Question

Assume: a = 150, b = .75, I = 200, Yf = 1600

The equilibrium level of output and income is?

The value of consumption at the equilibrium level of output and income is?

Aggregate spending at full employment is?

The value of savings at full employment is?

The recessionary gap is?

Answer 1

Part 1

Consumption function is as follows -

C = a + bY

C = 150 + 0.75Y

I = 200

At equilibrium,

Y = C + I

Y = 150 + 0.75Y + 200

Y - 0.75Y = 350

0.25Y = 350

Y = 350/0.25 = 1,400

The equilibrium level of output and income is 1,400.

Part 2

C = 150 + 0.75Y = 150 + (0.75*1,400) = 150 + 1,050 = 1,200

The value of consumption at the equilibrium level of output and income is 1,200.

Part 3

Full employment level of income, Yf = 1,600

C = 150 + 0.75Yf = 150 + (0.75 * 1,600) = 150 + 1,200 = 1,350

I = 200

Aggregate spending = C + I = 1,350 + 200 = 1,550

The aggregate spending at full employment is 1,550.

Part 4

Savings at the full employment = Full employment level of income - aggregate spending at full employment

Savings at the full employment = 1,600 - 1,550 = 50

The savings at full employment is 50.

Part 5

Recessionary gap = Full employment level of income - equilibrium level of output and income

Recessionary gap = 1,600 - 1,400 = 200

The recessionary gap is 200.