Chapter Summary • 35
In analyzing this game tree, we see what is known as a subgame perfect Nash equilibrium (SPNE). In an SPNE, each player chooses an optimal action at each stage in the game that it might conceivably reach and believes that all other players will behave in the same way.
To derive the SPNE, we use the so-called fold-back method: We start at the end of the tree, and for each decision “node” (represented by squares), we find the optimal decision for the firm situated at that node. In this example, we must find Beta’s optimal decision for each of the three choices Alpha might make: DO NOT EXPAND, SMALL, and LARGE. By folding back the tree in this fashion, we assume that Alpha anticipates that Beta will choose a profit-maximizing response to any strategic move Alpha might make. Given these expectations, we can then determine Alpha’s optimal strategy. We do so by mapping out the profit that Alpha gets as a result of each option it might choose, given that Beta responds optimally. The fold-back analysis tells us the following:
•If Alpha chooses DO NOT EXPAND, then given Beta’s optimal reaction, Alpha’s profit will be $15 million.
•If Alpha chooses SMALL, then given Beta’s optimal reaction, Alpha’s profit will be $16 million.
•If Alpha chooses LARGE, then given Beta’s optimal reaction, Alpha’s profit will be $18 million.
The SPNE is thus for Alpha to choose LARGE. Beta responds by choosing DO NOT EXPAND.
Note that the outcome of the sequential-move game differs significantly from the outcome of the simultaneous-move game. Indeed, the outcome involves a strategy for Alpha (LARGE) that would be dominated if Alpha and Beta made their capacity choices simultaneously. Why is Alpha’s behavior so different when it can move first? Because in the sequential game, the firm’s decision problems are linked through time: Beta can see what Alpha has done, and Alpha can thus count on a rational response by Beta to whatever action it chooses. In the sequential-move game, Alpha’s capacity choice has commitment value; it forces Beta into a corner. By committing to a largecapacity expansion, Alpha forces Beta into a position where Beta’s best response yields the outcome that is most favorable to Alpha. By contrast, in the simultaneous-move game, Beta cannot observe Alpha’s decision, so the capacity decision no longer has commitment value for Alpha. Because of this, the choice of LARGE by Alpha is not nearly as compelling as it is in the sequential game. We discuss commitment in detail in Chapter 7.
CHAPTER SUMMARY
The total cost function represents the relationship between a firm’s total costs and the total amount of output it produces in a given time period.
Total costs consist of fixed costs, which do not vary with output, and variable costs.
Average costs equal total costs divided by total output. Marginal costs represent the additional cost of producing one more unit of output. Average costs are minimized at the point where average costs equal marginal cost.
36 • Economics Primer: Basic Principles
Sunk costs are costs that cannot be recovered if the firm stops producing or otherwise changes its decisions.
Economic costs and economic profits depend on the costs and profits the firm would have realized had it taken its next best opportunity. These are distinct from costs and profits reported on accounting statements.
The demand curve traces the amount that consumers are willing to pay for a good at different prices, all else equal. Most demand curves are downward sloping. The price elasticity of demand measures the percentage change in the quantity purchased for a 1 percent change in price, all else equal.
Firms facing downward-sloping demand curves must reduce price to increase sales. A firm’s marginal revenue is the additional revenue generated when the firm sells one more unit.
Firms maximize profits by producing up to the point where the marginal revenue from an additional sale exactly equals the marginal cost.
In a perfectly competitive market, there are many firms selling identical products to many consumers. No firm can influence the price it charges.
The supply curve in a perfectly competitive market is the sum total of each firm’s marginal cost curve and represents the total quantity that firms are willing to sell at any given price. The market demand curve represents the total quantity that consumers are willing to purchase at any given price.
In a competitive equilibrium, the market price and quantity are given by the point where the supply curve intersects the demand curve.
In the competitive equilibrium, firms produce up to the point where price equals marginal cost. In the long run, entry forces prices to equal the minimum average cost of production.
Game theoretic models explicitly account for how one firm’s decisions may affect the decisions of its rivals. In a Nash equilibrium, all firms are making optimal choices, given the choices of their rivals.
Matrix forms may be used to analyze games in which firms make simultaneous choices. Extensive forms are more appropriate for analyzing games when choices are sequential.
QUESTIONS
1.What are the distinctions among fixed costs, sunk costs, variable costs, and marginal costs?
2.If the average cost curve is increasing, must the marginal cost curve lie above the average cost curve? Why or why not?
3.Why are long-run average cost curves usually at or below short-run average cost curves?
4.What is the difference between economic profit and accounting profit? Why should managers focus mainly on economic profits? Why do you suppose managers often focus on accounting profits?
5.Explain why we might expect the price elasticity of demand for nursing home care to be more negative than the price elasticity of demand for heart surgery.
Endnotes • 37
6.Why is marginal revenue less than total revenue?
7.Why does the elasticity of demand affect a firm’s optimal price?
8.Explain why long-run prices in a perfectly competitive market tend toward the minimum average cost of production.
9.Is the prisoners’ dilemma always a Nash equilibrium? Is a Nash equilibrium always a prisoners’ dilemma? Explain.
10. Does the equilibrium outcome of a game in extensive form depend on who moves first? Explain.
ENDNOTES
1This example is drawn from Richard Tedlow’s history of the soft drink industry in his book, New and Improved: The Story of Mass Marketing in America, New York, Basic Books, 1990.
2We will discuss this relationship in Chapter 9.
3The third, fourth, and fifth sections of this chapter are the most “technical.” Instructors not planning to cover Chapters 5–7 can skip this material.
4The first part of this section closely follows the presentation of cost functions on pp. 42–45 of Dorfman, R., Prices and Markets, 2nd ed., Englewood Cliffs, NJ, Prentice-Hall, 1972.
5Students sometimes confuse total costs with average (i.e., per unit) costs, and note that for many real-world firms “costs” seem to go down as output goes up. As we will see, average costs could indeed go down as output goes up. The total cost function, however, always increases with output.
6This term was coined by Thomas Nagle in The Strategy and Tactics of Pricing, Englewood Cliffs, NJ, Prentice-Hall, 1987.
7Some authors call these programmed costs. See, for example, Rados, D. L., Pushing the Numbers in Marketing: A Real-World Guide to Essential Financial Analysis, Westport, CT, Quorum Books, 1992.
8It is customary to put the minus sign in front, so that we convert what would ordinarily be a negative number (because DQ and DP have opposite signs) into a positive one.
9One complication should be noted: A given product’s price elasticity of demand is not the same at all price levels. This means that an elasticity that is estimated at a price level of, say, $10 would be useful in predicting the impact of an increase in price to $11, but it would not accurately predict the impact of an increase to, say, $50, a price that is far outside the neighborhood of the price at which the elasticity was originally estimated. This is due to the properties of percentages, which require dividing by base amounts. If the price is so high that the quantity demanded is close to zero, even small absolute increases in quantity can translate into huge percentage increases.
10The use of this formula is subject to the caveat expressed earlier about the use of elasticities. It is useful for contemplating the effects of “incremental” price changes rather than dramatic price changes.
11This result is subject to the following qualification. If certain key inputs are scarce, the entry of additional firms bids up the prices of these inputs The firm’s average and marginal cost functions then shift upward, and in the long run, the market price will settle down at a higher level. An industry in which this happens is known as an increasing-cost industry. The case we focus on in the text is known as a constant-cost industry.
12To keep the example as simple as possible, we will assume only two stages of decision making: Alpha makes its choice first, and then Beta responds. We do not consider the possibility that Alpha might respond to the capacity decision that Beta makes.
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PART ONE
FIRM BOUNDARIES
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