rimo Salt, Inc
, manufactures salt, according to the following production function: Q(K, L) = 2L1/2K1/3,
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
- Give the wage rate w (in $/labour-day), the number of machine-days rented (K), Q, and average cost per tonne (ATC).
- 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.
- 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.
- If Primo doubles the quantity of inputs it utilizes relative to 1a, give the values for the total costs, Q, and cost per tonne.