Econ 100b (Grossman) - Winter 2010 Final Exam - Version A Multiple Choice Test - University Of California Page 4
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2
3
4Free-response – 21 out of 50 pts. (2 qns., 10 pts. each + 1)
Answer these questions in your blue-book. Show your work and intermediate steps for partial credit. If you
cannot complete part of the problem, e.g. if you get stuck on some algebra, you may still earn partial credit
for explaining intuitively how you would solve if you were not stuck. You can expect to see fractions in your
answers. Your score will
be based on the marks in your blue-book. You will not receive any credit for
anything written on your exam paper. You will receive 1 point for correctly writing your name, perm number,
version (A,B,C, or D), and TA’s name on your blue-book.
1. Consider an exchange economy consisting of two people, A and B, endowed with two goods, 1 and 2.
A
2
Each person is initially endowed with 5 of each good. Their preferences are given by U
(x
, x
) = x
x
1
2
2
1
B
2
and U
(x
, x
) = x
x
. This question asks you to assume that p
= 1, then find the competitive
1
2
1
2
2
equilibrium allocations and p
. (Points split equally across parts)
1
(a) Find the MRS for each consumer
A
A
(b) Write the equation of the contract curve (express x
as a function of x
)
2
1
(c) Write the equation of the budget constraint (in person A’s coordinates) as a function of p
1
A
A
(d) What expression involving x
and x
can we substitute for p
in your answer to the previous part?
1
1
2
A
A
A
B
B
B
(e) Find the competitive equilibrium price, p
and allocations, x
= (x
, x
) and x
= (x
, x
)
1
1
2
1
2
2. A bakery and coffee shop operate next to each other downtown. The bakery sells bags of donuts (d)
for $30 each and the coffee shop sells bags of coffee (k) for $15. Making donuts and coffee is costless,
but each shop needs to advertise to attract customers. Some of the customers lured by the advertising
from one shop will also make a purchase at the other shop. Specifically, the bakery needs to spend
d
dk
k
dk
c(d) =
on advertising in order to sell d donuts and the coffee shop must spend c(k) =
15
30
15
30
on advertising in order to sell k cups of coffee.
(a) (2 points) What is the bakery’s marginal private benefit of selling a bag of donuts and the marginal
private cost? What is the coffee shop’s marginal private benefit of selling a bag of coffee and the
marginal private cost?
(b) (2 points) How many bags of donuts and coffee will be sold in the competitive marketplace?
(c) (2 points) The city looks out for its business owners and hires a consultant to determine how
much the two shops should advertise in order to maximize total profits. What level of d and k
does the consultant recommend?
(d) (4 points) The city decides to subsidize d and k so as to induce the owners to choose the amounts
recommended by the consultant. What should be the subsidy per bag of donuts, s
, and the
d
subsidy per bag of coffee, s
?
k
4
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