Question

1. Use the Keynesian cross model and show graphically in which direction will equilibrium level of income (or output) change. For each of the following, write down the formula for the size of the change of income (i.e. write down the formula for ∆Y):

(i) An increase in government purchases

(ii) An increase in taxes

(iii) An increase in government purchase and an increase in taxes of equal amount

(Nb: You must draw a SEPARATE graph for parts (i) and (ii). Part (iii) does not need any graph so only provide explanation).

2. In the Keynesian cross model, assume the consumption function is given by the following: C = 120 +0.8(Y-T)

Planned Investment is 200, planned government purchases and taxes are each 400.

(i) After substituting for C, I, G and T, write down the equation for Planned Expenditure PE.

(ii) According to the consumption function C above, what is the value of MPC?

(iii) Calculate government purchase multiplier.

3. The following equations describes an economy:

Y = C + I + G

C = 50 +0.75 (Y – T)

I =150 – 10r

(M/P)d = Y – 50r

G = 250

T = 200

M = 3000

P = 4

a) From the above list, use the relevant equations to derive the equation for IS curve. (Hint: Substitute C, I and G in to Y to find your answer)

b) From the above list, use the relevant set of equations to derive the LM curve.

c) Using your IS and LM curve equations from parts a and b, derive what is equilibrium level of Y and equilibrium interest rate (r)? (Hint: To solve this question, set the IS equation equal to LM equation and find equilibrium r first. Then substitute this equilibrium r in to either IS or LM equation to find equilibrium Y)

4) Suppose the Fed increases the money supply by 5%. Assume the velocity of money is constant.

a) What happens to AD curve?

b) Draw a graph starting from LR equilibrium as shown in class and show what happens to price and output in the short run.

c) Based on your answer to part b, draw another graph to show how we can return to LR equilibrium from the SR equilibrium point. You must also explain briefly your answer. (Hint: You need to explain what happens to unemployment in short run due to change in AD and consequently, what happens to wages and therefore price level P. Thus, explain how changes in production and employment can take us back to LR equilibrium).

Answer 1

(1)

In each of the following graphs, planned aggregate expenditure (PAE) and real GDP (Y) are measured vertically and horizontally respectively. C0, I0, G0 and PAE0 are initial consumption, investment, government spending and planned aggregate expenditure curves (where PAE0 = C0 + I0 + G0). Initial equilibrium is at point A where PAE0 intersects 45⁰ line with initial real GDP Y0.

Marginal propensity to consume (MPC) = c.

(a) Spending multiplier = 1 / (1 - c)

An increase in government spending from G0 to G1 will increase PAE, shifting PAE0 upward to PAE1. New equilibrium is at point B where PAE1 intersects 45⁰ line with higher real GDP Y1.

$\Delta$ Y = Y1 - Y0 = [1 / (1 - c)] x  $\Delta$  G

(b) Tax multiplier = -c / (1 - c)

An increase in tax will decrease disposable income, lowering consumption from C0 to C1 which will decrease PAE, shifting PAE0 downward to PAE1. New equilibrium is at point B where PAE1 intersects 45⁰ line with lower real GDP Y1.

$\Delta$ Y = Y1 - Y0 = [-c / (1 - c)] x  $\Delta$  T

(c) In this case,  $\Delta$  G =  $\Delta$  T

When G is increased by  $\Delta$  G,

$\Delta$ Yg = [1 / (1 - c)] x  $\Delta$  G

When T is increased by  $\Delta$  T,

$\Delta$ Yt = [-c / (1 - c)] x  $\Delta$  T

Net change in Y =  $\Delta$  Yg +  $\Delta$  Yt = [1 / (1 - c)] x  $\Delta$  G - [c / (1 - c)] x  $\Delta$  T = [(1 - c) / (1 - c)] x  $\Delta$  G =  $\Delta$  G =  $\Delta$  T