ECONOMICS

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)

And MC =  $10 for all the skiers.

1. 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.

1. 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.

1. Who does WMSR attract more, local or out of town skiers at that one price for all and why?

1. Assuming that there is no fixed cost involved for simplicity, what would be total profit from that one price strategy above?

1. 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.

1. 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?

1. How many local and out of town customers would White Mountain Ski Resort be able to attract from this two tier pricing strategy?

1. 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.

1. 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?

1. What would be the price to charge if the maximum number shows up.

1. 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.

 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               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 million 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.