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

CHAP. 4] CONSUMER DEMAND THEORY 89
he or she purchases 4X; and at an income level of $20, this consumer purchases 5.5 units of X. Since the Engel
curve for commodity X is positively sloped, e M is positive and commodity X is a normal good.
4.29 For the income-quantity relationship in Table 4.14, (a) sketch the Engel curve and (b) determine if this
commodity is a necessity, a luxury, or an inferior good at points A, B, D, F, H, and L.
Table 4.14
Point A B C D F G H L
Income
($/year)
Quantity
(lb/year)
4,000 6,000 8,000 10,000 12,000 14,000 16,000 18,000
100 200 300 350 380 390 350 250
(a)
Fig. 4-25
(b) The tangent to the Engel curve at points A and B is positively sloped and cuts the income axis.
Therefore, the income elasticity of demand is greater than one and the commodity is usually a
luxury at those points (see Chapter 3, Problem 3.15). At points D and F, the slope of the tangent
to the Engel curve is positive but cuts the quantity axis. Therefore, the income elasticity of demand
is larger than zero but smaller than 1 and the commodity is a necessity at those points (see
Chapter 3, Problem 3.14). At points H and L, the Engel curve is negatively sloped and the commodity
is an inferior good.
THE PRICE-CONSUMPTION CURVE AND THE CONSUMER’S DEMAND CURVE
4.30 Suppose that from the point of consumer equilibrium in Problem 4.20, the price of X falls from $2 per
unit to $1. (a) Find the new equilibrium point, sketch the price-consumption curve of this consumer for
commodity X, and derive d x .(b)Isd x price-elastic, price-inelastic, or unitary price-elastic over this price
range? (c) Does diminishing MRS xy necessarily imply diminishing MU x and MU y ? Is diminishing MU x
a prerequisite for d x to be negatively sloped?