Instruction: There Are Four Questions, Each Carrying the Same Points

Instruction: There are four questions, each carrying the same points. Answer any of three of them. Budget your time wisely.

1. Answer both parts.

(a) The Department of Economics allots to each faculty member a $1,000 annual budget used only for long-distance telephone calls. Assume that each faculty member spends his/her entire budget and no more or less. What is the faculty’s own-price elasticity of demand for department-provided long-distance telephone service?

(b) The MEcon program is planning for its twentieth anniversary buffet for its members (staff and students). The event is non-compulsory. Its members have equal number of small eaters and large eaters; the cost of serving each eater and the maximum payment each eater is willing to make, respectively, are as follows.

Small eater / Large eater
cost of serving / $40 / $120
maximum willingness to pay / $60 / $160

Since it is unable to tell the identity of each member, the event has to charge each buffet participant the same price. The program organizer also wants the event to break even (i.e., revenue equals costs).

Comment on the following remark by the program organizer:

“Since the number of small eaters equals the number of large eaters, the average cost of serving an eater is the average of $40 and $120, i.e., $80. Therefore, in order to break even, we should charge $80 for each buffet participant.”

2. A monopolist has two plants with the following total costs:

where and are outputs in the two plants. His demand curve is

where How much output (if any) will be produced in each plant? What price will be charged? Show your results graphically including the numerical values for and

3. Refer to the extensive game in the diagram.

(a) Find all the subgame perfect equilibria by backward induction.

(b) Construct the associated normal form game of the extensive game.

4. The game has two players: a criminal (C) and the government (G). The government selects a level of law enforcement, which is a number The criminal selects a level of crime, These choices are made simultaneously and independently. The government'spayoff is given by

where is the negative effect of crime on society and is the cost of law enforcement, per unit of enforcement. The number c is a positive constant. The criminal's payoff is given by

where is the value of criminal activity when the criminalis not caught, whereas is the probability that the criminal is not caught.

(a) Find the best-response functions. Graph the best-response functions.

(b) Compute the Nash equilibrium of this game.

End of Exam