重点是第二道题和第四道题，不必要全都解答出来。可以把答案发到我的幽香dechelen@gmail.com

                            

                                                     Final Examination

                                               (Cumulative up to Ch. 9)

1.   Suppose there are three firms with one demand function. This same (common) demand function is:                              

                                 

                   Q = 1,000 – 40P         with   MR = 25 – 0.05Q

However, each firm has its own cost function which is different. These three different cost functions are shown below respectively:

                                        Firm 1:   4,000 + 5Q

                                        Firm 2:   3,000 + 5Q

                                        Firm 3:   3,000 + 7Q

What price should each firm charge if it wants to maximize its profit (or minimize its loss)? Why are price and output of each firm between firm 1 and 2 but different in the case of firm 3? Explain. Is fixed cost relevant in their price determination or not? Explain why clearly. Discuss advantage and disadvantage of cost structure between firm 1 and firm 3.   If price war breaks out, most likely price will fall. Two most likely prices as a result are $13 and $12. Which company, firm 1 and firm 3, is more vulnerable to price war when P = $13? Which company, firm 1 or firm 3 is more vulnerable to price war when P = $12 Would the company most vulnerable change between your answer in (e) and (f) above? If it does, please explain reason for the difference in your answer between (e) and (f).

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. However, 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

a.        Calculate the range of marginal revenues on the vertical portion of the MR curves at the level of output where a kink 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.        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. 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?

d.       What would happen to the price and the quantity demanded implied above in the kinked demand curves if production cost for the whole industry increases due to a tighter environmental restriction? 

e.        How would your answer in (d) change if the cost increase, which still falls within the vertical range of MR curves, was only for one oligopolistic firm in the industry?

3.   White Mountain Ski Resort 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.

Suppose that White Mountain Ski Resort 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. 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 you 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. Assuming that there is no fixed cost involved for simplicity, what would be total profit from that one price strategy above? 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. 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? How many local and out of town customers would White Mountain Ski Resort be able to attract from this two tier pricing strategy? 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 the differences.

 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.

                                                                               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 for your convenience.                       

       

                                                                                    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.

5.   The Plymouth Software Company has the following demand curve with MC =  $10 and  P = 100 – Q with MR = 100 – 2Q. 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)

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 and discuss the difference in terms of Pareto’s optimality from a societal point of view.

c.       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.

d.      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.

e.       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 without quantitative support?