Dont just copy from others The following equations characterize a country’s clos

Question

Dont just copy from others

The following equations characterize a country’s closed economy.

Production function: Y = AKN – N2/2
Marginal product of labor: MPN = AK – N.

where the initial values of A = 10 and K = 8.

The initial labor supply curve is given as: NS = 40 + 9w.

a) (5 points) Find the equilibrium levels of the real wage, employment and output (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 these initial equilibrium points as point A.

(10 points for correct and completely labeled diagrams)

Initial conditions in the goods market

Cd = 1000 + .50(Y-T) – 500r
Id = 600 – 500r
G = 100
T= 100

Initial conditions in the money market

Md/P = 78 + .5Y - 1000 (r + e)

where M = 2400 and e = 0.02 (2%)

b) (5 points) Given these initial conditions in the goods market, solve for an expression of the IS curve (r in terms of Y).

c) (5 points) Given the initial output, as in part a), what is the goods market clearing interest rate?

d) (5 points) Given the initial output as in part a) and the goods market clearing interest rate as in part c), what is the general equilibrium price level?

e) (5 points) Please solve for an expression for the LM curve (r in terms of Y).

Explanation / Answer

(a) To find the equilibrum level of real wage , equate labor demand with labor supply.

At equilibrium marginal product of labor is equal to wage .

MP = w

AK- N = w (A= 10 and K=8)

(10)(8) - N = w

Nd= 80-w (this represents the labor demand function)

Now, equate labor demand with labor supply, i.e Nd = NS

80-w = 40+ 9w

40 = 10w

w = 4 (market clearing wage)

Nd = 80- 4 = 76 (Profit maximising level of labor input)

Now, put N in Y function,

Y = (10)(8)(76) - (76)2/2

Y = 6080 - 5776/2

Y= 6080 - 2888

Y = 3192 (Full employment level of output)

(b) Given, the initial conditions in the goods market, then IS equation will be:

Cd= 1000 +0.50(Y-T) -500r

Id= 600- 500r

G = 100

T=100

For IS equate C +I + G =Y

1000 +0.50(Y-100) - 500r + 600 - 500r + 100 = Y

1000- 0.50Y -50 -500r +600-500r +100 =Y

(1000- 50 +600+100) - 500r -500r = Y-0.50Y

(1650) -1000r = 0.5Y

1650/0.5 - 1000/0.5 = Y

3300 - 2000r = Y

Y = 3300 - 2000r [IS equation]

(c) Given the initial output , goods market clearing interest rate is

Put Y= 3192 in IS equation,

3192 = 3300 - 2000r

108 = 2000r

r = 0.054 [ Goods market clearing interest rate]

(d) Given the initial output and the market clearing interest rate, then general equilibrium price level:

When r= 0.054

Md/P = 78 +0.5 Y -1000 (r + expected inflation)

Md/P = 78 + 0.5 (3192) -1000(0.054 + 0.02)

= 78 + 1596 - 1000(0.074)

= 78 + 1596 - 74

Md/P = 1600 (and M=2400)

2400/ P =1600

P =1.5 (General equilibrium price)

(e) Expression for LM curve :

We got M/P = 1600 in part(d)

And, M/P = 78 +0.5Y - 1000(r + 0.02)

1600 = 78 + 0.5Y -1000r - 20

1600 - 78 +20 -0.5Y = -1000r

1542 - 0.5Y = -1000r

0.5Y - 1542 = 1000r

0.0005 Y - 1.542 = r

r = 0.0005 Y - 1.542 (Expression for LM curve , r in terms of Y)

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