Consider a firm that employs capital k and labor l in production. Its production function is f ( k,l ) = 2 k 1 / 3 l 1 / 2 . The price of output is p...

 Consider a firm that employs capital k and labor l in production. Its production function is f(k,l) = 2k1/3l1/2. The price of output is p = 6.

(a)    Does the technology exhibit constant, decreasing, or increasing returns to scale?

(b)    Find the marginal product of each factor and the technicalrate of substitution. Determine if the technology has diminishing marginal product in either factor.

(c)   Suppose in the short run, capital is fixed at k¯ = 64. What extra information do you need to determine the exact amount of labor to be employed in order to maximize short-run profits? Provide a suitable number yourself, and find how much labor is employed. Illustrate your answer with a graph.