Final Exam

Directions: The examination is closed book and closed notes.
Do all work on the exam itself.  If you cannot answer the problem
in the assigned space, answer on the back of the exam,
indicating that you have done so.

 

 

Name                                                                                                                                      

 

 

 

1a

1b

1c

1d

2a

2b

2c

2d

2e

3

4

5

 

Problem 1 (20 %)

(a)   A commodity has a demand function Q = 18-2P.  The good costs $3 to produce.  Compute the deadweight loss of a $2 tax on the commodity

(b)   A profit maximizing monopolist sells a product for $10; production costs are $6.  What is the price elasticity of demand?

(c)    John Smith has the following utility as a function of wealth:

                          Wealth            Utility

                                 $60               1250

                                 $70               1400

                              $100               1900

He has $80 and is offered the chance to bet $20 on a coin toss.   Will he take the bet?  Why or why not?

(d)   A commodity has a demand function Q = 800 – 20P.  Compute the arc price elasticity when Q changes from 400 to 200:

Problem 2 (35%)

This is a series of short answer questions:

 

a)     Ethyl Wilson has income of $300,000.  The figure above shows her utility U as a function of income Y.  I have plotted three dotted lines showing income of $200,000, $250,000 and $300,000.  (I deleted the 000 ).   There is a 50% chance that she will suffer a loss of $100,000.   Using this graph, indicate the maximum amount she will be willing to pay for insurance against this risk.  Explain and defend your answer. Hint: you will want to draw a couple of lines.  It will not be enough to simply label a point and say “this is it”.

 

b)     John Smith has a job selling shoes. Right now he works 50 hours a week, and he gets paid $20 an hour for the first 40 hours and $30 an hour for the overtime, for a total of $1100 a week. He is offered a new job selling shoes. He will be paid $22 an hour and he can work as many or as few hours as he wishes. Will he take the job? And if he does so, will he work more or fewer hours? Explain your answer using indifference curves

c)      Studies have shown that part-time (night) students place less demand on a university’s resources than full-time (day) student.  To give examples, they use less of faculty time, computer time, and library time.  Since they cost less to serve, it seems obvious that part-time tuition rates should be less per course than full-time rates.  Explain whether you agree or disagree

d)     If a demand function shifts to the right when the demand for another product rises, it is a superior good.  Explain whether you agree or disagree.

e)      A firm finds that the cost of a machine it uses in its production processes goes up.  Holding the level of production constant, this means that total cost and marginal cost will both rise.   Explain whether you agree or disagree.

Problem 3 (15%)

 

You have invented a new home burglar alarm system.  You plan to franchise the system to independent retail outlets.  Customers purchase alarm systems infrequently, and so they have little information.  You are fearful your franchisees will strive for short-term profits.  While you should try to monitor the installations of individual franchisees, it would be very expensive.  Assume that the retailers are price-taking firms and use the Klein-Leffler theory to explain how many franchises you would issue to prevent cheating.

 

Problem 4 (15%)

 

The industry demand curve for widgets is given by

 

Q = 360 - 8 P

 

Initially there are eight plants producing widgets. Each plant belongs to a different firm. (Indeed, there is a law restricting each firm to one plant). Each plant has a cost function

16 + q2

 

where q is the number of widgets produced by each plant.

 

a.      Assuming initially that only these eight firm/plants may produce widgets, determine the equilibrium price and quantity of widgets.

b.      Now assume that other firms may open a (single) plant and produce widgets if they wish. If they do, their cost function will be the same as the eight plants. What will be the equilibrium price and quantity of widgets? How many new plants will be built?

c.       Acme Widgets is given a monopoly in the production and sale of widgets?  How many plants will it operate?  How many widgets will it sell?  At what price?

d.      As you can tell, the Acme Widget monopoly makes a bundle.  The government decides to tax the monopoly.   There are two proposals.  One is to levy a tax of $1 on each widget sold.  The other is to impose a tax of 25% on Acme’s profits.   For each tax, compute the effect on the price the consumer pays for widgets and the number produced.

 

Problem 5 (15%)

 

The demand for a particular product is Q = 100 – P.  Two firms produce the product, at a marginal cost of $5 a unit. 

 

a)     Assuming the two firms can collude, and jointly agree on a price to maximize their combined profits what will be the price of the product?

b)     Such collusion is a violation of the law.  Legal issues aside, what barriers would you foresee to maintenance of any collusive agreement?

c)      Assuming the two firms split the market as a Cournot Duopoly, what will be the price of the product?

d)     If a third firm enters and turns the market into a Cournot “Triopoly”, what will be the price of the product?

e)      Explain why a Cournot Duopoly could be a Nash Equilibrium