E XERCISES FOR C HAPTER 5
6.5 Equilibrium output and the AD curve
Figure 6.9: Equilibrium GDP and aggregate demand
Y=AE
A0
A0+ (c − m)Y A1
A1+ (c − m)Y
a) Equilibrium Y=AE AE
Real GDP
Ye Ye′
∆Y
P0 AS0
AD0 AD1
b) Equilibrium AD=AS P
Real GDP
Ye Ye′
∆Y
∆A
45◦
Equilibrium in a) determined the position of the AD curve in b). A change in autonomousexpenditure in a) changes equilibrium Y and shifts AD by the change in autonomous expenditure times the multiplier.
In this model, investment and exports are the main sources of fluctuations in autonomous ex-penditures. The marginal propensities to consume and import describe the changes in aggregate expenditure caused by changes in income. These induced expenditures are the source of the mul-tiplier. When business changes its investment plans in response to predictions and expectations about future markets and profits, or exports change in response to international trade conditions, the multiplier translates these changes in autonomous expenditure into shifts in the AD curve.
6.5. Equilibrium output and the AD curve 143
Shifts in the AD curve cause changes in equilibrium output and employment.
Figure6.9shows how this works. Equilibrium real GDP in the upper panel determines the position of the AD curve in the lower panel.
Initially, equilibrium real GDP at the price level P0 is determined by the equilibrium condition Ye= A0+ (c − m)Y in the upper panel and by the equilibrium condition AD0= AS0 in the lower panel.
Changes in autonomous expenditure shift the AD curve. If autonomous expenditure increased from A0to A1as shown in panel (a), equilibrium output would increase from Y0to Ye1. The change in equilibrium output would be (∆A× multiplier). The AD curve would shift to the right to AD1
as a result of the increase in autonomous expenditure. The size of the horizontal shift would be (∆A× multiplier).
This model provides an important first insight into the sources of business cycles in the economy.
However, it is a pure private household/private business sector economy. Autonomous consump-tion, investment, exports and imports, and the multiplier drive real GDP and income and fluc-tuations in those measures of economic activity. There is no government, and thus no way for government policy to affect real output and employment. There is no financial sector to explain the interest rates and foreign exchange rates that affect expenditure decisions, and thus no monetary policy. In the next few chapters we extend our discussion of aggregate expenditure and aggregate demand to include the government sector and financial sectors, as well as fiscal and monetary pol-icy. The framework becomes a bit more complicated and realistic, but the basic mechanics are still those we have developed in this chapter.
Nonetheless, this basic model explains why, in the first half of 2015 both Steven Poloz, the Gov-ernor of the Bank of Canada and Joe Oliver, the Minister of Finance are both counting on a strong rise in exports to move the Canadian economy from a recession to growth in the second and third quarters of 2015.
Figure6.5 above shows that export growth has not provided the hoped for increase in aggregate demand nor did investment expenditures rise to add to aggregate demand. Recognizing these weak economic conditions the new Liberal government Minister of Finance, Bill Morneau, initiated an expansionary fiscal policy program. That policy planned for government budget deficits to finance expenditures on major infrastructure to increase the government component of aggregate demand and stimulate growth in real GDP.
Example Box 6.1: The algebra of the basic income – expenditure model.
The basic model has two components:
1. Aggregate expenditure = Autonomous expenditure plus induced expenditure:
AE= A0+ (c − m)Y (6.2)
2. Equilibrium condition: GDP = Aggregate expenditure Y = AE
Then equilibrium Y is found by substituting 1 into 2:
Y = A0+ (c − m)Y Y− (c − m)Y = A0
Y[1 − (c − m)] = A0
Y = A0/[1 − (c − m)]
Recall that(c − m) is the slope of the AE function (i.e. ∆AE/∆Y ). Then in equilibrium:
Y = A/(1 − slope of AE)
Using the numbers in the example in Table6.3AE= 100 + 0.5Y and for equilibrium:
Y = 100 + 0.5Y Y− 0.5Y = 100
Y = 100/(1 − 0.5) Y = 200
6.5. Equilibrium output and the AD curve 145
Example Box 6.2: The multiplier in a basic algebraic model.
Initial conditions in a basic model:
Aggregate expenditure : AE= 100 + 0.5Y Equilibrium condition : Y = AE
Then equilibrium national income is:
Y = 100 + 0.5Y 0.5Y = 100
Y = 200
Suppose autonomous expenditure increases by 25 to A1= 125:
Aggregate expenditure : AE1= 125 + 0.5Y Equilibrium condition : Y = AE1
Then the new equilibrium national income is:
Y = 125 + 0.5Y 0.5Y = 125
Y1= 250
The change in autonomous expenditure by 25 increased equilibrium national income by 50.
The Multiplier is defined as the change in national income(∆Y ) divided by the change in autonomous expenditure(∆A) that caused it. In this example the multiplier is:
∆Y/∆A = 50/25 = 2.
Notice the multiplier is also equal to 1/(1 − slope of AE). In this example the slope of AE is the marginal propensity to spend on domestic output(c − m) = 0.5. The multiplier is:
∆Y/∆A = 1/(1 − slope of AE) = 1/(1 − 0.5) = 1/0.5 = 2.
K EY C ONCEPTS
Aggregate demand determines real output (Y ) and national income in the short run when prices are constant.
Aggregate demand: aggregate expenditure (AE) at different price levels when all other con-ditions are constant.
GDP(Y ): the national accounts measure of the sum of actual expenditure and income in the economy.
Aggregate expenditure (AE): planned expenditure by business and households.
Induced expenditure: planned expenditure that is determined by current income and changes when income changes.
Marginal propensity to consume (mpc = c = ∆C/∆Y ): the change in consumption expendi-ture caused by a change in income.
Marginal propensity to import (mpm = m = ∆IM/∆Y ): the change in imports caused by a change in income.
Induced expenditure (c − m)Y : planned consumption and imports expenditures that change when income changes.
Autonomous expenditure (A): planned expenditure that is not determined by current income.
Aggregate expenditure (AE): the sum of planned induced and autonomous expenditure in the economy.
Short-run equilibrium output: Aggregate expenditure current output are equal (Y = AE).
Unplanned changes in business inventories: indicators of disequilibrium between planned and actual expenditures – incentives for businesses to adjust levels of employment and output (Y ).
Multiplier (∆Y /∆A): the ratio of the change in equilibrium income Y to the change in au-tonomous expenditure A that caused it.