Question

Q = E^2/3 * E^ 1/3 MPE = 2/3 (K/E)^1/3

WAGE = 10 PRICE = 50 CAPITAL = 1000 R = 25

A. HOW MANY LABORERS SHOULS FIRM HAVE ?

B. HOW MUCH PROFIT (POS OR NEG) IS THIS FIRM MAKING?

Answer 1

We are given that K = 1000. Hence Q = E^2/3 * (1000)^ 1/3 or Q = 10E^2/3 Now MPE is 10*2/3E^-1/3. The firm should hire labor using the optimal rule of MRP = wage rate

MRP = MPE x Price and here it is given by MRP = 10*2/3E^-1/3 x 50 = 1000/3E^-1/3.

Use MRP = wage rate

1000/3E^-1/3 = 10

E^1/3 = 100/3

E = 37037..04

A. When K is 1000, E should be 37037.04

B. With E = 37037..04 and K = 1000, output is Q = (37037.04)^2/3 * (1000)^ 1/3 = 11111.11

Profit = revenue - cost

= 11111.11*50 - (1000*25 +  37037.04*10)

= 160185.1