Question

Consider the following closed economy:

Cᵈ = 100−200r+0.7∗(Y−T)
Iᵈ = 200−200r
​ Government purchases, G equal 100 and the government runs a balanced budget. The liquidity function is given by: L(Y,i)=200+0.2Y−500i The nominal money supply, price level and expected inflation are: M = 300 P = 3 πᵉ = 0.10
(a) Derive the IS curve with the real interest rate r as a function of output Y.

Answer 1

The IS curve represents the relationship between output (Y) and the real interest rate (r) in a closed economy. The equation for the IS curve is Y = 2000. This equation shows the equilibrium level of output for different values of the real interest rate r.

Step-by-step explanation:

The IS curve represents the relationship between output (Y) and the real interest rate (r) in a closed economy. To derive the IS curve, we need to set aggregate expenditure (AE) equal to output. Using the given information:

AE = C + I
AE = (200+0.9(Y-T)) + 600
AE = 800 + 0.9Y - 0.3Y
AE = 800 + 0.6Y

Equating AE to output (Y):

Y = AE
Y = 800 + 0.6Y

Subtracting 0.6Y from both sides:

0.4Y = 800
Y = 2000

Thus, the IS curve is Y = 2000, which shows the equilibrium level of output for different values of the real interest rate r.