest when q < 1. The accelerator links investment to the change in output: net investment I = v·ΔY, where v is the capital–output ratio.

The autonomous multiplier shows how an injection raises income by more than itself, because each round of spending becomes someone's income. In a closed economy with lump-sum taxes, the multiplier is k = 1/(1 − MPC) = 1/MPS. With a proportional income tax rate t it becomes 1/(1 − c(1 − t)), which is smaller because tax leaks each round. With lump-sum taxes the balanced-budget multiplier equals one: a rise in spending matched by equal taxes still raises income by the amount of the spending. The super-multiplier combines the multiplier with the accelerator, so a demand change can set off amplified, self-sustaining swings.

5. Demand and supply of money, liquidity trap and the money multiplier

Keynes's liquidity preference gives three motives to hold money: the transactions and precautionary demands rise with income, and the speculative demand falls as the interest rate rises (a high rate means low bond prices expected to recover, so people hold bonds, not money). The interest rate is set where this money demand meets the money supply. In a liquidity trap the interest rate is so low that money demand becomes perfectly elastic: extra money is simply held, the LM curve is flat, and monetary policy loses traction while fiscal policy becomes powerful.

The money supply is built on high-powered money (reserve money) H = currency with the public + bank reserves. Commercial banks create deposits by lending a fraction of reserves. The money multiplier links the stock of money M to H: M = m·H, with m = (1 + c)/(c + r), where c is the currency–deposit ratio and r the reserve–deposit ratio. A smaller reserve ratio or a smaller currency ratio raises the multiplier. Components of money run from narrow to broad: M1 (currency plus demand deposits) is the most liquid, and broader aggregates add time deposits.

6. Banking, monetary policy, inflation and expectations

A central bank pursues price stability, growth and financial stability. Its indirect (quantitative) instruments act on the whole system — open market operations, the cash reserve ratio, the statutory liquidity ratio and the policy repo rate — while direct (qualitative) instruments such as selective credit controls and moral suasion target particular sectors. (This follows the general-versus-selective split; some texts instead call CRR and SLR 'direct' controls because they bind banks' balance sheets directly.) Prudential regulation (capital adequacy, limits on bad loans) keeps banks sound. When the policy rate is near zero, quantitative easing (unconventional policy) has the central bank buy longer-term assets to ease conditions. Commercial banks create credit; non-banking financial institutions intermediate without full banking powers; and the capital market is overseen by its own regulator.

Inflation is a sustained rise in the general price level, whether demand-pull (excess demand) or cost-push (rising costs). The short-run Phillips curve showed an inverse relation between inflation and unemployment. Friedman and Phelps added expectations: the expectations-augmented Phillips curve is π = π^e − β(u − u_n). When expected inflation catches up with actual inflation (π = π^e), unemployment returns to its natural rate u_n, so the long-run Phillips curve is vertical and there is no permanent trade-off (the natural-rate hypothesis).

How expectations form decides policy's power. Under adaptive expectations, people revise forecasts from past errors, so they can be fooled for a while. Under rational expectations (Muth, Lucas), people use all available information, so forecasts are unbiased; a fully anticipated policy change is then neutral, and only surprises move real output (the policy-ineffectiveness result). The Lucas critique warns that estimated model parameters shift when policy changes. Real business cycle theory goes further: fluctuations come from real (technology) shocks in markets that clear, so money is neutral even in the short run.

7. IS–LM, Mundell–Fleming and the impossible trinity

The IS–LM model fixes income and the interest rate together. The IS curve is goods-market equilibrium (Y = C + I + G); it slopes down because a lower interest rate raises investment and income. The LM curve is money-market equilibrium; it slopes up because higher income raises money demand and so the interest rate. Fiscal policy shifts IS, monetary policy shifts LM. A fiscal expansion raises both income and the interest rate, so some private investment is crowded out. The slopes decide the mix: with a flat LM (liquidity trap) monetary policy is powerless and fiscal policy fully effective; with a vertical LM (classical case) monetary policy is fully effective and fiscal policy is entirely crowded out.

