Economics Analysis homework help

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timer Asked: Aug 24th, 2014

Final Examination (Cumulative up to Ch. 9) 1. Suppose there are two firms with one demand function. This same (common) demand function is: [from HW] Q = 1,000 – 40P with MR = 25 – 0.05Q However, each firm has its own cost function which is different. These two different cost functions are shown below respectively: Firm 1: 4,000 + 5Q Firm 2: 3,000 + 7Q a. What price should each firm charge if it wants to maximize its profit (or minimize its loss)? Which firm, firm #1 or firm #2 intuitively (without solving the problem) would produce more and why, based upon the cost functions given above? Profit maximization will occur where the marginal revenue of the firm is equal to the marginal cost of the firm, so TC1 = 4000 + 5Q MC1 = 5 TC2 = 3000 + 7Q TC2 = 7 MR = 25 – 0.05Q Profit maximizing price of firm 1 25 – 0.05Q = 5 0.05Q = 20 Q = 400 Plugging the value of Q in the demand function we could find out the value of price Q = 1,000 – 40P 40P = 1000 – 400 P = 600/40 P = 15 Thus, the firm 1 will charge $15 as a price. 1 Profit maximizing price of firm 2 25 – 0.05Q = 7 0.05Q = 18 Q = 360 Plugging the value of Q in the demand function we could find out the value of price Q = 1,000 – 40P 40P = 1000 – 360 P = 640/40 P = 16 Thus, the firm 2 will charge $16 as a price. b. If price war breaks out, most likely price will fall. Two most likely prices in that event are $13 and $12. Which company, firm #1 and firm #2, is more vulnerable to price war when P = $13 and why? Which aspect of the cost functions given makes it more vulnerable? Profit = Total revenue – Total Cost Calculating profit for firm1 and firm2 when the price is equal to $13 Q = 1,000 – 40P Q = 1000 – 40*13 Q = 480 TR = P*Q = 480 * 13 = 6240 Firm 1: 4,000 + 5Q TC = 4000 + 5*480 = 6400 Firm 2: 3,000 + 7Q TC = 3000 + 3360 = 6360 Firm 1’s profit = 6240 – 6400 = - 160 Firm 2’s profit = 6240 – 6360 = - 120 The calculated values shows that the firm 1 is incurring more loss than firm 2 so we could say that the firm 1 is more vulnerable than firm 2 when the price level is equal to $13. 2 c. Which company, firm #1 or firm #2 is more vulnerable to price war when P = $12 and why? Again which aspect of the cost functions given makes it more vulnerable? Calculating profit for firm1 and firm2 when the price is equal to $12 Q = 1,000 – 40P Q = 1000 – 40*12 Q = 520 TR = P*Q = 520 * 12 = 6240 Firm 1: 4,000 + 5Q TC = 4000 + 5*520 = 6600 Firm 2: 3,000 + 7Q TC = 3000 + 3640 = 6640 Firm 1’s profit = 6240 – 6600 = - 360 Firm 2’s profit = 6240 – 6640 = - 400 The calculated values shows that the firm 2 is incurring more loss than firm 1 so we could say that the firm 2 is more vulnerable than firm 1 when the price level is equal to $12. d. In view of your answers in (b) and (c), discuss advantage and disadvantage of cost structure between firm 1 and firm 2. Hint: Consider FC and contribution margin. e. Long run average cost curve decreases when output elasticity is greater than one, i.e., negatively sloped. What is the implication of your answer in (b) and (c) for the shape of long run average cost curve? Hint: Read about LRAC curves Fig 7.9, 7.10, and 7.11 2. A firm in an oligopolistic industry has identified two sets of demand curve. If the firm is the only one that changes price (i.e., other firms do not follow), its demand curve takes the form: Q = 82 – 8P (1) with MR = 10.25 - 0.25Q. If it is 3 expected that competitors will follow the price action of the firm, however the demand curve is of the form: Q = 44 – 3P (2) with MR = 14.66 – 0.66Q [from HW] a. Calculate the range of marginal revenues on the vertical portion of the MR curves at the level of output where a kink in demand curves takes place. Identify the level of output where there is a kink in the demand curves. Call this portion of demand curves as “reverse L shaped portion” of the kink demand curves. b. Identify the other portion of the reverse L shaped kink demand curves (call it “L shaped portion” of the kink demand curves). Discuss the difference in the implications behind this “L shaped portion” and “reverse L shape portion” of the kinked demand curves. Explain which one is considered to be “optimistic” and which one, “pessimistic,” and why? c. Find the price at the kink