The ISLM Model and Aggregate Demand: Understanding the LM Curve

Economic Fluctuations

Unit Overview

• Unit 17: Business Cycles
• Unit 18: The ISLM Model and Aggregate Demand
• Unit 19: Aggregate Demand and Aggregate Supply
• Unit 20: Aggregate Demand Policies
• Unit 21: Inflation and Unemployment

The ISLM Model and Aggregate Demand

Preview of Unit 18

1. The basic model for the analysis of the business cycle is based on an aggregate demand and aggregate supply framework, the equilibrium of which determines gdp and the general price level: the business cycle can then be looked at as resulting from changes in AD and/or AS.
2. We now look at the first building block, aggregate demand, the role of which was at the centre of JM Keynes's work.
3. Aggregate demand is arrived at in three stages: we first build a simpler scheme ("Keynesian cross"), then introduce the money market to arrive at the ISLM model, from which the AD function can be derived.

The Keynesian Cross

JM Keynes (1883-1946) is perhaps the greatest economist of the XX century, and the founding father of macroeconomics as a specific discipline. Keynes's primary message was that recessions and depressions can occur because of insufficient aggregate demand. His emphasis is on the short run behaviour of the economy, and in this sense he was a critic of classical economics because it could explain only the long-run effects of policies. . "In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell that when the storm is long past, the ocean will be flat."

Keynesian Analysis: Planned vs. Actual Behavior

Keynesian analysis makes a crucial distinction between planned and actual behaviour. (e.g., a manufacturer may plan to maintain a stock of 50,000 of its widgets but if sales slow it may actually find it has 150,000 widgets in stock).

• Planned spending, saving or investment are the intended actions of households and firms.
• Actual spending, saving or investment is the realized outcome resulting from actions of households and firms.
• Full employment occurs when those people who want to work at the going rate are able to find a job.
• If planned and actual outcomes can differ, then it's possible for the equilibrium level of national income to be below the full employment level.

National Income Identity

Consider our national income identity: Y = C + I + G + NX This is an identity in the ex post sense that actual income (Y) has always to be equal to actual expenditure (C + I + G + NX). However, one can think of planned expenditure as depending on income: given some income level Y', agents plan to spend C + G + NX = E(Y'). In equilibrium, actual spending has to be equal to income (i.e. actual expenditure generates incomes which in turn generate that expenditure). There will be some equilibrium level of gdp, Y*, such that: E(Y*) = Y*

Key Points of the Keynesian Cross

There are two key points: (a) All this presumes that prices play no role: think of expenditure etc for given prices: assume for the sake of argument that firms are willing to supply whatever is demanded of them without any change in prices. (b) Once we introduce the notion of planned expenditure, E(Y*) = Y* becomes and equilibrium relationship which determines equilibrium gdp Y*, and there is no reason to suppose that Y* is consistent with full employment.

Equilibrium Level of Output/Income

In order to identify the equilibrium level of output/income, suppose that E(Y) is such that It is a linear function of Y; It includes a level of expenditure which does not depend on income (so called autonomous component); It has a slope less than one: higher income means higher planned expenditure, but less than proportionally so. Then E(Y) = A+cY with c < 1

Deflationary Gap

The economy is in equilibrium where the expenditure line cuts the 45° line, i.e. E(Y1) = Y1 Here, that equilibrium is below the full employment level of output Yf: there is a deflationary gap. Total expenditure 45° C+ 1+ G + (X-M)1 Deflationary gap C+ 1+ G + (X-M) E1 Eo Y1 Yf National income

Inflationary Gap

The economy is in equilibrium where the expenditure line cuts the 45° line, i.e. E(Y1) = Y1 Here, that equilibrium is above the full employment level of output Yf: there is an inflationary gap. Total expenditure 45° C + 1 + G + (X-M) Inflationary gap C+1+ G + (X-M)2 Eo E1 Yf Y1 National income

Components of Expenditure

We now go beyond this, and ask why E (Y) should take such a shape. A. Suppose consumers spend a (survival) fixed amount on consumption, plus a variable component cY which grows linearly with income. That is, we define the Keynesian consumption function C(Y) = C+ cY where C is the autonomous component of consumption c is the marginal propensity to consume (mpc): according to Keynes's "psychological law" an increase in income drives an increase in consumption less than proportional, i.e., c < 1.

Investment, Government, and Net Exports

B. Suppose also that I, G, and NX are independent of income (firms do not plan their investment on the basis of the consumers' income, public expenditure is decided upon by the government, net exports may be thought of as depending on foreign choices - we go back to this later). Then E(Y) = C(Y) +I +G+NX = (C+I+G + NX) + cY = A+ cY so that the slope of the expenditure function is equal to mpc.

