Assume a firm currently operating as such: Y = 60K^0.5 L^0.5 , W=$500, R=$2000, P=$100, K=20, L=10.
a) Find the marginal product of capital from the 20th up to the 25th machine. Make your computations using the output value rounded to two decimal places.
b) Is there evidence of diminishing marginal product? Why?
c) How many machines are required to maximize capital income, ceteris paribus?
d) Compute the amount of firm’s total profits associated to the number of machines you recommended, and then the firm’s total profits when the firm leases one additional machine, to show that in fact profits decrease if the firm surpasses the optimal number of machines you recommended.