CHAPTER 23: EXPENDITURE MULTIPLIER

Consumption and Savings Function:

n Consumption is primarily a function of Yd (disposable income) or “after-tax” income. Although it is also influenced by the rate of interest, expectations about future Yd, wealth effects etc.

n if plot Consumption as a function of Yd it will have a positive vertical intercept (‘autonomous consumption’) and a positive slope but less than one (i.e, the slope of the consumption function is the coefficient on Yd in the Consumption equation and represents the Marginal Propensity to Consume (MPC). Therefore, 0<MPC<1

n if plot the consumption function versus a 45 degree line (with the mathematical property that any point on the 45 degree line has the same vertical coordinate as horizontal coordinate, or x = y) then where Consumption intersects the 45 degree line is referred to as “breakeven level of Yd”.

n at Yd < Yd breakeven, then C > Yd (the individual is ‘dissaving’ as savings <0)

n at Yd > Yd breakeven, then C < Yd and the individual is “saving”, Savings >0.

n the Savings function is derived from the consumption function (if the consumption function changes then so does the savings function). For example, if

C = a + b (Y - T) where a>0, 0<b<1 and Yd= Y-T

then the implied savings function is:

S = - a + (1-b) (Y - T) where (1-b) = MPS (marginal propensity to save)

Note: MPC + MPS = 1

n Mathematical example:

if C = 1000 + 0.80 (Y -T) then the implied savings function is:

S = -1000 + 0.20 (Y - T)

where MPC = 0.80 and MPS = 0.20. See the graphs pg. 529

Effects of other variables on Consumption function:

n if the interest rate falls or expected future disposable income increases, then the consumption function shifts upwards and the implied savings function shifts downwards (see pg. 531)

Other Components of Aggregate Expenditure (AE):

i) Investment function:

n depends on interest rate, expected future profits. Not related to current GDP or Yd. Therefore, if we plot the investment function in diagram with Investment expenditures on the vertical axis and real GDP on the horizontal axis, the Investment (I) line is horizontal at I₀. That is, we assume that:

I = I₀.

ii) Government expenditures:

n changes in government expenditures (G) or taxes (T) represents a “fiscal policy” decision of the federal government. Therefore, a change in G is a policy choice and does not respond automatically to the level of GDP (Y). So in a diagram, G is also assumed to be autonomous,

G = G₀.

iii) Exports:

n exports represent Canadian goods sold abroad. The level of exports will depend primarily on the Canadian price level (P), foreign price level (Pf), the exchange rate (E) and foreign GDP (Yf). Therefore, once again, X does not respond to the level of Canadian GDP so exports are autonomous.

X = X₀.

iv) Imports:

n depends on relative prices (Canadian and foreign prices), the exchange rate (E), and Canadian GDP (Y). As GDP (Y) increases, we buy more goods and services and some of these will be imported from the rest of the world. Therefore,

Imports (M) = m Y where 0<m<1 and m=MPM (marginal propensity to import)

Aggregate Expenditure function (AE):

n will have a positive intercept (see graph pg. 534)

n the slope of the AE function is given by:

n slope of AE = MPC (1-t) - MPM where 0<t<1

and t represents the tax rate

n Note if we have lump sum taxes, T = To ( a constant) then t=0 and the slope of the AE function is just = MPC - MPM

n Numerical Example:

If MPC = 0.80, MPM = 0.10 and t = 0.25 then the slope of the AE function is:

slope of AE = 0.80 (1 - 0.25) - 0.10

slope of AE = 0.50

Equilibrium GDP (Y):

n when AE = Y (planned spending = production) we have an equilibrium

n graphically this occurs anywhere along the 45 degree line with AE on the vertical axis and real GDP (Y) on the horizontal axis. Specifically, the equilibrium is where the given AE function intersects the 45 degree line. (see pg. 536)

Calculation of Equilibrium GDP (Y):

n Suppose you are given the following equations:

C = 1000 + 0.80 (Y- T)

I = 180

G = 100

X = 200

M = 0.20 Y

T = 100

n To find equilibrium GDP, follow these steps:

n Step 1: Calculate the AE equation by adding C, I G, X and M together and substitute the T value into the consumption equation

AE = C + I + G + X - M

so AE = 1000 + 0.80(Y -100) + 180 + 100 + 200 - 0.20 Y

or AE = 1400 + 0.60 Y

-Step 2: Impose the equilibrium condition, AE = Y

so 1400 + 0.60 Y = Y

and since the equilibrium condition has been imposed, the value of Y solved for is then equilibrium Y.

n Step 3: Solve for equilibrium GDP

0.40 Y = 1400

so Y = 3500

The Multiplier:

n the definition of the multiplier is: multiplier = change in equilibrium Y

change in autonomous spending

n the formula for the expenditure multiplier is: multiplier = 1

1 - slope of AE function

Example: If the MPC = 0.80, t = 0, and MPM = 0.05 then

the slope of the AE function is = 0.75 and the multiplier is = 4

Therefore, for everyone $1 increase in spending (whether it be from C, I, G, X) it will generate a $4 increase in equilibrium GDP.

n continuing the example from above where equilibrium Y = 3500, if full employment GDP (Y*) = 4300 then in order to get to full employment GDP the government could increase its spending by 200 (once subject to the multiplier, the overall increase in GDP is going to be $800 bringing the new equilibrium GDP level to $4300 (=Y*)

The Lump sum Tax multiplier:

n if the government has a lump sum tax (so the tax rate, t = 0),then a $1 increase in taxes would reduce Consumption expenditures by the value of the MPC (eg 0.80). This reduction in expenditures is then subject to the multiplier. The end result is that when taxes (T) change, equilibrium GDP changes according to the value of the tax multiplier,

n definition of the tax multiplier: tax multiplier = - MPC

1 - slope of the AE function

Example:

If the MPC = 0.80, t = 0 and MPM = 0.05 then the tax multiplier is:

tax multiplier = -0.80

1 - 0.75

then the tax multiplier is -3.2

The tax multiplier is always a negative number because from the definition of the tax multiplier above, we know that if taxes increase (decrease), then real GDP will decrease (increase) so the tax multiplier is negative.

n you use the tax multiplier to determine the required change in taxes to bring about full employment GDP. Suppose again that Y (eq’l) = 3500 and Y* = 4300 and the tax multiplier is -3.2

then from the definition of the tax multiplier:

tax multiplier = change in equilibrium GDP

change in taxes (lump sum)

so if the tax multiplier is -3.2 and to get to full employment GDP we want the change in equilibrium GDP to be +$800, then the change in taxes should be = 800/-3.2 or = -$250

The Multiplier and the Price Level:

n the price level (P) was held constant in deriving the AE function. Therefore, if the price level changes it will shift the AE curve (due to the wealth effect and the substitution effects, see page 543).

n specifically, if the price level increases, AE shifts down (the increase in price reduces real wealth and encourages international and intertemporal substitution so consumption expenditures decrease and imports increase lowering equilibrium GDP). See graphs on page 544.

Derivation of the AD curve:

n can derive the AD curve (from chapter 22) by changing the price level and tracing out what happens to equilibrium GDP following the shift in the AE curve. See page 544.

n we can also trace out the effects of changes in other variables (eg changes in the interest rate or exchange rate etc) on the AD curve itself. See page 545. If the AE curve shifts upwards due to any effect but a change in price, then the AD curve will shift in response. See page 545.

Note: you should read over the Appendix to Chapter 23 (the mathematical note at the end of the chapter).