(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 182

CHAPTER 4 • Individual and Market Demand 157

budget line moves to RT), we take away enough income so that the individual
is no better off (and no worse off) than he was before. To do so, we draw a
budget line parallel to RT. If the budget line passed through A, the consumer
would be at least as satisfied as he was before the price change: He still has the
option to purchase market basket A if he wishes. According to the Hicksian
substitution effect, therefore, the budget line that leaves him equally well off
must be a line such as R’T’, which is parallel to RT and which intersects RS at a
point B below and to the right of point A.
Revealed preference tells us that the newly chosen market basket must lie on
line segment BT'. Why? Because all market baskets on line segment R' B could
have been chosen but were not when the original budget line was RS. (Recall
that the consumer preferred basket A to any other feasible market basket.)
Now note that all points on line segment BT' involve more food consumption
than does basket A. It follows that the quantity of food demanded increases
whenever there is a decrease in the price of food with utility held constant.
This negative substitution effect holds for all price changes and does not
rely on the assumption of convexity of indifference curves that we made in
Section 3.1 (page 69).

• Hicksian substitution
effect Alternative to the Slutsky
equation for decomposing price
changes without recourse to
indifference curves.

In §3.1, we explain that an
indifference curve is convex
if the marginal rate of substitution diminishes as we
move down along the curve.

In §3.4, we explain how information about consumer preferences is revealed through
the consumption choices that
consumers make.

EXERCISES
1. Which of the following utility functions are consistent
with convex indifference curves and which are not?
a. U(X, Y) = 2X + 5Y
b. U(X, Y) = (XY).5
c. U(X, Y) = Min (X, Y), where Min is the minimum of
the two values of X and Y.
2. Show that the two utility functions given below generate identical demand functions for goods X and Y:
a. U(X, Y) = log(X) + log(Y)
b. U(X, Y) = (XY).5
3. Assume that a utility function is given by Min(X, Y),
as in Exercise 1(c). What is the Slutsky equation that
decomposes the change in the demand for X in response
to a change in its price? What is the income effect? What
is the substitution effect?
4. Sharon has the following utility function:
U(X, Y) = 1X + 1Y

where X is her consumption of candy bars, with price
PX = $1, and Y is her consumption of espressos, with
PY = $3.
a. Derive Sharon’s demand for candy bars and
espresso.
b. Assume that her income I = $100. How many
candy bars and how many espressos will Sharon
consume?

c. What is the marginal utility of income?
5. Maurice has the following utility function:
U(X, Y) = 20X + 80Y - X 2 - 2Y 2
where X is his consumption of CDs with a price of
$1 and Y is his consumption of movie videos, with a
rental price of $2. He plans to spend $41 on both forms
of entertainment. Determine the number of CDs and
video rentals that will maximize Maurice’s utility.