ECS2220 EXAM PAPER MAY 2011 ANSWERS PART 1 Question 1 a) If the monopolist is not regulated, the price will be set at P2. It is the point where marginal cost equals marginal revenue and the resulting optimum quantity is replaced into the demand function. b) The price will be P4. This is the point where the marginal cost equals the average revenue, which in a perfectly competitive industry is also the marginal revenue of the firm. c) The minimum feasible price is P3.
The firm will not produce below its average total cost. Question 2 a) A perspective.
Body Shop was founded with a strong ethical view of how a business should be conducted (the “perspective”). Its staff and its customers strongly relate to that perspective. The takeover of Body Shop by a company having a completely different perspective could undermine the motivation of staff and put off customers if both groups believe Body Shop’s values would not be respected. As a result, the takeover could lead to a loss for L’Oreal.
b) L’Oreal’s strategy is by external expansion by takeover. External expansion happens when a firm engages with another either by merger or strategic alliance.
Question 3: Consider the following diagram where a perfectly competitive firm faces a price of $40. a) The profit-maximizing output is 67 because this is the point where the price equals the marginal cost. b) The average total cost is equal to $31 and the average variable cost is equal to around $26. c) The total revenue is equal to PxQ, TR=$40×67=$2680, and the total profit is TRTC=$40×67-$31×67=$2680-$2077=$603 Question 4 a) In a noncooperative game the players do not formally communicate in an effort to coordinate their actions. They are aware of one another’s existence, and typically know each other’s payoffs, but they act independently.
The primary difference between a cooperative and a noncooperative game is that binding contracts, i. e. , agreements between the players to which both parties must adhere, is possible in the former, but not in the latter. An example of a cooperative game would be a formal cartel agreement, such as OPEC, or a joint venture. A noncooperative game example would be a research and development race to obtain a patent. b) A Nash equilibrium is an outcome where both players correctly believe that they are doing the best they can, given the action of the other player.
A game is in equilibrium if neither player has an incentive to change his or her choice, unless there is a change by the other player. The key feature that distinguishes a Nash equilibrium from an equilibrium in dominant strategies is the dependence on the opponent’s behavior. An equilibrium in dominant strategies results if each player has a best choice, regardless of the other player’s choice. Every dominant strategy equilibrium is a Nash equilibrium but the reverse does not hold. c) A maximin strategy is one in which a player determines the worst outcome that can occur for each of his or her possible actions.
The player then chooses the action that maximizes the minimum gain that can be earned. If both players use maximin strategies, the result is a maximin solution to the game rather than a Nash equilibrium. Unlike the Nash equilibrium, the maximin solution does not require players to react to an opponent’s choice. Using a maximin strategy is conservative and usually is not profit maximizing, but it can be a good choice if a player thinks his or her opponent may not behave rationally. The maximin solution is more likely than the Nash solution in cases where there is a higher probability of irrational (non-optimizing) behaviour.
Question 5 The curve is backward bending because it reflects the main trade-off between work and leisure at different levels of wages. The more hours worked, ie, the more leisure is given up in favour of work, the higher the income. So the worker substitutes leisure for work, up to the level of wage W1. This is called the substitution effect. When the wage is higher than W1, then the worker may feel that she/he needs to work less hours to achieve the same income. Alternatively, if the wage is higher than W1 the worker may feel that the leisure time she/he is giving up is more valuable than labour income.
Part 2 Question 1 a) The 2 strategies are (a) try to achieve cost reductions by seeking economies of scale, hence the spate of mergers between brewers and b) diversification into other related businesses such as hotels and restaurants. Strategy a) aims to work on the cost side of the equation and b) seeks to enhance the income side. b) The dangers are twofold. First, there is a limit to the gains in terms of cost reductions that can be made from economies of scale in the brewing industry. There could be also objections from the competition authorities to too much horizontal integration in the brewing industry.
Second, the skills necessary to succeed in the brewing industry are not necessarily transferable to the hotel and restaurant business. So diversification can actually backfire and result on losses. Question 2 Suppose that two identical firms produce widgets and that they are the only firms in the market. Their costs are given by C1 = 60Q1 and C2 = 60Q2, where Q1 is the output of Firm 1 and Q2 the output of Firm 2. Price is determined by the following demand curve: P = 300 – Q where Q = Q1 + Q2. Cournotprofit a. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium.
