Answer to Question #158099 in Economics of Enterprise for Abdul Mannan

Question

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 = 10L2 – 0.5 L3   where 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.70  where 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?

Answer 1

a. Marginal product first has increasing returns, meaning each new worker adds more to total output than the last. Then marginal product has decreasing returns, meaning each new worker still causes total output to grow, but at a decreasing rate.

Then finally, although it is rare, the marginal product can have negative returns, meaning total output actually decreases with additional workers.

b. Total Production increases, Marginal Product first increases, and then decreases after intersection with Average Product, which decreases.

c. The production function is estimated to be Q = 60L.30K.70, initial L1 = 1 and K1 = 1, Q = 60. If inputs were increased to L2 = 2 and K2 = 2, then $Q = 60×2^{0.3}×2^{0.7} = 120,$

so we observe increasing returns to scale.

d. 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, then Kia should hire more workers in Karachi plant.