S07 Prelim 2 - Econ313-1 Spring 2007 Talia Bar Prelim 2...

Econ313-1
Spring 2007
Talia Bar
Prelim 2
This exam consists of four questions. Please answer questions 1 and 2 in one exam
book and questions 3 and 4 in another exam book. You may add books if needed. Label
your exam books clearly with your name and question numbers. The exam is worth 65
points. To help you allocate time you can plan on spending about one minute per credit
point. The exam is closed-book. You may use a calculator (answers might not be whole
numbers).
Show your work. A complete answer to any part of a question must have an argument,
explanation or proof.
Don°t turn the page until instructed to do so!
Good luck.
1

Part I - Questions 1 and 2. (Consumer theory)
Question 1 (25 points.)
Mr. Woodcock consumes two goods x and y . His preferences for bundles of these two
goods are represented by the utility function
u
W
( x; y ) = ln x + 2 ln y:
The price of x is p
x
and the price of y is p
y
= 1 : His income is m:
(a) Formally write Mr. Woodcock°s utility maximization problem.
(b) If p
x
= 3 ; at what income m
0
will Mr. Woodcock demand x = 25?
(c) If m
0
is the income level you found in part b, but p
x
may vary ±nd Mr. Woodcock
°s Marshallian demand for good x .