For each of the following statements, define all of the underlined terms. Then, explain why the statement is true or false

Question

a. If a consumer views two goods as perfect substitutes then their optimal choice will be a corner solution.
b. The substitution effect from a price increase states that the consumer will always choose a smaller amount of that good to consume. However, the income effect states that consumption can move in either direction.
c. Suppose Alf and Bo have convex indifference curves. Alf likes units of "X" more than units of "Y" but Bo likes units of "Y" much more than units of "X." Then, in the optimum, Alf's marginal rate of substitution will be different from Bo's even if they face the same prices.
d. All Giffen goods are normal goods, but not all normal goods are Giffen goods.
e. Economists assume that preferences are ordinal. This implies that given two utility functions and one is a monotonic transformation of the other, then they represent the same preferences over bundles of goods.

Answer 1

a. Perfect substitutes are goods for which at any point you will trade one good in the same proportion for the other. The specific utility function is U(x,y) = ax + by, and the ICs are linear throughout. A corner solution is when the optimal bundle is all of one good and none of the other (i.e. the solution is at the intercept of the BC and one of the axes). True, since the MRS is constant for p.s.'s, the optimal bundle will occur at a corner
b. The substitution effect is the change in consumption that occurs following a price change based purely on the fact that relative prices have changed while holding utility fixed. The income effect is the change in consumption following a price change that results from the person feeling richer or poorer, while holding relative prices fixed. True, the IE direction depends on whether a good is normal or inferior, whereas since MRS is diminishing, the SE is always in the opposite direction of the price change.
c. Convex indifference curves are ICs with diminishing MRS (averages are preferred to extremes, bowed inward, etc.). Marginal rate of substitution is how much of one good a person would give up to consume another unit of the other good. False, in the optimum, both Alf and BO will be choosing a bundle where the MRS equals the relative prices. Since they both face the same relative prices, their MRS's are equal at the optimum.
d. Giffen goods are goods for which consumption increases as the price increases (and vice versa). Normal goods are where consumption increases as income increases (and vice versa). False, since the SE is always in the opposite direction of the price change, the IE for a Giffen good is in the same direction of the price change and of a greater magnitude than the SE. Thus all Giffen goods are inferior, not normal.
e. Ordinal means that utility is only a measure of what bundles are preferred, not of how much a bundle is preferred. A monotonic transformation is a function which is always increasing (or decreasing). True, utility functions that differ only by a monotonic transformation will have the same MRS. Therefore, consumers with utility differing only by a MT will have the same demand equations and therefore make all of the same choices.