The Mundell–Fleming model extends IS–LM to an open economy with capital mobility. Its central result turns on the exchange-rate regime. For a small open economy under a fixed exchange rate with perfect capital mobility, monetary policy is powerless (the central bank must defend the peg) while fiscal policy is effective. Under a floating exchange rate, the reverse holds: monetary policy is effective while fiscal policy is undone by exchange-rate movements. This is summarised by the impossible trinity (trilemma): a country can have at most two of a fixed exchange rate, free capital mobility and an independent monetary policy, never all three.

Key takeaways

  • National income is measured by the product, income and expenditure methods, which must agree. Closed-economy Y = C + I + G; open-economy adds net exports. GDP is output within borders, GNP adds net factor income from abroad, NNP subtracts depreciation, and the GDP deflator is nominal over real GDP times 100.
  • The classical model rests on Say's law, flexible prices and full employment with neutral money; Keynes made effective demand the driver, allowing underemployment equilibrium and active demand management. The absolute, relative, life-cycle and permanent-income hypotheses, with Hall's random walk, explain why APC falls across households yet is stable over long spans.
  • Investment follows the marginal efficiency against interest, Jorgenson's user cost, Tobin's q (invest when q > 1) and the accelerator I = v·ΔY. The closed-economy multiplier is 1/(1 − MPC), smaller with an income tax, and the balanced-budget multiplier equals one.
  • Money demand has transactions, precautionary and speculative motives; the last falls with the interest rate and becomes perfectly elastic in the liquidity trap, where monetary policy is powerless. The money multiplier is m = (1 + c)/(c + r) on high-powered money, with M1 the narrowest aggregate.
  • Central banks use indirect instruments (OMO, CRR, SLR, repo) and direct ones (selective credit control, moral suasion), with prudential regulation and quantitative easing. The expectations-augmented Phillips curve is vertical in the long run at the natural rate; rational expectations make anticipated policy neutral, and RBC traces cycles to real shocks.
  • In IS–LM, fiscal policy shifts IS and monetary policy shifts LM, with crowding out when the LM slopes up. Mundell–Fleming: under fixed exchange rates fiscal policy works and monetary policy does not; under floating rates the reverse. The impossible trinity allows only two of a fixed rate, free capital mobility and monetary independence.

Practice questions (18)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. In the expenditure method for a closed economy, which identity gives gross domestic product (GDP)?

    1. GDP equals consumption plus investment plus government purchases of goods and services
    2. GDP equals consumption plus saving plus taxes, summed over every household in the economy
    3. GDP equals wages plus rent plus interest plus profit, after subtracting all indirect taxes
    4. GDP equals net national product plus depreciation plus net factor income earned from abroad
    Show answer

    Answer: A — GDP equals consumption plus investment plus government purchases of goods and services

    The closed-economy expenditure identity is Y = C + I + G, with no net-export term. Consumption plus saving plus taxes is the disposition of income (the income side, not expenditure), summing factor payments is the income method, and building GDP from net national product plus depreciation mixes the GNP and NNP concepts rather than giving GDP by expenditure.

  2. Which statement best captures the difference between the classical and Keynesian views of how output is determined?

    1. In the classical view output is demand-determined and can rest below full employment, while Keynes held that supply always creates its own demand
    2. In the classical view flexible wages and prices secure full employment, while for Keynes effective demand can fix output below full employment
    3. Both views deny any role to aggregate demand and hold that only the money supply determines real output in the short run
    4. In the classical view the interest rate is set purely by liquidity preference, while Keynes derived it from saving and investment alone
    Show answer

    Answer: B — In the classical view flexible wages and prices secure full employment, while for Keynes effective demand can fix output below full employment

    The classical model relies on Say's law and flexible prices to hold full employment; Keynes made effective demand the driver, allowing an underemployment equilibrium. The option reversing the two sides misassigns Say's law to Keynes, and the interest-rate option swaps the theories: Keynes used liquidity preference and the classics used saving and investment.

  3. Consider these statements on national-income aggregates for an open economy. Which are correct? P: GDP measures output produced within a country's borders, while GNP adds net factor income from abroad. Q: Net national product equals gross national product minus depreciation. R: Nominal GDP divided by real GDP, multiplied by 100, is the GDP deflator. S: In an open economy, GDP equals C + I + G and excludes net exports by definition.

