Dominick Salvatore Schaums Outline of Microeconomics, 4th edition Schaums Outline Series 2006

106 ADVANCED TOPICS IN CONSUMER DEMAND THEORY [CHAP. 5
EXAMPLE 4. Figure 5-3 gives a total utility curve which first faces down and then up, plotted against income. Suppose
that the individual’s income is OA with utility AA 0 without a fire, and OB with utility BB 0 with a fire.
Fig. 5-3
If the probability of no fire is p, then the expected income (Ī) of the individual is given by
I ¼ ( p)OA þ (1
If Ī ¼ OC, then the utility of Ī is CC 0 on dashed line B 0 A 0 . If, at the same time, the cost of insurance is AD, the individual’s
assured income with insurance is OD, with utility DD 0 . CC 0 . Thus, the individual should buy insurance. Furthermore,
starting with income OD (with insurance), the same individual would also purchase a lottery ticket costing DF. Then the
individual’s income would be OF with probability p 0 of not winning, or OG with probability (1 2 p 0 ) of winning. Thus,
the expected income (Ī 0 ) with insurance and the lottery ticket is:
I ¼ ( p 0 )(OF) þ (1
p)OB
p 0 )(OG)
If Ī 0 ¼ OH with utility HH 0 . DD 0 , then the individual should also purchase the lottery ticket. (Problem 5.7 shows this with
actual numbers, and Problem 5.8 shows a related method that was once believed to measure utility cardinally.)
5.5 A NEW APPROACH TO CONSUMER THEORY—THE DEMAND FOR
CHARACTERISTICS
According to the new approach to consumer theory pioneered by Lancaster, a consumer demands a good
because of the characteristics or properties of the good, and it is these characteristics and not the good itself that
give rise to utility. For example, a consumer does not demand sugar as such but rather the characteristic of
sweetness, which is the direct source of utility. In general, a good possesses more than one characteristic,
and a given characteristic is present in more than one good. For example, sugar gives sweetness and calories
and these characteristics are also present (but in a different proportion) in honey. This new approach is superior
to traditional consumer theory because (1) substitute goods are explained in terms of possessing some common
characteristic, (2) the introduction of new goods can be considered, and (3) the effect of changes in quality can
be studied. Traditional consumer theory could not deal with these important considerations.
EXAMPLE 5. In panel A of Fig. 5-4, the horizontal axis measures the characteristic of sweetness and the vertical axis
measures calories. One-dollar’s worth of sugar gives the combination of sweetness and calories indicated by point A,
and one-dollar’s worth of honey gives point B. (It is assumed that two-dollar’s worth of sugar gives a point twice as
distant from the origin as point A along ray OA.) The consumer’s budget constraint or frontier is then given by line AB.
If the consumer’s indifference curve in characteristic space is given by I, the consumer is in equilibrium at point C,