Primo Salt, Inc., manufactures salt, according to the following production function: Q(K, L) = 2L 1/2K 1/3 , where output Q is measured in tonnes, L in labour-days, and K in machine-days. With both L and K variable, it is maximizing its output for an expenditure of $800, hiring 64 labour-days with the rental rate on machines r = $40 per machine day.
a. Give the wage rate w (in $/labour-day), the number of machine-days rented (K), Q, and average cost per tonne (ATC).
b. Suppose that w and r are unchanged, but that Primo can rent only one machine-day. If it still spends $800, give its output level and cost per tonne.
c. If Primo decides instead to produce the same output as in 1a, with K = 1 machine-day, give the values for L, total cost, and cost per tonne.
d. If Primo doubles the quantity of inputs it utilizes relative to 1a, give the values for the total costs, Q, and cost per tonne.