1. The Zinger Company manufactures and sells a line of sewing machines. Monthly demand for one its most popular models is given by the following relationship:
Q = 400 – 0.5P
where P is price and Q is quantity demanded. Total costs of production (including a “normal” return on owners’ investment) per month are:
C = 20,000 + 50Q + 3Q2
a. Express total profits (() in terms of Q.
b. At what level of output are total profits maximized? What price will be charged? What are total profits at this output level? c. What market structure did you assume? Why?
d. Would your answers in b change if the market for sewing machines were competitive? How? (Specify price, quantity, and profit levels.)
2. Zar Island Gas Company is the sole producer of natural gas in the remote island country of Zar. The State Energy Commission regulates the company’s operations. The demand function for gas in Zar has been estimated as:
P = 1,000 – 0.2Q
where Q is output (measured in gas units) and P is price (measured in dollars per gas unit). Zar Island’s cost function is:
C = 300,000 + 10Q
This cost function does not include a “normal” return on the firm’s invested capital of $4 million.
a. In the absence of any government price regulations, determine Zar Island’s optimal (i) output level, (ii) selling price, (iii) total profits, and (iv) rate of return on its asset base. b. The State Energy Commission has ordered the firm to charge a price that will provide it with no more than a 12 percent return on its total assets. Determine Zar Island’s optimal (i) output level, (ii) selling price, and (iii) total profits under this constraint. You will need to use the quadratic equation on the next page to solve this problem. c. Is this a perfectly competitive solution? Why or why not?
3. Two companies (A and B)...
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