You have been hired by Kia as manager for its Pakistan operations.Assume following is the short-run production function at their assembly plant outside Karachi:

Q = 10L^2 - 0.5 L^3where L is variable input labor, Q is output of Cars assembled

a. Find the ranges of the three stages of production.

b. Demonstrate the relationship between Total Production, Marginal Product and AverageProduct in a hypothetical graph and clearly label the three stages as per the values of Lyou observed in (a) above.

c. At the end of the year it is expected that output will double with purchase ofnew equipment and machinery. The production function is estimated to be

Q = 60L^.30K^.70where L is labor and K is capital.

Suppose initial L1 = 1 and K1 = 1. When inputs are in increased to L2 = 2 and K2 = 2,

do you observe increasing, decreasing or constant returns to scale?

d. Assume Kia Head Office is considering hiring more laborers either at their Gwadarplant or alternatively at the Karachi plant. What will be your advice if workers' marginal product is 40 at wage of Rs=5/hour in Karachi and marginal product is 28 at wage of Rs=4/hour in Gawdar?