Elevator maintenance contractors must have trained service personnel to provide routine and emergency service. Shan On Elevator, Hong Kong, has 200...

1.    Elevator maintenance contractors must have trained service personnel to provide routine and emergency service. Shan On Elevator, Hong Kong, has 200 service personnel to maintain 1,000 elevators.

(a)  Suppose that Shan On has received a contract to maintain an additional 1,000 elevators. Do you expect that Shan On will need to double service personnel? Why or why not?

(b)  Does the example in (a) illustrate economies of scale or scope?

(c)  Escalators and elevators use quite different technology and parts. But many clients operate both escalators and elevators. Are there any economies of scope for a contractor to maintain both escalators and elevators?

2.    You manage a plant that mass produces engines by teams of workers using assembly machines. The production function is Q = 4 KL, where Q is the number of engines per week, K is the number of assembly machines, and L is the number of labor teams. The MPL is 4K and the MPK is 4L. Each assembly machine rents for r = $12,000 per week and each team costs w = $3000 per week. Engine costs are given by the cost of labor teams and machines, plus $2000 per engine for raw materials. Your plant has a fixed installation of 10 assembly machines as part of its design.

a.     What is the cost function for your plant?

b.    What is the average costs for producing Q engines?

c.     In the short run, how many teams are required to produce 80 engines?

d.    You are asked to make recommendations about the design of new production facilities. What would you suggest?

3.    The Green Company produces a chemical in a perfectly competitive market. The current market price is $40; the firm's total cost function is C = 100 + 4Q + Q2  

(MC = 4 + 2Q).