Profit for Firm 1, TR1 – TC1, is equal to ?1 = 300Q1 ? Q12 ? Q1Q2 ? 60Q1 = 240Q1 ? Q12 ? Q1Q2 . Therefore, ?? 1 = 240 ? 2 Q1 ? Q 2 . ? Q1 Setting this equal to zero and solving for Q1 in terms of Q2: Q1 = 120 – 0. 5Q2. This is Firm 1’s reaction function. Because Firm 2 has the same cost structure, Firm 2’s reaction function is Q2 = 120 – 0. 5Q1 . Substituting for Q2 in the reaction function for Firm 1, and solving for Q1, we find Q1 = 120 – (0. 5)(120 – 0. 5Q1), or Q1 = 80. By symmetry, Q2 = 80. Substituting Q1 and Q2 into the demand equation to determine the equilibrium price:
P = 300 – 80 – 80 = $140. Substituting the values for price and quantity into the profit functions, ? 1 = (140)(80) – (60)(80) = $6400, and ? 2 = (140)(80) – (60)(80) = $6400. Therefore, profit is $6400 for both firms in the Cournot-Nash equilibrium. b. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm’s profit. Given the demand curve is P = 300 – Q, the marginal revenue curve is MR = 300 – 2Q. Profit will be maximized by finding the level of output such that marginal revenue is equal to marginal cost: 300 – 2Q = 60, or Q = 120.
When total output is 120, price will be $180, based on the demand curve. Since both firms have the same marginal cost, they will split the total output equally, so they each produce 60 units. Profit for each firm is: ? = 180(60) – 60(60) = $7200. c. Suppose Firm 1 were the only firm in the industry. How would market output and Firm 1’s profit differ from that found in part (b) above? If Firm 1 were the only firm, it would produce where marginal revenue is equal to marginal cost, as found in part (b). In this case Firm 1 would produce the entire 120 units of output and earn a profit of $14,400. . Returning to the duopoly of part (b), suppose Firm 1 abides by the agreement, but Firm 2 cheats by increasing production. How many widgets will Firm 2 produce? What will be each firm’s profits? Assuming their agreement is to split the market equally, Firm 1 produces 60 widgets. Firm 2 cheats by producing its profit-maximizing level, given Q1 = 60. Substituting Q1 = 60 into Firm 2’s reaction function: Q2 = 120 ? 60 = 90. 2 Total industry output, QT, is equal to Q1 plus Q2: QT = 60 + 90 = 150. Substituting QT into the demand equation to determine price:
P = 300 – 150 = $150. Substituting Q1, Q2, and P into the profit functions: ? 1 = (150)(60) – (60)(60) = $5400, and ? 2 = (150)(90) – (60)(90) = $8100. Firm 2 increases its profits at the expense of Firm 1 by cheating on the agreement. Question 3 a) None of the firm has dominant strategy. If firm A chooses to produce small cars, it will only make a profit if firm B chooses to produce small cars as well. If firm B chooses to produce big cars, firm A makes a loss. Analogously, if firm B chooses to produce small cars and firm A chooses to produce big cars, firm B makes a loss.
In summary, in this game the outcome (loss or profit) always depends on the action of the competitor. The optimal strategy for any of the two firms is to adopt exactly the same production strategy as the competitor, either by chance or by collusion. c) There are two Nash equilibria, one is “big cars, big cars” i. e. , both firms produce big cars. The other Nash equilibrium is “small cars, small cars” d) The Nash equilibrium is for both players to choose the “Do Nothing” strategy. The game tree is indicated below. b) Question 4 a) Their MRP would increase and hence the demand for them would increase.
Thus it is possible that minimum wage rates could lead to an increase in employment (or, at least, no decrease). b) (a) No. It may encourage the firm to invest more in the latest technology, which in the long run may give it a competitive advantage over its rivals and therefore gain a larger share of the market. Thus reducing the number of workers per unit of output may be more than compensated for by a greater number of units sold. (b) No. If the government were to invest more in training, thereby increasing the marginal revenue product of workers, firms would find it profitable to employ workers at a higher rate of pay.
