1. (Short Run and Long Run Costs) You manage a plant that produces engines by teams of workers using assembly machines.The technology is summarized by the production function Q = 4KL, where Q is the number of engines per week, K is the number of assembly machines, and L the number of labor teams.Each assembly machine rents for r = $15,000 per week and each team costs w = $3,000 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 8 assembly machines as part of its design.

a)(Short run) What is the short-run cost function for your plant - namely, how much will it cost in the short-run to produce Q engines?Write an equation for short run total costs as a function of Q.HINT: Start by writing the firm's short-run production function, then re-arrange the function so that you have L as a function of Q.Then plug everything into the cost function: labor costs, capital costs, and raw materials.

b)(Short run) What are the short-run average and marginal costs for producing Q engines?Write equations for ATC and MC in the short-run.

c)(Short run) How do average costs vary with output in the short-run?(In other words, are short run average costs increasing, decreasing, or constant as output rises?)