Implications of the Keynesian Cross

All this has two major implications: (a) Any change in the autonomous component of expenditure will result in a parallel shift of the expenditure function. E.g., the government might bring the economy to full employment by increasing G (which is part of the autonomous component A) Total 45° expenditure C+ 1+ G + (X- M)1 Increase in A C+ 1+ G + (X- M) E1 E0 Y1 Yf National income

Equilibrium Output and the Multiplier

(b) The size of any such change affects equilibrium output in a well-defined way: Y = E(Y) = A + CY -> (1 - c)Y = A >> Y =- A 1 - c AY = 1 - c ΔΑ The final effect on equilibrium income of a change AA in autonomous expenditure (e.g., public spending), is AA . - 1-c' , where 1 1 - c > 1 is called the multiplier, as it magnifies the impact on income of an initial increase in A.

Government Expenditure and Income Increase

1. Suppose government expenditure G goes up by AG = AA: this higher expenditure (commodities and services) becomes a change in income 41Y = AG. 2. This higher income will trigger higher consumption expenditure c41Y, which turns into a further change in income for people involved in the production of consumption goods, 42Y = c41Y. 3. This will in turn support a further increase in consumption, c42Y = c(cA1Y) = c2 A1Y = c2AG .... and so on. 4. At the end of the day, the overall increase in income is AG 41Y + 42Y + ·· · = 41Y (1 + c + c2 + ... ) = AG(1 + c + c2 + ... ) = 1 - c 1 € of government purchases generates more than 1€ of aggregate demand

Lessons from the Multiplier

This teaches us two main lessons: 1. The multiplier What held for G in our examples holds for any autonomous component of aggregate demand: thus, e.g., if investment or net exports grow by AA, the final impact on equilibrium income will be ΔΑ AA. Notice that c is the (1-c) part of additional income spent on consumption (it is the marginal p.c): hence 1 - c is the part which is saved, i.e. not spent: the higher the marginal propensity to save, the lower the multiplier effect.

Withdrawals and Injections

2. Withdrawals and injections ... and indeed, the logic behind the multiplier is that out of an initial change in expenditure, a portion equal to the mpc is re-injected as further demand in the economy, giving rise to a cycle expenditure->income->expenditure ... At each stage a portion 1 - c of additional income leaks out of the system in the form of savings. Are there any further leakages? Generally speaking, the answer is yes, which is revealed once one takes explicitly into account of taxation and imports.

Taxation and the Multiplier

2a. Taxation Suppose government taxation is some constant share of income t < 1, such that tax revenue is T = tY. Consumers will then consume out of their disposable income, Y - T = Y -tY = (1 -t)Y: C= C+c(Y-T) = C+c(1-t)Y and the multiplier will be 1/1-c(1-t) = 1/1-c+c : the higher t, the lower the multiplying effect, as a fraction ct of expenditure is taken out of the circular flow of income at each round.

Balanced Budget Multiplier

However, if the autonomous component is public expenditure financed with taxation ("balanced budget"), so that AG = AT Y = A + c(Y -T) -> (1 - c)Y = A - CT -> Y = A - CT - 1 - c In this case ΔΑ = AG = ΔΤ AY = A(A - cT) 1 - c ΔΑ - CAT 1 - c AG(1 - c) 1 - c so that AY/c = 1 ("balanced budget multiplier"): there is anyway an expansionary effect (though not multiplied), as the government propensity to spend is one - i.e., all taxes are put back in the system as public expenditure, while just a fraction c would have been spent by consumers.

Imports and the Multiplier

2b. Imports Suppose imports depend on income, in the sense that a fraction m of any additional income is spent on imported commodities. Then NX = X-mY -> C+I+G+ NX = (C+cY) + I + G + (X -mY) = A' + (c - m)Y, the re-defined autonomous component being A' = C + I + G + X ΔΑ' E(Y) = A' + (c -m)Y -> Y = 1 - (c -m) A' AY = 1-c+m The multiplier is now lower.

The ISLM Model: The IS Curve

Autonomous Components and Interest Rate

The autonomous components of expenditure in the Keynesian cross (A = C + I + G + NX) do not depend on income, but are likely to be affected by other variables not included in our picture. We now focus on one of these, and precisely the real rate of interest r Suppose a firm considers buying a new piece of machinery at the cost of €100,000: when installed it will produce commodities for 5 years, resulting in a cash flow of €5,000 per year (at the end of the 5th year it will be dumped away with no value): is this worth doing? The answer depends on the available alternatives: if the yearly interest rate afforded by financial markets is higher than 5% the answer is no (better buy bonds!), but should it be 3% the answer is yes.

Interest Rates and Investment

More generally, lower interest rates make for higher investment levels: I = I (r), a decreasing function. Two observations: (a) The relevant interest rate is in principle the real interest rate (though recall that at this stage we are simply assuming no change in prices, so there is no actual difference with nominal interest rate). (b) To the extent that interest rates affect savings, higher interest rates may also make for lower consumption. All this means that planned expenditure can be written as E(Y,r) = C(Y) + I(r) + G + NX Increasing in income and decreasing in the interest rate.