A firm produces canned food by teams of workers that use machines in the production process. The technology is summarized by the production function q = 2000*K*L, where q is the number of produced food cans per week, K is the number of machines, and L is the number of labor teams. Each machine rents for r = $10000 per week, and each team costs w = $5000 per week. The costs of production are given by the cost of labor teams and machines, plus 20 cents per can for raw materials (food and aluminum). Suppose that in the short-run, the firm’s plant has a fixed installation of 5 machines.
Determine the production function in the short-run.
a) What is the (total) cost function, c(q), for the plant - namely, how much would it cost to produce q food cans? What are average and marginal costs for producing q food cans? How do average costs vary with output? What are the fixed costs?
b) How many teams are required to produce 50,000 food cans ? What is the average cost per can ?
c) You are asked to make recommendations for the design of a new production facility. What capital/labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing any level of output q?