Popsi Inc. produces soft drinks in quantity q in a manufacturing plant in Canada
ID: 1141574 • Letter: P
Question
Popsi Inc. produces soft drinks in quantity q in a manufacturing plant in Canada with labor input L and machines K according to the production function q = f(K, L) = 7L + (3/2)K1/2L 2 L 3 /3(K to the power of 1 over 2, times L to the power of 2, minus L to the power of 3 devided by 3). In the short run, no additional machinery can be used, but workers can work overtime, so that labor input is flexible.
(a) What is the short-run marginal and average product of labor for a given capital stock K? (2)
(b) For the following, assume that K = 4. For which value of L do the functions MPL and APL intersect? What is the maximum of the APL function? What is the connection? (2)
(c) When is the production function no longer defined? Why is it not defined? (1)
(d) Does the law of diminishing marginal returns hold? Why? (1)
Explanation / Answer
The law of diminishing marginal utility is a law of economics stating that as a person increases consumption of a product while keeping consumption of other products constant, there is a decline in the marginal utility that person derives from consuming each additional unit of that product.