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Appendix to Chapter 3 Consumer Preferences and Demand 127

indifference curves). The figure also shows a price-consumption curvethat

passes through the optimal consumption points. This curve shows the con-

sumer’s optimal consumption as the price of X is varied continuously. Using

this curve, we can record the consumption of X at each price. If we plot the

quantity of X demanded versus its price, we arrive at the consumer’s demand

curve for X; it has the usual downward slope. The consumer increases her opti-

mal consumption of X in response to lower prices.

Of course, different individuals will have varying preferences for goods

and varying incomes. For these reasons, they obviously will have different

demand curves. How do we arrive at the market demand curve (the total

demand by all consumers as price varies)? The answer is found by summing

the quantities demanded by all consumers at any given price. Graphically, this

amounts to horizontallysumming the individual demand curves. The result is

the market demand curve.^3

Questions and Problems

1. a. Consider a different consumer who has much steeper indifference
   curves than those depicted in Figure 3A.1. Draw a graph showing such
   curves. What do these curves imply about his relative valuation for
   good X versus good Y?
   b. Using the curves from part (a) and the budget line in Equation 3A.1,
   graph the consumer’s optimal consumption bundle. How does his
   consumption bundle compare with that of the original consumer? Is it
   still true that MRS PX/PY2?


2. a. Suppose the income the consumer has available to spend on goods
   increases to $30. Graph the new budget line and sketch a new
   indifference curve to pinpoint the consumer’s new optimal
   consumption bundle. According to your graph, does the consumer
   purchase more of each good?
   b. Sketch a graph (with an appropriate indifference curve) in which one
   of the goods is inferior. That is, the rise in income causes the
   consumer to purchase less of one of the goods.


3. Suppose that the price of good X rises and the price of good Y falls in
   such a way that the consumer’s new optimal consumption bundle lies on
   the same indifference curve as his old bundle. Graph this situation.
   Compare the quantities demanded between the old and new bundles.

(^3) Of course, market researchers do not investigate demand individual by individual. Rather, they sur-
vey random, representative samples of potential consumers. The main point is that properties of
individual demand curves—their downward slope stemming from optimal consumption behavior—
carry over to the market demand curve itself.
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