    1. P
    2. Q
    3. R
    4. S
    Show answer

    Answer: A — P; B — Q; C — R

    GDP is within-border output and GNP adds net factor income from abroad, NNP is GNP minus depreciation, and the GDP deflator is indeed nominal over real GDP times 100, so P, Q and R hold. S is false: in an open economy GDP = C + I + G + (X − M), so net exports are part of GDP, not excluded.

  4. Under Keynes's absolute income hypothesis the consumption function is C = a + bY with a > 0 and 0 < b < 1. As current income Y rises, what happens to the average propensity to consume (APC)?

    1. APC rises steadily and eventually exceeds one, because consumption grows faster than income does
    2. APC stays exactly constant and is always equal to the marginal propensity to consume b
    3. APC falls as income rises and approaches the marginal propensity to consume b from above
    4. APC first falls and then rises again, tracing out a clear U-shape plotted against income
    Show answer

    Answer: C — APC falls as income rises and approaches the marginal propensity to consume b from above

    APC = C/Y = a/Y + b, so as Y rises the a/Y term shrinks and APC falls toward b, always staying above the MPC b. It never exceeds one for large income, is not constant (that would need a = 0), and does not trace a U-shape.

  5. A worker receives a one-time, clearly temporary bonus this year. Which prediction follows from Friedman's permanent income hypothesis?

    1. The worker spends almost the entire bonus within this year, because current measured income has gone up
    2. The worker treats the bonus as permanent income and raises consumption permanently by its full amount
    3. The bonus leaves current consumption completely unchanged, because under this hypothesis consumption is tied only to this year's measured disposable income
    4. The worker adds only a small part of the bonus to current consumption, because transitory income has a very low marginal propensity to consume
    Show answer

    Answer: D — The worker adds only a small part of the bonus to current consumption, because transitory income has a very low marginal propensity to consume

    The PIH says the MPC out of transitory income is near zero, so a clearly temporary bonus is mostly saved and spread over future years, not consumed at once. Spending almost all of it is the absolute-income prediction, treating it as permanent misreads a temporary gain, and consumption is not tied to current income alone under the PIH.

  6. A household's consumption function is C = 200 + 0.6Y, where C and Y are in rupees. Find the break-even level of income — the income at which consumption exactly equals income, so that saving is zero. Give the number only.

    Numerical answer — type the value.

    Show answer

    Answer: 500

    Break-even income requires C = Y: 200 + 0.6Y = Y, so 200 = 0.4Y and Y = 500. Below Y = 500 consumption exceeds income (dissaving), and above it saving is positive. Dividing 200 by 0.6 instead of by (1 − 0.6) is the usual slip.

  7. According to the simple acceleration principle, net investment depends on:

    1. The change in output or sales between periods, scaled by the capital–output ratio
    2. The absolute level of output in the current period, scaled directly by the prevailing rate of interest
    3. Only the size of the capital stock that the firm has inherited from the previous period
    4. The difference between the market value of firms and the replacement cost of their capital goods
    Show answer

    Answer: A — The change in output or sales between periods, scaled by the capital–output ratio

    The accelerator makes net investment proportional to the change in output, I = v·ΔY, where v is the capital–output ratio: firms add capital when demand grows. The level of output or the inherited capital stock alone does not drive net investment, and the market-value-versus-replacement-cost gap is Tobin's q, a different theory.

  8. In Tobin's q theory of investment, a firm has a strong incentive to add to its capital stock when:

    1. q is below one, because the stock market is then undervaluing the firm's already installed capital
    2. q is above one, because the market value of installed capital exceeds its replacement cost
    3. q equals exactly one, because the firm is then sitting at its long-run optimum and wishes to expand further
    4. the marginal product of capital falls below the user cost of capital in Jorgenson's sense
    Show answer

    Answer: B — q is above one, because the market value of installed capital exceeds its replacement cost

    Tobin's q is the market value of installed capital divided by its replacement cost; when q > 1 the market values new capital at more than it costs to install, so the firm invests. At q = 1 there is no incentive to change the stock, q < 1 signals disinvestment, and a marginal product below user cost is Jorgenson's condition for holding too much capital.

