Question

Answer the following questions based on the following production function: Does this production function represent the long run or the short run? Explain. Suppose capital (K) is held fixed at 3 units and the firm hires 5 workers. What is the average product? What is the marginal product of adding the 6^th worker? Does the production function eventually exhibit diminishing returns? If so, where and why does this occur? Depict the isoquants for the production function for output levels 27 and 30. What do the shapes of these isoquants suggest about the relationship between the two inputs? Does this production function exhibit IRTS, DRTS, or CRTS? Explain.

Answer 1

a. The production function represent the long run as both the inputs labour and capital are variables here, whereas in the short run, one of the inputs is fixed.

b. i. Average Product = Total product/Number of workers = 37/5 = 7.4

ii. Marginal product of 6th worker = Total product with 6 worker - Total product with 5 worker = 42 - 37 = 5

iii. Yes, production function eventually does exibit diminshing returns, it exibits diminishing returns after 5 workers, i.e while adding 6th worker. it happens so because the fixed capital of 3, is optimally utilized with 5 workers only, hence adding 6th worker reduces the marginal returns.

C. The shapes of two isoquants suggest that the marginal product of both the inputs is extectly same.

D. the production function exibits constant returns to scale CRTS as it can be seen from the table that when both the inputs are increased by same proportion output also increases in the fixed amount. As L and K increases from 1,1 to 2,2 then output increases from 5 to 15.