The Keynesian Model

The Keynesian Model the possibility of macroeconomic equilibrium with unemployment

Great Depression • From 1929-1941, the United States (and the world) was in a huge economic depression, in the U.S. the official unemployment rate was 25%. This doesn’t count the millions living in the “Hoovervilles” the homeless camps named for the President. Not until the U.S. entered WWII did the economy recover.

Questioning Neoclassical Theory • Economists and others began to ask the question: why isn’t the economy recovering, where is the self-adjusting mechanism. • Neoclassical theory says the economy will recover in the long run, but how long is that? One famous economist, Joseph Schumpeter said: “The short run is long enough to bring about the ruin if a nation.

John Maynard Keynes • Another famous economist from Cambridge University in England, he remarked: “In the long run we’re all dead.” • Keynes, writing in the midst of the Great Depression, criticized neoclassical theory, and put forward an alternative way of looking at the macroeconomy.

Keynes on consumption and income • Keynes began with a very simple proposition: when income goes up, consumption increases, but not by as much as income. So: 0 < ΔC/ΔYd < 1

Keynes on income and savings • If that is true, then it must also be true (since Yd = C + S) that when income goes up, savings increases, but not by as much: 0 < ΔS/ΔYd < 1

the mpc and the mps • ΔC/ΔYd is called the mpc (marginal propensity to consume) • ΔS/ΔYd is called the mps (marginal propensity to save)

ΔC/ΔYd + ΔS/ΔYd = 1 and mps = 1 – b

ΔC/ΔYd + ΔS/ΔYd = 1 and mps = 1 – b • Proof:

ΔC/ΔYd + ΔS/ΔYd = 1 and mps = 1 – b • Proof: • If Yd = C + S, then

ΔC/ΔYd + ΔS/ΔYd = 1 and mps = 1 – b • Proof: • If Yd = C + S, then • Any change in Yd must resolve itself some part of a change in C and some part a change in S.

ΔC/ΔYd + ΔS/ΔYd = 1 and mps = 1 – b • Proof: • If Yd = C + S, then • Any change in Yd must resolve itself some part of a change in C and some part a change in S. • So, ΔYd = ΔC + ΔS

ΔC/ΔYd + ΔS/ΔYd = 1 and mps = 1 – b • Proof: • If Yd = C + S, then • Any change in Yd must resolve itself some part of a change in C and some part a change in S. • So, ΔYd = ΔC + ΔS • Divide both sides by ΔYd, and we get:

ΔC/ΔYd + ΔS/ΔYd = 1 and mps = 1 – b • Proof: • If Yd = C + S, then • Any change in Yd must resolve itself some part of a change in C and some part a change in S. • So, ΔYd = ΔC + ΔS • Divide both sides by ΔYd, and we get: • 1 = mpc + mps (from 1 = mpc + mps)

the consumption function

the consumption function • mpc = additional consumption from an additional dollar of disposable income.

the consumption function • mpc = additional consumption from an additional dollar of disposable income. • mps = additional saving from an additional dollar of disposable income.

the consumption function • mpc = additional consumption from an additional dollar of disposable income. • mps = additional saving from an additional dollar of disposable income. • So we can think of present consumption as a function of disposable income:

the consumption function • mpc = additional consumption from an additional dollar of disposable income. • mps = additional saving from an additional dollar of disposable income. • So we can think of present consumption as a function of disposable income: C = bYd

autonomous consumption • But is present income the only determinant of present consumption?

autonomous consumption • But is present income the only determinant of present consumption? No. What else?

autonomous consumption • But is present income the only determinant of present consumption? No. What else: • accumulated past savings

autonomous consumption • But is present income the only determinant of present consumption? No. What else: • accumulated past savings • access to credit

autonomous consumption • But is present income the only determinant of present consumption? No. What else: • accumulated past savings • access to credit • expectations of future income

autonomous consumption • But is present income the only determinant of present consumption? No. What else: • accumulated past savings • access to credit • expectations of future income • social standards • etc.

Keynesian consumption function • all these and other determinants of present consumption other than present disposable income we will call a, or autonomous consumption; so: C = a + bYd

Keynesian consumption function • all these and other determinants of present consumption other than present disposable income we will call a, or autonomous consumption; so: C = a + bYd This is our consumption function.

Keynesian consumption function • all these and other determinants of present consumption other than present disposable income we will call a, or autonomous consumption; so: C = a + bYd (takes form y = mx + b; linear function; m is slope and b is y-intercept) This is our consumption function. We can graph this in expenditure/output (=income) space.

45 Degree Line exp. 45° 15 10 5 45° Y 0 5 10 15

Keynesian Model 45° Expenditure C = a + bY C < Y a + I C = Y a C > Y I 0 Y Y1 Yf - a

C = a + bYd

C = a + bYd What is the slope of the consumption function?

C = a + bYd What is the slope of the consumption function? b (b = mpc = marginal propensity to consume = ΔC/ΔYd = rise/run = slope)

C = a + bYd What is the slope of the consumption function? b (b = mpc = marginal propensity to consume = ΔC/ΔYd = rise/run = slope) What is the y intercept of the C function?

C = a + bYd What is the slope of the consumption function? b (b = mpc = marginal propensity to consume = ΔC/ΔYd = rise/run = slope) What is the y intercept of the C function? a (a = autonomous consumption = y intercept)

savings function S = -a + (1 - b) Yd

savings function S = -a + (1 - b) Yd What is the y intercept of the savings function?

savings function S = -a + (1 - b) Yd What is the y intercept of the savings function? –a (= autonomous savings)

savings function S = -a + (1 - b) Yd What is the y intercept of the savings function? –a (= autonomous savings) What is the slope of the savings function?

savings function S = -a + (1 - b) Yd What is the y intercept of the savings function? –a (= autonomous savings) What is the slope of the savings function? (1 – b) ( = mps = marginal propensity to save = ΔS/ΔYd = rise/run = slope)

Keynesian Model 45° Expenditure C = a + bY C < Y a + I S = - a + (1 – b) Y C = Y → S = 0 a C > Y I S > 0 0 Y S< 0 Y1 Yf - a “Dissaving”

savings function • When the savings function is below the x-axis savings is negative, when the savings function is above the x-axis savings is positive and when the savings function intersects the x-axis savings = 0.

Relation of consumption and savings functions At all those levels of income where the C func is above the 45 d line, the savings func is below the x-axis, meaning C > Yd so S is negative. And at all those levels of income where the C func is below the 45 d line the savings func is above the x-axis, meaning C < Yd, so savings is positive. And at exactly that one and only one level of income where the cons func intersects the 45 d line, the savings func intersects the x-axis, so C = Yd so savings is zero.

autonomous investment • In Keynes, investment is determined by a number of factors, most importantly investor expectations of future conditions. • The important point here, though, is that investment, unlike consumption and savings, is NOT a function of income. It is autonomous in the same sense as autonomous consumption. • Neither is it a simple function of interest rates, as in the neoclassical model. • The investment function will be horizontal.

Keynesian Model 45° Expenditure I = I I 0 Y Y1 Y* Yf

aggregate spending (C+I) • We add the constant amount of autonomous investment to consumption to derive the aggregate spending function (no government, no foreign trade). • The y-intercept of the aggregate spending function is (a+I), and the slope is b. This is because the only thing changing when income changes is consumption.

Keynesian Model 45° Expenditure AS = C + I C = a + bY a + I S = - a + (1 – b) Y a I I 0 Y Y1 Y* Yf - a

The Keynesian Model