An economy is described by the following equations C = 100 + (3/4)*(Y – T) IP = 50 – 500 * r G = 75 NX = 0 T = 100 Y* = 500 Find an equation linking planned aggregate expenditure to output

1.

AE = C + Ip + G + NX

AE = 100 + 0.75(Y - 100) + 50 - 500r + 75 + 0

AE = 225 + 0.75Y - 75 - 500r

AE = 150 + 0.75Y - 500r

Autonomous expenditure = 150 - 500r

Induced expenditure = 0.75Y

2.

MPC is the change in consumption out of a given change in disposable income, defined as

MPC = Change in consumption / Change in disposable income = 0.75

3.

When r = 10% = 0.1, Setting Y = AE,

Y = 150 + 0.75Y - 500 x 0.1

0.25Y = 150 - 50

0.25Y = 100

Y = 400

4.

From AE curve: When Y = r = 0, AE = 150 (vertical intercept)

In following graph, planned aggregate expenditure (PAE) and real GDP (Y) are measured vertically and horizontally respectively. Initial Equilibrium is at point A where 45⁰ line intersects initial aggregate expenditure curve PAE0, with equilibrium GDP Y0 and planned aggregate expenditure E0. As Y0 lies to the left of Y*, this is a recessionary phase of business cycle with recessionary gap of (500 - 400) = 100.

5.

To close recessionary bank, central bank will employ expansionary monetary policy to increase money supply. This can be done by:

i) open market purchase of securities

ii) decreasing required reserve ratio or

iii) decreasing discount rate.

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