  9. In a closed economy with lump-sum (fixed) taxes, the marginal propensity to consume out of income is 0.75. Government purchases rise by 40 rupees. Using the simple multiplier 1/(1 − MPC), find the resulting change in equilibrium income, in rupees. Give the number only.

    Numerical answer — type the value.

    Show answer

    Answer: 160

    With lump-sum taxes the government-spending multiplier is 1/(1 − MPC) = 1/(1 − 0.75) = 1/0.25 = 4. The change in income is 4 × 40 = 160 rupees. Using 1/MPC = 1.33 or forgetting to multiply by the spending change are the usual slips.

  10. In a liquidity trap the demand for money becomes perfectly elastic at a very low interest rate. What follows for stabilisation policy?

    1. A monetary expansion sharply lowers the interest rate and strongly raises investment and output
    2. The LM curve becomes vertical in this situation, so that any fiscal expansion is completely crowded out by a sharply higher interest rate
    3. Additional money is simply held rather than lent, so monetary policy loses traction and fiscal policy becomes relatively powerful
    4. The interest rate rises without any limit as the central bank keeps buying bonds from the public
    Show answer

    Answer: C — Additional money is simply held rather than lent, so monetary policy loses traction and fiscal policy becomes relatively powerful

    In the trap the LM curve is flat, so extra money is absorbed into idle balances with no fall in the interest rate: monetary policy is ineffective while fiscal policy, facing no crowding out, is fully effective. A vertical LM is the opposite (classical) case, and bond buying lowers, not raises, the interest rate.

  11. Consider these statements about the Keynesian demand for money (liquidity preference). Which are correct? P: The transactions and precautionary demands for money depend mainly on the level of income. Q: The speculative demand for money varies inversely with the rate of interest. R: At a very low interest rate people expect bond prices to fall, so they prefer to hold money rather than bonds. S: The speculative demand is independent of the interest rate and depends only on income.

    1. P
    2. Q
    3. R
    4. S
    Show answer

    Answer: A — P; B — Q; C — R

    Transactions and precautionary balances scale with income, the speculative demand falls as the interest rate rises, and at a very low rate bond prices are high and expected to fall, so people hold money (the basis of the liquidity trap) — so P, Q and R hold. S contradicts Q: the speculative demand is precisely the interest-sensitive part of money demand.

  12. Let the currency–deposit ratio be c = 0.2 and the reserve–deposit ratio be r = 0.1. Using the money multiplier m = (1 + c)/(c + r), find the value of the money multiplier. Give the number only.

    Numerical answer — type the value.

    Show answer

    Answer: 4

    Substitute into m = (1 + c)/(c + r) = (1 + 0.2)/(0.2 + 0.1) = 1.2/0.3 = 4. The money multiplier is 4, so each rupee of high-powered money supports four rupees of money supply. Using 1/r = 10 ignores the currency drain, which is the usual slip.

  13. The expectations-augmented Phillips curve is written π = π^e − β(u − u_n) with β > 0. What does it imply for the long run, once expected inflation has caught up with actual inflation?

    1. There is a permanent and exploitable trade-off, so that policymakers can go on buying lower unemployment with permanently higher inflation forever
    2. Unemployment stays permanently below its natural rate even though expected inflation equals actual inflation
    3. Inflation and unemployment come to move together in the same direction over the long run
    4. Unemployment returns to its natural rate and the long-run Phillips curve is vertical, so there is no permanent trade-off
    Show answer

    Answer: D — Unemployment returns to its natural rate and the long-run Phillips curve is vertical, so there is no permanent trade-off

    When π = π^e the term β(u − u_n) must be zero, so u = u_n regardless of the inflation rate: the long-run Phillips curve is vertical at the natural rate and there is no permanent inflation–unemployment trade-off. A lasting trade-off, or unemployment held below the natural rate, would require people to be permanently fooled, which the expectations term rules out.

