Question

1.     Suppose the United States economy is represented by the following equations:

Z = C + I + G            C = 100 + .5Y_D                     T = 200                     I = 30

Y_D= Y - T                G = 100

a)     Which variables are endogenous and which are exogenous?

b)     Calculate equilibrium levels of output, consumption and disposable income

c)     What is the multiplier for this economy

d)     What is the effect of increasing G by $100 on Y and the deficit

2)     Suppose that the wage and price setting relations are given by

W = P^e(1-u)

P = (1+μ) W

a.     If P = P^eand the mark-up is 20% find the real wage

b.     Calculate the natural rate of unemployment

c.     Calculate the real wage and the natural rate of unemployment if the mark-up decreases to 10%

d.     Now if P ≠ P^eand P^e=105, but markup is still 20%, what unemployment rate is compatible with the price level = 100?

e.     Derive the aggregate supply if the production function is Y = N

Q3) Suppose the Okun'e law is given by

u t - u t-1 = -0.4(g yt - 3%)

Where variables are as defined in class.

1.      What is the output growth needed to result in reducing unemployment by 1% in a year.

2.      What is the output growth needed to reduce unemployment by 2% over the next 4 years.

3.      what is your interpretation of the 3% in Okun's law above?

Answer 1

1) C = 100 + 0.5Yd where 0.5 is MPC

T = 200

I = 30

G = 100

Yd = Y - T

a) Endogeneous variable is that variable which is dependent upon other variable while exogeneous variable does not get affected by any other variable.

Here, consumption function is endogeneous variable while all other variable are exogenous.

b) Y = C + I + G

C = 100 + 0.5 * (Y - 200)

Y = 100 + 0.5 * (Y - 200) + 30 + 100

Y = 100 + 0.5Y - 100 + 30 + 100

0.5Y = 130

Y = 260

At this level of output, C = 100 + 0.5 * (260 - 200) = 130

Disposable income is income left after paying taxes which is 260 - 200 = 60

c) Multiplier = [1 / (1 - MPC)] = [1 / (1 - 0.5)] = 2

d) If G rises by 100

Y = 100 + 0.5 * (Y - 200) + 30 + 200

Y = 100 + 0.5Y - 100 + 30 + 200

0.5Y = 230

Y = 460

Earlier, there was deficit of T - G = 200 - 100 = 100 while now there is there is surplus of G - T = 460 - 200 = 260