Economics 3130 – Fall 2008 – PRELIM 1 - J. Wissink – Wednesday October 8

Directions: ANSWER ALL THE QUESTIONS. Write legibly, concisely, and coherently. Be sure to label all axes, functions, and variables you use. READ QUESTIONS CAREFULLY. Draw pictures whenever possible. Show all your work! Total time for the test is 50 minutes. Total points on test = 100. Each question is worth 20 points.
TURN IN THESE EXAM QUESTIONS WITH ANSWERS.
Please print your name here: ______

1.  Horace consumes only Beans and Carrots (B and C) measured in ounces. Part of his indifference curve map is illustrated.

a.  Write down a utility function that would be an acceptable representation of his preferences.

b.  Some would say that Horace’s preferences are convex; others would say they are not. In what way are they convex? In what way might you say they are not? Are Horace’s preferences monotonic? Explain briefly.

c.  In general, i.e., for any values of prices for beans and carrots, $PB, $PC and income $I, what is the function for the optimal amount of Beans, B*(.), in Horace’s utility maximizing bundle?

d.  Suppose $PB=$PC=$1. What is the value of Horace’s marginal utility of income?

2.  Suppose Prof. Douglas gets utility from only wine (W) and cheese (C). Suppose his preferences can be represented by a Cobb-Douglas utility function.

a.  Write down a plausible utility function for Prof. Douglas.

b.  Suppose Prof. Douglas has income “I” and suppose the prices for wine and cheese are $Pw and $Pc. Find Prof. Douglas’ demand system. Show a wee bit of work so we know you know what you are doing.

c.  Using the notation developed in class (but applied to THIS problem), write down any TWO equations from Prof. Douglas’ set of Slutsky equations and indicate the “sign” of each term in your Slutsky equations.

d.  On a sufficiently detailed indifference curve budget line diagram, illustrate Prof. Douglas’ income offer curve. Put WINE on the horizontal and CHEESE on the vertical.

e.  On a SEPARATE and sufficiently detailed indifference curve budget line diagram, illustrate Prof. Douglas’ total, income and substitution effects for an increase in the price of WINE. Put WINE on the horizontal and CHEESE on the vertical.

3.  Consider a day in the life of Julia. She has 24 hours each day to allocate to either leisure hours (Z) or labor hours (L). Julia sells labor hours to the market for an hourly wage rate ($w). Labor income is Julia’s only source of income. Julia has very nicely behaved preferences over leisure (Z) and $all other goods ($aog). Suppose, originally, that Julie maximizes her utility by working 12 hours each day.

a.  Graph Julia’s initial position on an indifference curve-budget line diagram putting Z on the horizontal axis and $aog on the vertical axis.
Now suppose that a law is passed that prohibits women from working more than 8 hours a day, since they are needed at home to care for their children and husbands and houses.

b.  What impact would such a law have on Julia’s budget line? Show in your graph.

c.  What impact would such a law have on Julia’s choice of hours to work? Show in your graph.

d.  Does Julia end up on a higher or lower indifference curve? Show in your graph.

e.  If Julia could pay the government (that is lobby the government with cash) to prevent the imposition of this law, what is the maximum she would willingly pay? Show in your graph.

f.  How is your answer above related to the notions of surplus measures we introduced in lecture?

4.  Suppose that the market demand curve for apples and the market demand curve for oranges are both linear. Suppose that in both markets the current market equilibrium price is such that $Po = $Pa. Suppose it is also the case that at the current market equilibrium price the equilibrium number of apples consumed equals the equilibrium number of oranges consumed, that is A* = O*. At this equilibrium point suppose that the demand for apples is relatively more price inelastic than the demand for oranges.
For which demand curve will an identical price decrease cause a larger gain in ordinary market Dupuit consumers’ surplus? Illustrate using market demand curves.

5.  Consider Buster’s two period consumption model like the one illustrated in class. All income is earned and Buster has utility over consumption dollars when he is young and when he is old. Assume Buster’s endowment of income is the same when he is young compared to when he is old. Suppose interest rates are currently quite low and that Buster is a borrower when he is young. Now suppose interest rates shoot up.

a.  Putting “young” on the horizontal and “old” on the vertical axes, illustrate Buster’s original position in an indifference curve budget line diagram.

b.  Illustrate what happens to Buster’s inter-temporal budget line after the interest rate shoots up.

c.  Does Buster HAVE TO remain a borrower after the interest rate increase? Briefly defend.

d.  Based only on the limited information given, can we know if Buster is better off or worse off after the interest rate increase? Briefly defend your position using your graph.
Have a great Fall Break, if I don’t see you on Friday!

e1_313_f08_v2.doc