Chapter 6
Doing the “Best” We Can
1
We began our introduction of microeconomics with the simple premise that economic agents try to
do the best they can given their circumstances. For three types of economic agents — consumers,
workers and individuals planning for the future — we showed in Chapters 2 and 3 how choice sets
can be used to illustrate the
circumstances
these economic agents face when making choices. We
then illustrated in Chapters 4 and 5 how we can model individual tastes — giving us a way of
now addressing how individuals will judge which of their available choices is indeed the “best”.
Chapters 2 through 5 therefore developed our basic
model
of individual choice sets and tastes, the
first step in our economic analysis of choice. We now begin the second step — the analysis of how
individuals in our basic model
optimize
— i.e. how they would behave if they are indeed doing the
best they can.
6A
Graphical Optimization Approaches
We begin by building some intuition about how tastes and choice sets interact to determine optimal
choices. This means that we will essentially combine the graphs of Chapters 2 and 3 with those
of Chapters 4 and 5 as we return to some of the examples we raised in those chapters.
In the
process, we’ll begin to get our first glimpse at the important role played by market prices in helping
us exploit all the potential
gains from trade
that would be difficult to realize in the absence of
such prices. Then, in Section 6A.2, we consider scenarios under which individuals may choose to
not purchase any quantity of a particular good – scenarios we will refer to as
corner solutions
.
And, in Section 6A.3, we will uncover scenarios under which individuals may discover that more
than one choice is optimal for them, scenarios that arise when either choice sets or tastes exhibit
nonconvexities
.
6A.1
The “Best” Bundle of Shirts and Pants
Suppose we return to my story of me going to WalMart with $200 to spend on shirts and pants,
with shirts costing $10 each and pants costing $20 per pair. We know from our work in Chapter 2
that, in a graph with pants on the horizontal axis and shirts on the vertical, my budget constraint
1
Chapters 2,4 and 5 are required as reading for this chapter. Chapter 3 is not necessary.
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Chapter 6. Doing the “Best” We Can
3
intersects at 20 on the vertical and at 10 on the horizontal. Its slope — which gives expression to
the opportunity cost of one more pair of pants in terms of how many shirts I have to give up — is
−
2. Suppose further that the marginal rate of substitution is equal to
−
2 at all bundles where I
have twice as many shirts as pants, that it is equal to
−
1 at bundles where I have an equal number
of shirts and pants, and that it is equal to
−
1
/
2 at bundles where I have twice as many pants
as shirts. (This is an example of what we called “homothetic” tastes in Chapter 5.) My budget
constraint and choice set are then graphed in Graph 6.1a, and some of the indifference curves from
the indifference map that represents my tastes are graphed in Graph 6.1b. To determine which of
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 Fall '07
 ROTHSTEIN
 Microeconomics, Optimization

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