1.    Suppose an airline flying on the Charlotte - Chicago route has estimated the demand curves for three di?erent types of customers: business (no advance purchase), leisure (7 day advance puchase), and discount (14 day advance purchase) travellers. They are: Business: P = 600 − Q and MR = 600 − 2Q Leisure: P = 500 − 2Q and MR = 500 − 4Q; Discount: P = 400 − 3Q and MR = 400 − 6Q. Assume there is only one class of service, hence the marginal cost of providing the service is equal for all customers and is $100. What prices will the airline charge to each of the three diferent segments of customers. (Hint: Set MR=MC for each class of travel). 

2. The relationship between Price elasticity of demand and Marginal Revenue

can be shown to be:            

MR = P 1 −    1 |e|        

There are two types of customers that come to the Barnegat Fish Company to have their signature crabcakes: An a?uent group with a price elasticity of demand for crabcakes of e = −2; and a less wealthy type with a price elasticity of demand for crabcakes of e = −5. The restaurant wants to introduce a coupon to encourage more people to visit their restaurant. Thus every buyer pays the posted price of $P per crabcake but those who tender the coupon get a discount of $X o? the posted price. If the Marginal Cost of a crabcake is $2.00, what is the price of the crabcake and what is the value of the coupon?(Set MR=MC).

3.    Consider a model of two firms (Firm 1 and Firm 2)competing against each other and setting prices simultaneously. Suppose they have a choice of setting either P = $5 or P = $8. If both of them set the lower price they split the total profits of $44 equally(i.e. each of them gets $22). If they both set the higher price, they split the total profits of $82 equally(i.e. each of them gets $41). However, if one of them charges the lower price while the other firm charges the higher price, the lower price firm earns a profit of $60, while the other firm earns a profit of $14. The payo? matrix is given below. Does Firm 1 and 2 have a dominant strategy each? What is the Nash Equilibrium? Explain briefly.

        Strategies    for Firm 2

        $5    $8

Strategies    $5    (22, 22)    (60, 14)

for Firm 1    $8    (14, 60)    (41, 41)