Question

Consider the following model of the economy

Production function: Y = A·K·N – N²/2
Marginal product of labor: MPN = A·K – N.

where the initial values of A = 10 and K = 10.

The initial labor supply curve is given as: N^S = 50 + 4w

Initial conditions in the goods market

C^d = 790 + .50(Y-T) – 500r
I^d = 1000 – 500r
G = 800
T = 100

M^d/P = 110 + 0.5Y- 1000(r + π^e)
    
Nominal Money supply   M = 5000
    
Expected inflation is equal to 2% (π^e = 0.02)

1 a) (6 points) Solve for the labor market clearing real wage (w*), the profit maximizing level of labor input (N*), and the full employment level of output (Y*). Please show work.

Draw two diagrams vertically with the labor market on the bottom graph and the production function on the top graph. Be sure to label everything including this initial equilibrium point as point A. (10 points for completely labeled and correct diagrams)

b) (4 points) Derive an expression for the IS curve (r in terms of Y). Please show all work

c) (3 points) Find the real interest rate that clears the goods market. Please show all work

d) (3 points) Find the price level needed to clear the money market. Please show all work

e) (4 points) Find the expression for the LM curve (r in terms of Y). Please show all work

Answer 1

5 2 (f) 어000-8100/2-49 50 n 4956

ฮ.sy (240-5° + roơo-+ Soy 100 0 Y - e)

2585-1σσο (0.065) ton (0.02.) _ maney manket mert 5000 2508 2 LM Cuve