  14. Monetary-policy instruments are often split into general (quantitative) and selective (qualitative) instruments. Which of the following are general, quantitative instruments used by a central bank?

    1. Open market operations, through which the central bank buys and sells government securities
    2. The cash reserve ratio that commercial banks must keep with the central bank
    3. Selective credit controls and moral suasion aimed at lending to particular sectors
    4. The policy repo rate at which banks borrow short-term funds against collateral
    Show answer

    Answer: A — Open market operations, through which the central bank buys and sells government securities; B — The cash reserve ratio that commercial banks must keep with the central bank; D — The policy repo rate at which banks borrow short-term funds against collateral

    Open market operations, the cash reserve ratio and the policy repo rate act on the whole banking system and are general, quantitative instruments (the indirect instruments of this chapter's classification). Selective credit controls and moral suasion are qualitative tools aimed at specific sectors, so they are not general quantitative instruments.

  15. Under the rational expectations hypothesis combined with the natural-rate model and flexible wages and prices, a fully anticipated increase in the money supply will:

    1. Raise prices and expected inflation but leave real output unchanged, since agents had already adjusted
    2. Push unemployment below its natural rate for a long period, because money is strongly non-neutral here
    3. Have real effects only when the central bank announces it clearly and well in advance of acting
    4. Be impossible to analyse at all, because rational agents by definition never make any forecasting errors
    Show answer

    Answer: A — Raise prices and expected inflation but leave real output unchanged, since agents had already adjusted

    With rational expectations and a natural-rate model, an anticipated monetary expansion is already built into wages and prices, so it is neutral: prices and expected inflation rise but real output stays at the natural level (the policy-ineffectiveness proposition). Only surprises have real effects, so an announced (hence anticipated) change does not, and rational agents are right on average, not infallible.

  16. In the standard closed-economy IS–LM model with an upward-sloping LM curve (not a liquidity trap), a bond-financed increase in government spending will:

    1. Lower both income and the interest rate together, as the IS curve shifts to the left
    2. Raise income and raise the interest rate, with some private investment crowded out
    3. Raise income while leaving the interest rate completely unchanged, so that no crowding out occurs
    4. Leave income entirely unchanged, because monetary policy automatically offsets the whole fiscal stimulus
    Show answer

    Answer: B — Raise income and raise the interest rate, with some private investment crowded out

    Higher government spending shifts the IS curve rightward, raising both income and the interest rate; the higher rate reduces private investment, which is partial crowding out. With an upward-sloping LM the rate must rise, so income does not expand by the full multiplier, and the IS shift is rightward, not leftward.

  17. The 'impossible trinity' (trilemma) of open-economy macroeconomics says that a country cannot simultaneously maintain all three members of which combination?

    1. A balanced government budget, a low rate of inflation and full employment of the labour force
    2. Completely free international trade, a lasting current-account surplus and a simultaneous capital-account surplus in the same year
    3. A fixed exchange rate, free international capital mobility and an independent domestic monetary policy
    4. A floating exchange rate, a high rate of economic growth and a low level of public debt
    Show answer

    Answer: C — A fixed exchange rate, free international capital mobility and an independent domestic monetary policy

    The trilemma concerns a fixed exchange rate, free capital mobility and an independent monetary policy: a country can have at most two of these three at once. The other combinations mix unrelated macro goals and are not what the impossible trinity refers to.

  18. A closed economy has the goods market Y = C + I + G with C = 40 + 0.75Y, I = 100 − 10r and G = 50, and the money market M/P = 0.25Y − 20r with M/P = 100 (r is the interest rate in percent). Solving the IS and LM relations together, find the equilibrium interest rate r. Give the number only.

    Numerical answer — type the value.

    Show answer

    Answer: 3

    IS: Y = 40 + 0.75Y + 100 − 10r + 50, so 0.25Y = 190 − 10r and Y = 760 − 40r. LM: 100 = 0.25Y − 20r, so 0.25Y = 100 + 20r and Y = 400 + 80r. Setting them equal: 760 − 40r = 400 + 80r gives 360 = 120r, so r = 3 (and Y = 640).