Also, if firms invest more in modern technology, this could give a boost to the economy, leading to a growth in output and firms in general taking on more labour. Question 5 Sal’s satellite company broadcasts TV to subscribers in Los Angeles and New York. The demand functions for each of these two groups are QNY = 60 – 0. 25PNY QLA = 100 – 0. 50PLA where Q is in thousands of subscriptions per year and P is the subscription price per year. The cost of providing Q units of service is given by C = 1000 + 40Q where Q = QNY + QLA. profita.
What are the profit-maximizing prices and quantities for the New York and Los Angeles markets? Sal should pick quantities in each market so that the marginal revenues are equal to one another and equal to marginal cost. To determine marginal revenues in each market, first solve for price as a function of quantity: PNY = 240 – 4QNY, and PLA = 200 – 2QLA. Since the marginal revenue curve has twice the slope of the demand curve, the marginal revenue curves for the respective markets are: MRNY = 240 – 8QNY , and MRLA = 200 – 4QLA.
Set each marginal revenue equal to marginal cost, which is $40, and determine the profit-maximizing quantity in each submarket: 40 = 240 – 8QNY, or QNY = 25, and 40 = 200 – 4QLA, or QLA = 40. Determine the price in each submarket by substituting the profit-maximizing quantity into the respective demand equation: PNY = 240 – 4(25) = $140, and PLA = 200 – 2(40) = $120. b. As a consequence of a new satellite that the Pentagon recently deployed, people in Los Angeles receive Sal’s New York broadcasts, and people in New York receive Sal’s Los Angeles broadcasts.
As a result, anyone in New York or Los Angeles can receive Sal’s broadcasts by subscribing in either city. Thus Sal can charge only a single price. What price should he charge, and what quantities will he sell in New York and Los Angeles? Sal’s combined demand function is the horizontal summation of the LA and NY demand functions. Above a price of $200 (the vertical intercept of the LA demand function), the total demand is just the New York demand function, whereas below a price of $200, we add the two demands: QT = 60 – 0. 25P + 100 – 0. 50P, or QT = 160 – 0. 75P. Solving for price gives the inverse demand function:
P = 213. 33 – 1. 333Q, and therefore, MR = 213. 33 – 2. 667Q. Setting marginal revenue equal to marginal cost: 213. 33 – 2. 667Q = 40, or Q = 65. Substitute Q = 65 into the inverse demand equation to determine price: P = 213. 33 – 1. 333(65), or P = $126. 67. Although a price of $126. 67 is charged in both markets, different quantities are purchased in each market. QNY = 60 ? 0. 25(126. 67) = 28. 3 , and QLA = 100 ? 0. 50(126. 67) = 36. 7. Together, 65 units are purchased at a price of $126. 67 each. c. In which of the above situations, (a) or (b), is Sal better off?
In terms of consumer surplus, which situation do people in New York prefer and which do people in Los Angeles prefer? Why? Sal is better off in the situation with the highest profit, which occurs in part (a) with price discrimination. Under price discrimination, profit is equal to: ? = PNYQNY + PLAQLA – [1000 + 40(QNY + QLA)], or ? = $140(25) + $120(40) – [1000 + 40(25 + 40)] = $4700. Under the market conditions in part (b), profit is: ? = PQT – [1000 + 40QT], or ? = $126. 67(65) – [1000 + 40(65)] = $4633. 33. Therefore, Sal is better off when the two markets are separated.
Under the market conditions in (a), the consumer surpluses in the two cities are: CSNY = (0. 5)(25)(240 – 140) = $1250, and CSLA = (0. 5)(40)(200 – 120) = $1600. Under the market conditions in (b), the respective consumer surpluses are: CSNY = (0. 5)(28. 3)(240 – 126. 67) = $1603. 67, and CSLA = (0. 5)(36. 7)(200 – 126. 67) = $1345. 67. New Yorkers prefer (b) because their price is $126. 67 instead of $140, giving them a higher consumer surplus. Customers in Los Angeles prefer (a) because their price is $120 instead of $126. 67, and their consumer surplus is greater in (a).
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