5 Steps to a 5 AP Microeconomics, 2014-2015 Edition

Constrained Utility Maximization, Two Goods

Economists see a consumer, constrained by income and prices, as living within a budget

constraint. In a simple case where one good is consumed, the consumer maximizes utility

by buying units of good X up to the point where the marginal utility of the last unit of

good X is equal to the price. Most consumers allocate limited income between many

goods and services, each with a price that must be paid. To see how a consumer maximizes

utility in this situation, we consider a two-good case where, in addition to daily cups of

coffee, Joe also purchases scones. We start with a “rule” and then proceed to solve a couple

of problems.

Utility Maximizing Rule

Given limited income, consumers maximize utility when they buy amounts of goods X and

Y so that the marginal utility per dollar spent is equal for both goods. Another way to think

about it is that they seek the most “bang for their bucks.” Mathematically, this utility max-

imizing ruleis expressed

MUx/Px=MUy/Pyor MUx/MUy=Px/Py

If the consumer has used all income and the above ratios are equal, they are said to be

in equilibrium. Under this condition, no other combination of X and Y provides more total

utility.

Example:

Joe has daily income of $20, each cup of coffee costs Pc=$2 and each scone costs

Ps=$4. Table 7.6 provides us with Joe’s marginal utility received in the con-

sumption of each good.

Table 7.6

CUPS OF COFFEE MU OF COFFEE # OF SCONES MU OF SCONES

110130

28224

36320

44416

52514

6168

• It is very important to remember that consuming more of one good causes the marginal
  utilityto fall, but the total utilityto rise.

In order to maximize Joe’s utility, he seeks a combination of coffee and scones so

that MUc/$2 =MUs/$4 and spends exactly his income of $20. Another way to

solve this problem is to rearrange these ratios so that:

MUc/MUs=$2/$4 = .5

There are several combinations of coffee and scones in Table 7.6 where the ratio of mar-

ginal utilities is one-half. For example, Joe could consume one cup of coffee (MU =10) and

96 á Step 4. Review the Knowledge You Need to Score High

TIP

“Learn the

definitions first.

This will make

the logic much

more obvious.”

—David,

AP Student

TIP

http://www.ebook3000.com