Economics 10a Study Guide - Final Guide: Utility, Risk Premium, Risk Neutral
13 Dec 2018
School
Department
Course
Professor
)1
iHarvard University
De,artment of Economics
General Examination in Microeconomic Theory
FaD 2002
y~u have FOUR hours.
Solve all questions.
The Exam has 5 parts. Each part has it'~ own sheet. Please spend the following time bn each part.
60 minutes
60 minutes
60 minutes
60 minutes
I.
II.
III.
IV.
PLEASE USE A SEPARATE BLUEI BOOK FOR EACH QUESTION AND WRITE THE
QUESTION NUMBER ~N THE FRONT OF THE BLUE BOOK.
PLEASE PUT YOURIEXAM NUMBER ON EACH BOOK.
PLEASE DO NOT WRIT. YOUR NAME ON YOUR BLUE BOOKS.
Micro General
Question 1
Part I (60 minut~s)
A household consumes Xt and X2" X
~is purchased on a market with a price Pt" X2 cannot be
purchased direcdy; it is made by the household out of two inputs y and z which th~
household can buy at prices Py and z respectively. It takes two units of y and 3 u4its of z to
make one unit of Xv The househol 's initial wealth is w.
a. Define the household's indirect tility function as it depends on wealth and o~ the prices
of the goods it can purchase (XI' y, and z).
b. For a given utility level u*, defin the household's expenditure function as it d1pends on
these prices. jc. Show that y and z must be com ~ements. ~:(-,
d. Show that XI and y must be sub tillites. 'j,
'c
Question 2
A consumer has the von Neumann-~orgenstem utility function:
r
u(x) = x O<r<j
The consumer has an initial Wealth
+> O. w can be invested in "bonds," which return R
( > 1 ) pet dollar invested, or in "st cks" which have a random return z per do~ invested,
with distribution function F (z). ' i
Assume:
E F Z > R.
a) Set up the consumer's investmen problem and show the first-order condition ~or the
optimal portfolio allocation. ib) Show that the fraction of wealth. vested in "stocks" is independent of w.
c) Based on the result in b, which 0 e of the following properties characterized
consumer's preferences for "bonds nd "stocks"
0 quasi-linearity
0 homotheticity
0 linear, parallel Engle curves.
Document Summary
Please spend the following time bn each part. Please use a separate bluei book for each question and write the. Question number ~n the front of the blue book. A consumer has the von neumann-~orgenstem utility function: u(x) = x r. An entrepreneur, player e"hcurrently owns all of the stock in her company. Player e offers victor an equity share s of the company, ere 0 ~ s ~ 1. Victor observes s but not 1(, and then either accepts or rejects the offer. If v rejects, he gets 0 and player e gets 1l: if v accepts, he gets s(7[+ n) I is the value of the new project. I and e gets (l-s)(1t+ n), where n> Show that there are no pure-strategy pbe in which both types of e offer the same s > 0 and v accepts. Compare the pbe here to w~at would happen if 1fwere public information. a) b) c) d) e)
