ECON 8010
TEST #2
FALL 2014
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.
(20)
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 a
where Px and Py are the per-unit prices of goods X and Y, respectively, M is money
income, and a is a fixed parameter. The value of the parameter a is _____. Why?
b.
Suppose that the consumer has the following expenditure function:
M*(Px,Py,U) = PyU + 2Px1/2Pyb
where Px and Py are per-unit prices of goods X and Y, respectively, U is utility, and b
is a fixed parameter. The value of the parameter b is _______. Why?
(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-Fisher-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.
(25)
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. Use your answers in part (a) to derive the indirect utility function.
(10)
4. Suppose that an individual’s preferences, defined over the two goods X and Y, are
homothetic, so that the ratio of uncompensated demands for the two goods is a
function only of the price ratio Px/Py and is therefore independent of money income M.
Show that the income elasticities of demand for X and for Y are both equal to 1.
(20)
5. Suppose that a consumer’s preferences are represented by the expenditure function,
M*(Px, Py, U) = Py [1 + U + loge(Px/Py)],
where Px and Py are the per-unit prices of X and Y, respectively, and U is utility.
Derive the compensated demand functions for X and Y.
(5)
6. TRUE or FALSE and EXPLAIN: Label the statement TRUE or FALSE and explain
how you arrived at your answer.
“In a model with three goods (X, Y, and Z), if Y and Z are net complements then X
and Z are net substitutes.”