each oligopolist would charge at the kink. . d. Suppose that there are two firms within this range under this oligopoly: one with higher MC (VC) but lower fixed cost and other with lower MC but higher fixed cost. Please refer to Prob. #1 above. But both MC’s are within the range of marginal revenue on the vertical portion of the MR. Would they charge the same or different prices at the kink given this new information? Why or why not? e. What would happen to the price and the quantity implied above in the kinked demand curves if production cost for the whole industry increases due to a tighter environmental restriction? f. How would your answer in (e) change if the cost increase, which still falls within the vertical range of MR curves, was only for one oligopolistic firm in the industry? In which case, in (e) or in (f) is price more likely to change and why? g. What does this kink demand curve example try to teach us in view of the various questions asked so far in this question? 3. White Mountain Ski Resort has the following demand equations for its customers. [Relating the final to Module I on D/S and Elasticity] The demand equation for the resort as a whole: Q = 1,000 -30P (P = 33.33 – 0.033Q with MR = 33.33 – 0.067Q) The demand equation for Out of Town Skiers: Qo = 500 – 10P (P = 50 – 0.1Q with MR = 50 – 0.2Q) The demand equation for Local Skiers: Ql = 500 – 20P (P = 25 – 0.05Q with MR = 25 – 0.1Q) 4 And MC = $10 for all the skiers. a. Suppose that White Mountain Ski Resort (WMSR) charges one price for all skiers, local as well as out of town skiers, what would be that one price? Please use two digits after dollar, say $10.52 in your answer. b. How many local and out of town skiers would White Mountain Ski Resort be able to attract at that one price for all? Please round up your number of customers in your answer. For instance, if your answer were 105.60, round it up to 106 customers and if 83.30, round it down to 83 customers. c. Who does WMSR attract more, local or out of town skiers at that one price for all and why? Please look at respective demand equations and tell me why. d. Assuming that there is no fixed cost involved for simplicity, what would be total profit from that one price strategy above? Use Q(P – VC) in your computation of profit. e. Would White Mountain Ski Resort be able to do better if the company chooses two different pricing strategy than one price strategy above, given the above information about its demand equations? Please provide quantitative basis for your answer prior to running number. This question is different from question (c) above. Hint: price elasticity. f. If the company decided to charge two different prices for local and out of town skiers, what would be the respective prices, one for local customer and the other for out of town customer? g. How many local and out of town customers would White Mountain Ski Resort be able to attract from this two tier pricing strategy? h. Compare potential profits from these two pricing strategies, one price for all and two different prices for local and out of town customers and discuss reason for the differences. Review your answer in (d). i. As a promotion for out of town skiers, WMSR decided to offer free skiing for first day if they stay more than one night at the resort hotel on its premise. What is the maximum number of skiers the company can expect if they are going to waive $10 marginal cost as incentive? Hint: this question is similar to 2c in first mid-term exam of Module One on D and S. j. What would be the price to charge if the maximum number shows up. Mind you that MC of $10 was waived in (i) as incentive. k. Suppose only one half of the maximum number of out-of-towners showed up and stayed one more night. Is this promotional free skiing for the first day a smart strategy assuming that the price charged was the one you found in (j)? Please do not consider the revenue from staying at the resort overnight for this calculation. This question is akin to martine’ pricing (daytime show at discounted price) of Broadway Show in NYC 5 4. Ace and Baumont Corporations make and sell electrical equipment. Both have to decide whether or not to discount. The payoff matrix of “Discount” and “Not to Discount” expressed in terms of profit (+) or loss (-) for each firm is given below for each combination