Download ECON 8010 Test #2 Fall 2016

ECON 8010
TEST #2
FALL 2016
Instructions: All questions must be answered on this examination paper. No additional sheets of
paper are permitted; use the backs of the pages if necessary. For every question, show all of your
work in arriving at your answers. Time limit: 75 minutes.
(15)
1.
a.
RESTRICTIONS: Calculate the missing parameter values from the restrictions
imposed by the theory of consumer behavior.
Suppose that a consumer has the following uncompensated demand function:


X * ( Px , Py , M )  M – Py1/2 Px1/2 Py b
where Px and Py are the per-unit prices of goods X and Y, respectively, M is money
income, and b is a fixed parameter. The value of the parameter b is _____. Why?
b.
Suppose that the consumer has the following expenditure function:
M*(Px,Py,U) = PyU + 2Px1/2 Pyc
where Px and Py are per-unit prices of goods X and Y, respectively, U is utility, and c
is a fixed parameter. The value of the parameter c is _______. Why?
c.
Suppose that a consumer has the following indirect utility function:
V ( Px , Py , M ) = - [( Px1/2 + Py1/2 )d ] / M
where Px and Py are per-unit prices of goods X and Y, respectively, M is money
income, and d is a fixed parameter. The value of the parameter d is _______.
Why?
Page 2
(20)
2. TRUE or FALSE and EXPLAIN: Label each statement TRUE or FALSE and
explain how you arrived at your answer.
a. __________ “Suppose that a utility function U(X,Y) is strongly (“additively”) separable
so that Uxy = 0 = Uyx. Then the uncompensated demand functions for goods X and Y
exhibit zero cross-price effects; that is, ∂X*/∂Py = 0 = ∂Y*/∂Px.”
b. __________ “If X and Y are Edgeworth-Pareto complements (Uxy > 0) and X and Y
are each subject to diminishing marginal utility, then the utility function U(X,Y) is
quasi-concave.”
c. __________ “In a model with three goods (X, Y, and Z), if Y and Z are net
complements then X and Z are net substitutes.”
d. ____________ “In a two-period model of the consumption-saving decision, a
decrease in the real interest rate will unambiguously increase present consumption
for a (net) borrower, assuming present consumption is a normal good.”
Page 3
(30)
3. Suppose that an individual maximizes the utility function
U(X,Y) = X1/2 + Y
subject to the budget constraint M = Px X + Py Y.
a.
Derive the uncompensated demand functions for X and Y.
b. Are X or Y normal or inferior goods? Justify your answer rigorously.
c.
Use your answers in part (a) to derive the indirect utility function
Page 4
(15) 4. Suppose that an individual’s preferences are represented by the expenditure function
M*(Px,Py,U) = Py[U – (Py/4Px)],
where Px and Py are the per-unit prices of X and Y, respectively, and U is utility.
a.
Derive the individual’s compensated demand functions X *c (Px,Py,U) and
Yc* (Px,Py,U).
b. What is the individual’s direct utility function U(X,Y)?
(10)
5. Professor Mercedes N. Lexus derives utility from consuming tomatoes (T) and all
other goods (X), and grows tomatoes in her backyard garden. For Professor Lexus, T
and X are normal goods. Rigorously answer each of the following questions.
a. Last year, Professor Lexus harvested fewer tomatoes than she desired to consume,
and bought the shortfall at market price P = P0. How would her quantity demanded
respond to an increase in P?
b. This year, Professor Lexus harvested exactly the number of tomatoes she desired to
consume when the market price was P = P1. How would her quantity demanded
respond to an increase in P?
Page 5
(10)
6. Suppose that an individual’s labor-supply function is
h*(w, I; T) = w/4 – I/w.
where h is hours of work, w is the hourly wage rate, I is non-labor income, and T = h
+ ℓ is the total time available to allocate between work and leisure, ℓ.
a. Rigorously analyze the effect of an increase in the wage rate on her labor supply.
~ ) such that
b. An individual’s reservation wage is defined as the value of w (denoted w
~ , I; T) = 0. Derive her reservation-wage function w
~ (I; T).
h*( w