Problems 1:
Kelson Electronics a manufacturer of DVR's estimates the following relations between in marginal cost of production and monthly output: MC = $150 + 0.005Q
a. What does this function imply about the effect of the law of the law of diminishing returns on Kelson's short-run cost function?
b. Calculate the marginal cost of production at 1500, 2000, and 3500 units of output.
c. Assume Kelson operates as a price taker in a competitive market. What is this firm's profit-maximizing level of output if the market price is $175?
d. Compute Kelson's short-run supply curve for its product.
Problem 2:
A manufacturer of electronics products is considering entering the telephone equipment business. It estimates that if it were to begin making wireless telephones, its short-run cost function would be as follow:
Q (Thousands) AVC AC MC
9 41.10 52.21 30.70
10 40.00 50.00 30.70
11 39.10 48.19 30.10
12 38.40 46.73 30.70
13 37.90 45.59 31.90
14 37.60 44.74 33.70
15 37.50 44.17 36.10
16 37.60 43.85 39.10
17 37.90 43.78 42.70
18 38.40 43.96 46.90
19 39.10 44.36 51.70
20 40.00 45.00 57.10
a. Plot the average cost, average variable cost, marginal cost, and price of a graph.
b. Suppose the average wholesale price of a wireless phone is currently $50. Do you think this company should enter the market? Explain. Indicate on the graph the amount of profit (or loss) earned by the firm at the optimal level of production.
c. Suppose the firm does enter the market and that over time increasing competition causes the price of telephones to fall to $35. What impact will this have on the firm's production levels and profit? Explain. What would you advise this firm to do?
Problem 3
This same manufacturer of electronic products has just developed a handheld computer. Following is the cost schedule for producing these computers on a monthly basis. Also included is a schedule of prices and quantities that the firm believes it will be able to sell (based on previous market research).
Q (Thousands) Price MR AVC AC MC
0 1650
1 1570 1570 1281 2281 1281
2 1490 1410 1134 1634 987
3 1410 1250 1009 1342.33 759
4 1330 1090 906 1156 597
5 1250 930 825 1025 501
6 1170 770 766 932.67 471
7 1090 610 729 871.86 507
8 1010 450 714 839 609
9 903 290 721 832.11 777
10 850 130 750 850 1011
a. What price should the firm charge if it wants to maximize its profits in the short run?
b. What arguments can be made for charging a price higher that this price? If a higher price is indeed established what amount would you recommend? Explain.
c. What arguments can be made for charging a lower price than the profit-maximizing level? If a lower price is indeed established what amount would you recommend? Explain.
Problem 4
A firm in an oligopolistic industry has identified two sets of demand curves. If the firm is the only one that changes price (i.e., other firms do not follow), its demand curves takes the form Q = 82 - 8P. If however it is expected that competitors will follow the price actions of the firm then the demand curve is of the form Q = 44 - 3P.
a. Develop demand schedules for each alternative and draw them on a graph.
b. Calculate marginal revenue curves for each.
c. If the present price and quantity position for the firm is located at the intersection of the two demand curves and competitors follow any price decrease but do not follow a price increase show the demand curve relevant to the firm.
d. Draw the appropriate marginal revenue curve.
e. Show the range over which a marginal cost curve could rise or fall without affecting the price the firm charges.
Problem 5
Oligopolistic models are based on behavioral assumptions. One behavioral assumption associated with differentiated product markets is that price increase will not be matched but price decrease will be matched. This rather pessimistic view of pricing leads to the kinked demand curve. To examine why consider the following simple model: Market inverse demand is given by P (Q) = 140 - Q.
a. Suppose firm A controls 50 percent of the market. What is the demand curve faced by this firm? Write inverse demand in slop-intercept form.
Suppose the current price of the product is $6.
b. What is demand faced by firm A given P = $6? Call this quantity Qb.
c. Suppose that if firm A increase price form this point other firms do not match the price increase. But if A decrease price other firms decrease price to maintain their market share. The demand in this instance has two segments: the segment above P = $6 and the segment below P = $6. what should happen to market share for prices above $6? What happens to market share for prices below $6?
The final question that must be answered is how quickly does market share decline as price increase. Suppose A's demand is linear above P = $6 and A is unable to sell any output above P = $8
d. Describe algebraically the inverse demand curve faced by the firm in this instance. Provide a graph thaw is consistent with your answer. Based on this graph explain why this is called the kinked demand model. (Hint: The equation for the inverse demand curve must be done in two parts.)