Q1. Suppose there are two firms with one demand function. This same (common) demand function is:
Q = 1,000 - 40P; P = 25 - 0.025Q & MR = 25 - 0.05Q
However, each firm has its own cost function. These two different cost functions are shown below respectively: Note: variable cost (VC) = MC in a linear (straight line) cost equation.
Firm 1: TC = 4,000 + 5Q
Firm 2: TC = 3,000 + 7Q
a. What are the optimum prices (Ps) and quantities (Qs) for each firm? Which firm, firm #1 or firm #2 produce more and why?
b. If price war breaks out, price will fall. Two most likely prices are $13 and $12, which is around breakeven quantity (BEQ) of two cost functions. Which firm, firm #1 or firm #2, is more vulnerable to price war when P = $13 why?
c. Which firm, firm #1 or firm #2 is more vulnerable to price war when P = $12 and why?
d. What are the factors that played the role in your answer in (b) and (c)?
e. Long run average cost curve decreases when there is an economy of scale (when LRAC curve negatively sloped.) What is the implication of your answer in (b) and (c) for the shape of long run average cost curve? Read about LRAC curves Fig 7.9, 7.10, and 7.11
Q2. 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 expected that competitors will follow the price action of the firm, the demand curve is of the form: Q = 44 - 3P (2) with MR = 14.66 - 0.66Q [from HW]
a. Find the price and the quantity at the intersection of two demand curves with a kink.
b. Identify the portions of the two demand curves, with "L shape above the kink" and the portion of the other two demand curves with "reverse L shape below the kink."
Discuss the difference in implication behind the portions of two demand curves, one "L shape" above the kink and the other "reverse L shape" below the kink. Explain which one is considered to be "optimistic" and which one, "pessimistic" and why?
c. Calculate the range of marginal revenues on the vertical portion of the MR curves at the level of output where there is a 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, similar 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? Why or why not?
e. What would happen to the price and the quantity implied above 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 questions asked so far?
Q3. White Mountain Ski Resort (WMSR) has the following demand equations for its customers.
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)
And MC=$10 for all the skiers.
a. Suppose that WMSR charges one price for all skiers. What would be that one price?
b. Assuming that there is no fixed, what would be operating profit from that one price strategy above? Use Q(P - VC) operating profit.
c. The manager of WMSR suggested the company would do better if they choose two different pricing strategies than one price strategy above. Without crunching any number, what is his reasoning? Please explain why.
d. If the company decided to charge two different prices for local and out of town skiers, what would be the respective prices and respective number of skiers?
e. Compute operating profit from these two pricing strategies, and compare it to the operating profit for one price strategy and discuss the differences and why
f. 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?
g. What would be the price to charge if the maximum number shows up.
h. 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 This question is akin to' martine' pricing (daytime show at discounted price) of Broadway Show in NYC
Q4. 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 Discount
No Discount ($10mil, $10mil) (-$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. What are the optimum strategy for each, the resulting profit/loss for each and why?
b. 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?
c. How would you compare this case to the so called "prisoner's dilemma" case? Explain it clearly.
d. How would you compare this case to the so called "Nash Equilibrium"? Explain the difference between this case and Nash Equilibrium clearly.
e. 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?
f. 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.
Baumont Corporation
No Discount Discount
No Discount ($10mil, $10mil) (-$4mil, $8mil)
Ace Corporation
Discount ($8mil, - $4mil) ($4mil, $4mil)
What would be the optimum strategy for each and why?
g. 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.
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.
Q5. 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. Compare operating profit, Q x (P - V), of duopoly and monopoly in presenting your argument.
f. Suppose that the two firms under the above duopoly have now two different demand curves, 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.
Q = 200 - 5P; P = 40 - 0.2Q and MR = 40 - 04Q
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),
c. What should the firm do in the face of a new demand schedule shown in (b) in the short run? You need to crunch some number in answering this question.
d. In your answer in (c), what kind of strategies you need to consider for the long run decision and why, based upon the numbers you got in (c)?
e. It is sometimes said that a firm has to be "good and 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.