irst Midterm Examination
February 27, 2001

Do all work on the examination.  If you use the back of a page, indicate you have done so.

 

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First Part (10 point questions

1.       Explain whether you agree or disagree with this statement.  In equilibrium, the last little bit of satisfaction derived from all goods must be equal.

2.       The demand function for a product is Q = 2000 – 40P.  Compute the point price elasticity of demand at P = 20.

3.       Smith now works 40 hours a week for $5 an hour.  (He could work more or fewer hours, but the pay rate is set)

·        He is offered a new job where he can choose the number of hours he works.  He will be paid $6 an hour for the first 20 hours, and $4 an hour after that.   Will he take it?  Why or why not?

·        Suppose he had instead been offered a new job where he can choose the number of hours he works, but with the pay set at $4 an hour for the first 20 hours and $6 an hour after that?  Would he take that?  Why or why not?

4.       Explain whether you agree or disagree with the following statement: In underdeveloped countries, many activities done by machine in the United States are done by hand.  This reflects different production technologies.

5.       Explain whether you agree or disagree with the following statement: In the United States real income per capita income has risen over time, whereas the number of domestic servants per capita has fallen.  That means domestic service is an inferior good.

Second Part (25 point questions)

Directions:  Work any two (2) of the following three (3) questions.  In the boxes below, check which problems you have worked:  If you do not check the boxes, I will assume you want to work problems 1 and 2.

I have worked(Check 2)

Problem 1

 

Problem 2

 

Problem 3

 

1.       Acme Widgets has a single plant, whose average cost function is

C=9800 +30q + 8q2

 

(a)   What level of output minimizes Acme’s Average Cost?

(b)   What is the marginal cost when q = 70?

(c)    A new technology for producing widgets has been developed.  It is now possible for Acme to build new plants whose cost function is given by the following table

Q

C

0

800

1

1000

2

1100

3

1200

4

1400

5

1750

6

2250

7

2800

 

Assume Acme wants to continue to produce 70 widgets.  Given time to build and operate the new plants, how many widgets should it continue to build at its old plant.

2.  In the Emerald City, public water is currently free.  Next year the projected demand for water is 100,000 gallons per household per year.  But the projected capacity of the Emerald City’s water system is only 80,000 gallons per household per year.  Two plans are proposed.  One is to build a new pumping plant, which will provide another 20,000 gallons per household per year of capacity.  The cost of building and operating that plant will be $30 per household per year; the plan is to cover the costs of the plant by billing households $30 per year for the water rights (i.e., a lump sum pricing system).  The second proposal is to begin charging households by the gallon for water they use.

A team of eminent econometricians has estimated the demand curve for water as of next year.  They report the following demand curve:

q = 100 - 20p

where

q = demand by household in thousands of gallons per year and

 p = price in dollars per thousand gallons.

In answering this question, you may assume that (a) all households are identical, (b) the demand curve is accurate, and (c) all households are connected to the water system.

·        One fear is that, faced with a charge for water, some citizens will elect to stop using city water and hence save the $30 charge.  Do the calculation that will either validate or assuage this fear.  (Remember, this is a question in economics, not medicine).

·        A price of $1 per thousand gallons will reduce demand to 80,000 gallons per household per year; the annual water bill will then be $80 per household.  Which scheme do you think households would prefer? Why?  (Remember that the citizens have all taken a course in economics and understand the concept of Dead Weight Loss; they will prefer the price rationing plan if DWL is less than the cost of the plant)

3.    Last week, Arthur Hart appeared on Who Wants to be a Millionaire.  As time ran out, he successfully answered the $500,000 question.   If he appears next week, he will be asked a question worth $1,000,000.  If he answers it correctly, he will get $1,000,000; if he answers it incorrectly, he will get the $32,000 consolation prize.  Art must make an irrevocable decision of whether to take his $500,000 winnings or reappear.  If he reappears, he firmly believes that he has a 1/3 chance of answering correctly.  For peculiar reasons, he does not have the option of quitting if, after he is asked the question, he thinks it too hard:  he would walk way with either $32,000 or $1,000,000.  (I know I have stated some rules of the show incorrectly and probably stated some other rules incorrectly as well.  Answer the question according to my rules.)

Of course, Art has calculated his utility from different levels of income as follows:

Income

Utility

32,000

8,000

500,000

22,000

1,000,000

28,000

 

·        Should Art fish or cut bait?  Should he come back or take his winnings?  Show your work?

·        The producers of the show want to make it interesting.  They can affect the probability of Art’s winning by altering the difficulty of the question.  What probability would leave Art indifferent between appearing and not appearing?