# What then would be the average cost per engine?

The Show more Suppose 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 produced per week K is the number of assembling machines and L the number of labor teams. Each assembly machine rents for r = $12000 per week and each labor team costs w = $3000 per week. Total engine costs are given by the cost of labor teams and assembling machines plus $2000 per engine for raw (component) materials. Your plant currently has a fixed installation of 10 assembly machines as a part of its design. a. What is the total cost function [TC = f(Q)] for your plant- namely how much will it cost to produce Q engines given the production function and input costs above? What are the average [ATC = f(Q)] and marginal costs [MC = f(Q)] of producing Q engines? How do average costs vary with output? b. How many labor teams are required for producing a batch of 80 engines given the plants current makeup? What is the average total cost per engine? c. You are now asked to make recommendations for the design of a new production facility. What would you suggest? In particular what capital/labor ratio should the new plant accommodate? If lower average cost per engine was your prime consideration what would be the optimal capital/labor levels to produce 80 engines? What then would be the average cost per engine? And lastly should you suggest that the new plant have more or less production capacity than the plant you currently manage? Explain why you chose as you did and the circumstances by which you answered as you did. Show less