Page 114 - Microeconomics, Fourth Edition

c03consumerpreferencesandtheconceptofutility.qxd 6/14/10 2:54 PM Page 88

88 CHAPTER 3 CONSUMER PREFERENCES AND THE CONCEPT OF UTILITY

In June 2009 the Family Smoking Prevention and Food and Drug Administration to add graphic
Tobacco Control Act was enacted in the United States. warning labels similar to those used in other coun-
It bans promotions and advertising believed to be tries. Studies by economists have found that such
focused on youth. It also requires that the top half warnings and advertising restrictions can have sig-
of cigarette packs, front and back, have stern health nificant negative impacts on consumer demand for
warnings. Within two years the law requires the cigarettes.

For instance, the slope of Eric’s indifference curve at point A is 5, which means that
at the level of consumption represented by basket A, Eric would be willing to trade 5
glasses of lemonade for 1 additional hamburger: his marginal rate of substitution of
hamburgers for lemonade at point A is therefore 5. At point D, the slope of the indif-
ference curve is 2: at this level of consumption, Eric’s marginal rate of substitution
is 2—he would be willing to give up only two glasses of lemonade for an additional
hamburger.
This discussion suggests a clear relationship between the marginal rate of substi-
tution of x for y (denoted by MRS ) and the slope of the indifference curve. On a
x, y
graph with x on the horizontal axis and y on the vertical axis, MRS x, y at any point is
the negative of the slope of the indifference curve at that point.
We can also express the marginal rate of substitution for any basket as a ratio of
the marginal utilities of the goods in that basket. To see how, consider any specific bas-
ket on the indifference curve U . Suppose the consumer changes the level of con-
0
sumption of x and y by x and y, respectively. The corresponding impact on utility
U will be 4
¢U MU (¢x) MU (¢y) (3.4)
y
x
But it must be that U 0, because changes in x and y that move us along the indif-
ference curve U must keep utility unchanged. So 0 MU ( x) MU ( y), which
0
y
x
can be rewritten as MU ( y) MU ( x). We can now solve for the slope of the
y
x
indifference curve ¢y ¢x :
¢y MU x
2
¢x holding utility constant MU y
Finally, since MRS x, y is the negative of the slope of the indifference curve, we
observe that
¢y MU x
2 MRS x,y (3.5)
¢x holding utility constant MU y

4 You may recognize that this equation is an approximation of the change in utility that results from
changing x and y by x and y, respectively. The approximation becomes more accurate when x
and y are small because the marginal utilities will be approximately constant for small changes in
x and y.