Question

You manage a plant that mass produces engines by teams of workers using assembly machines. The technology is summarized by the production function Q = 5KL where Q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. Each assembly machine rents for r = $10,000 per week and each team costs w= $5,000 per week. Engine costs are given by the cost of labor teams and machines, plus $2,000 per engine for raw materials. Your plant has a fixed installation of 5 assembly machines as part of its design. Calculate the cost functions.

Answer 1

Production function is given by:

Q = 5KL => L = Q/(5K)

It is given that plant has a fixed installation of 5 assembly machines as part of its design and So, K = 5 and is constant.

So total amount of L required in order to produce Q units is given by ; L = Q/(5K) and as K = 5 => L = Q/(5*5)

=> L = Q/25

Cost function is given by :

C = wL + rK + Cost of raw materials per Engine*Q , where Q = the number of engines per week

=> C = 5000(Q/25) + 10,000*5 + 2000Q

=> C = 200Q + 50,000 + 2000Q

=> C = 2200Q + 50,000

=> C = 50,000 + 2200Q -------------------------------Cost Function