Download Economics 313 - Fall 2004 – FINAL EXAM

Economics 313 – Fall 2007 – PRELIM 1 - J. Wissink – Thursday October 4
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 75 minutes. Total points on test = 100.
TURN IN THESE EXAM QUESTIONS WITH ANSWERS. USE SEPARATE EXAM BOOKLETS
FOR EACH SECTION: PART I, Part II and Part III.
Please print your name here: _____________________________________________________________
Part I: (12 points each)
PLEASE START A NEW ANSWER BOOKLET & LABEL IT PARI I and PUT YOUR NAME ON IT
1. Wilfred consumes only Tea and Honey (T and H) measured in ounces. Part of his indifference curve map is
illustrated.
a. Write down two utility functions that would be
equally good and acceptable representations of his
preferences.
b. Some would say that Wilfred’s preferences are
monotonic; others would say they are not. In what
way are they monotonic? In what way might you say
they are not? Are Wilfred’s preferences convex?
Explain briefly.
c. In general, i.e., for any values of prices for tea and
honey, PT, PH and income I, what is the function for
the optimal amount of Tea, T*(.), in Wilfred’s utility
maximizing bundle?
Helping Line
Tea
IC1
12
IC0
6
2
4
Honey
2. Suppose Venus gets utility from only X and Y. Her “Slutsky Equations” are thus: (Note: M refers to the
Marshallian/market demand responses where SSE refers to the Slutsky/compensated substitution effect
responses.
(∂X/∂Px)M = (∂X/∂Px)SSE + (-X)(∂X/∂I)M
(∂X/∂Py)M = (∂X/∂Py)SSE + (-Y)(∂X/∂I)M
(∂Y/∂Py)M = (∂Y/∂Py)SSE + (-Y)(∂Y/∂I)M
(∂Y/∂Px)M = (∂Y/∂Px)SSE + (-X)(∂Y/∂I)M
If Venus’s utility function is of the quasi-linear variety and equal to u = Y + √X (and she is always able to
consume a bundle with strictly positive amounts of both X and Y), then what are the signs of the following
terms in her Slutsky Equations, using all you know about this quasi-linear preference? NOTE: you can
choose + or – or 0 or “can’t know without more info”.
a.
b.
c.
d.
e.
f.
(∂X/∂Px)M
(∂X/∂Px)SSE
(∂X/∂I)M
(∂X/∂Py)M
(∂Y/∂I)M
(∂Y/∂Px)SSE
Part II: (12 points each)
PLEASE START A NEW ANSWER BOOKLET & LABEL IT PARI II and PUT YOUR NAME ON IT
3. Suppose that Fred’s Marshallian/market demand for grapes (G) is downward sloping and that he is currently
consuming 200 pounds of grapes at the prevailing market price of $1.00/pound of grapes. Suppose for Fred,
grapes are a normal good.
a. Suppose the price of grapes increases to $1.20/pound and consequently Fred demands only 100 pounds
of grapes. Estimate Fred’s own price elasticity of demand from this information using the arc formula.
For Fred, are grapes price elastic or inelastic?
b. FOR FRED, will the ordinary measure of change in Dupuit/Marshallian/market consumer's surplus
underestimate or overestimate the compensating variation of this price increase? Demonstrate using
appropriate Marshallian and Hicksian demand curves and appropriate areas.
4. Suppose both Abe and Betty have very nicely behaved Cobb-Douglas preferences. Suppose that Abe’s
utility function is: uAbe=f(X, Y). Suppose that Betty’s utility function is a monotonic transformation of
Abe’s. That is uBetty = g(f(X, Y)) where (dg/df) is positive. Suppose Px is the price of x and Py is the price
of y. Let IA be Abe’s income and let IB be Betty’s income and assume that IA ≠ IB. Suppose Abe and Betty
shop at the same store and face the same prices for X and Y.
Are the statements below true, false or uncertain? Defend your position. No/zero points will be awarded
for just saying true or false or uncertain.
a. Under the circumstances described above, Abe’s and Betty’s demand functions for X and Y will
always have the same functional form.
b. Under the circumstances described above, Abe and Betty will actually buy exactly the same number
of units of X and Abe and Betty will actually buy exactly the same number of units of Y.
c. Under the circumstances described above, Abe and Betty will have the same marginal utility of
income when consuming an optimal bundle.
5. Tom, Dick and Harry constitute the entire market for scrod. Tom’s demand curve is given by:
Xtom = 100-2P. Dick’s demand curve is given by Pdick = 40 - .25X. Harry’s demand curve is given by:
Xharry = 150 – 5P.
a.
b.
c.
d.
Graph each individual’s demand curve.
Graph the market demand curve and be as careful as you can.
What is the equation for the market demand curve?
What is the exact value of Dick’s own price elasticity of demand for scrod at a market price of P=$10
using the point formula?
Part III: (20 points each)
PLEASE START A NEW ANSWER BOOKLET & LABEL IT PARI III and PUT YOUR NAME ON IT
6. Suppose Carly Caffeine has the following utility function: u = $aog + C where C is ounces of coffee and
$aog is “$ on all other goods.” Let Paog = $1 and let Pc be price of coffee per ounce. Initially, suppose that
Pc < $1 and that Carly’s income is $25.
a. Graph Carly’s initial optimal bundle in an indifference curve – budget line diagram with coffee on the
horizontal axis.
b. What is the market/Marshallian demand function for coffee for Carly assuming income = $25 and Paog
= $1?
NOW… unlike in PS#3’s answers and on Jinhwan’s review sheet…., suppose the local government
decides to place a per unit tax on coffee. The coffee tax raises the price Carly pays for coffee so that
now Pc>$1.
c. Using your indifference curve - budget line diagram in part (a), show that this distortionary coffee tax
does the following:
i) it raises no revenue, and
ii) it creates a large 313-style excess burden
d. Suggest an alternative underlying preference relationship for Carly over coffee and $aog which would
result in no excess burden from a coffee tax and show that there would be no 313-style excess burden if
Carly had those preferences and we taxed coffee.
7. Prof. Wissink is a die-hard Bruce Springsteen fan and she has just learned that Bruce Springsteen is going
on tour with the E-Street Band for his new CD Magic. Suppose Wissink has very nicely behaved
preferences over only two goods: $“all other goods” and Springsteen tickets. Suppose she has $500 to
spend. Suppose the ticket prices are $100/ticket and that the price of “all other goods” is $1. Suppose Prof.
Wissink determines that the solution to her constrained utility optimization problem is to buy 2 tickets once
they go on sale.
a. Illustrate this solution on an indifference curve/budget line diagram.
b. Suppose that now, due to very large expected demand for Bruce tickets, the concert promoter decides to
limit tickets to only one per customer. Show where Prof. Wissink now ends up in her IC/BL diagram.
Indicate to what extent she is better off or worse off as a consequence of this policy.
c. Given the ticket number limit policy, suppose Prof. Wissink runs into you. You also bought and hold
one Bruce ticket. Would Prof. Wissink be willing to pay you more or less or exactly the market price
for the ticket you hold? Explain/defend your position using the IC/BL diagram you have drawn for Prof.
Wissink.
d. (Bonus…) If you sell your ticket to her for a much higher price than the market price, what are you?
Have a safe and relaxing FALL BREAK, see you next Thursday.