Determine the profit-maximizing price and quantity
LEARNING GOALS: Upon completing this section, we will understand how perfectly competitive firms differ from monopolies and from monopolistically competitive firms. We will be able to determine profit-maximization in both situations, and how entry and exit in the long run affects profitability. We will also become familiar with various tools of measuring market power. We will have a few tools with which to analyze strategic decisions, and how decisions made by one firm affect decisions made by others (competitors or otherwise).
1. You are given the following data for your firm, which sells high-capacity video MP3 players.
| Q | P | TC |
| 0 | $78 | $100,000 |
| 1,000 | $76 | $125,000 |
| 2,000 | $74 | $144,000 |
| 3,000 | $72 | $158,000 |
| 4,000 | $70 | $172,000 |
| 5,000 | $68 | $187,000 |
| 6,000 | $66 | $208,000 |
| 7,000 | $64 | $236,000 |
| 8,000 | $62 | $276,000 |
| 9,000 | $60 | $329,000 |
| 10,000 | $58 | $400,000 |
a. Determine equations for P=f(Q), MR=f(Q), ATC=f(Q, Q2), AVC=f(Q, Q2), MC=f(Q, Q2). Recall that your marginal equations should be derivatives of your totals!
b. Determine the profit-maximizing price and quantity. (Since MC is in terms of Q2, solving with calculus and algebra can be messy. Your table should give an exact answer.)
c. How much total profit would your firm earn if you set P and Q according to part b?
d. Describe the competitiveness of the market by calculating the Lerner index.
2. Do Applied Problem about Coke’s attempt at gaining market share.
In a recent “earnings call,” a teleconference call to shareholders in which the CEO reports and discusses quarterly earnings per share, Coca-Cola’s CEO Muhtar Kent bragged about “winning” market share from rival beverage company PepsiCo. However, rising sugar costs in 2011 are forcing Coke to raise soft drink prices by 3 to 4 percent, and this could undermine Coke’s market share gains if Pepsi does not also raise its soft drink prices The Wall Street Journal (April 27, 2011) reports that, in an effort to continue “winning the market share battle,” Kent plans to maintain relatively low prices in soft drinks by raising prices disproportionately higher in other categories such as fruit juices and sport drinks. The WSJ raises the concern that “winning market share may come at too great a financial cost” Discuss some reasons why Coke’s pricing tactics to win market share could in fact reduce Coke’s profit and earnings per share.
3. Do Applied Problem about laws restricting Sunday sales. Note that the trade associations attempt to represent the interests of all businesses in the industry.
Some states have had laws restricting the sale of most goods on Sunday. Consumers, by and large, oppose such laws because they find Sunday afternoon a convenient time to shop. Paradoxically, retail trade associations frequently support the laws Discuss the reasons for merchants’ supporting these laws.
4. The following is a payoff matrix showing profit in millions of dollars when two companies simultaneously decide on various advertising budgets ($1 million, $2 million, or $3 million):
|
Pizza Hut |
||||
| $1 mill | $2 mill | $3 mill | ||
|
Papa Johns |
$1 mill |
$60 / $55 |
70 / 60 |
20 / 65 |
| $2 mill |
80 / 40 |
40 / 55 |
60 / 50 |
|
| $3 mill |
85 / 35 |
67 / 45 |
65 / 55 |
|
a. In the first round of strategy elimination, which ad budget would the companies exclude?
b. After the first round of elimination, would either company make a second-round elimination?
c. What would be the likely outcome of this simultaneous advertising decision (i.e. what ad budget would each company end up choosing)?