of strategies. Read my lecture note on game theory Baumont Corporation No Discount No Discount ($10mil, $10mil) Discount (-$4mil, $16mil) Ace Corporation Discount ($16mil, -$4mil) (4mil, $4mil) In the above matrix, the first number is for Ace and the second, for Baumont respectively. a. b. c. d. e. f. What are the optimum strategy for each, the resulting profit/loss for each and why? Is there any other strategy better than the one they took in (a), which makes each firm better off as opposed to the strategy taken? If there is, why did they not take it? How would you compare this case to the so called “prisoner’s dilemma” case? Explain it clearly. How would you compare this case to the so called “Nash Equilibrium”? Explain the difference between this case and Nash Equilibrium clearly. Does it matter whether this is one-shot deal or meant to be a situation in which each corporation faces continuously for some time? Why or why not? Suppose that the profits for “discount strategy” for both Ace and Baumont are reduced to $8 millions from the current profit of $16 million respectively. The revised payoff matrix is shown below for your convenience. Baumont Corporation Ace Corporation g. No Discount Discount No Discount ($10mil, $10mil) (-$4mil, $8mil) Discount ($8mil, - $4mil) ($4mil, $4mil) What would be the optimum strategy for each and why? What fundamental changes took place in the revised matrix above, which made the situation quite different from the original payoff matrix at the beginning? Please be succinct and to the point in your explanation. 6 h. How does such a corporation as General Electric use the concept involved in the revised payoff matrix above in its marketing strategy? Be specific in your explanation. 5. The Plymouth Software Company has the following demand curve with MC = $10 and P = 100 – Q with MR = 100 – 2Q. The company has option of charging monopolist price or perfect competitor price. Here it is assumed that monopoly demand curve is identical with market demand curve of perfectly competitive market (i.e., they share the same demand curve): Read my lecture note on Pure Competition and Monopoly a. Compute profit maximizing price and output under perfectly competitive market and under monopoly. And compare the difference between them in terms of P and Q and discuss reason for the difference. b. Compute consumer surplus under perfect competition and monopoly. c. Is there any additional downside of monopolist vis-à-vis pure competition from a society’s point of view in terms of Pareto’s efficiency? Hint: reexamine consumer surplus discussed in (b). d. Many amusement parks charge entrance fee and separate fees for each ride. In view of the above discussion, what do you think is the reason for it? Hint: consider consumer surplus. e. What is the advantage for duopoly (two oligopoly firms) with equal size sharing the identical demand to behave as one monopolist and split the profit afterward rather than behave as two different firms under oligopoly? Under duopoly, each duopoly each firm would be able sell 30 units each. Present your arguments clearly with quantitative support for your answer. f. Suppose that the two firms under the above duopoly have now two different demand curves, not one identical market demand curve; one is more elastic than the other. Would it be still advantageous for them to behave as one monopolist or not? Why or why not? You do not need quantitative support in answering this question. 6. A firm has the following short run demand and cost schedule for a product. [from HW] Q = 200 – 5P TC = 400 + 4Q a. What are price, quantity and profit for this company? b. Suppose the above demand shifted to Q = 100 – 5P. If this is a firm under monopolistic competition, what a plausible reason is there for such a shift in view of your answer in (a), 7 c. What should the firm do in the face of a new demand schedule shown in (b) in the short run? Explain why. d. In your answer in (c), what kind of strategies you need to consider for the long run decision? e. It is sometimes said that a firm has to be either “good or lucky” in this kind of situation. Explain what is meant by this statement. Hint: Review the case history of Pepsi’ surviving strategy v Coke at the beginning of my lecture note. 8

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