4. A new shop has opened and has the following production function:
Q=2E3/4 K2/5
The price of output is $15, the wage rate is $8, and the rental rate for capital is $6 per unit.
a. Find the short-run profit maximizing level of labor demand if capital is fixed at 20 units.
b. Find the long-run profit maximizing level of labor demand and capital demand. Do not state Q=K=E=infinity since increasing returns to scale. Instead maximize the function and find optimal Q, E, and K.
c. Find the long-run the elasticity. You do not need to show your math on the answer page you will submit for grading.
d. Interpret the elasticity from part c. Does it make sense? Why or why not?
e. In class it was stated that increasing returns to scale long run results are Q=K=E=infinity, prove this is true. Hint look at your answer from a and b.