Question

It is common for supermarkets to carry both generic (store-label) and brand-name (producerlabel) varieties of sugar and other products.

Many consumers view these products as perfect substitutes, meaning that consumers are always willing to substitute a constant proportion of the store brand for the producer brand. Consider a consumer whose utility function is U(G, B) = G + 2B, where G is the quantity of generic variety of sugar consumed and B is the quantity of brand-name sugar consumed. The marginal utility of G is equal to 1, MUG = 1. The marginal utility of B is equal to 2, MUB = 2.

a) With G on the horizontal axis and B on the vertical axis, illustrate the indifference curves for the consumer. (5 points)

b) Assume that this consumer has income m = $24 to spend on sugar, and the price of G is PG = $1 and the price of B is PB = $3. What is the consumer’s optimal consumption point? (5 points)

c) Suppose that income and PB stay the same while PG increases to $2. What is the new consumption point? (5 point)

d) After the price change in part (c), given the new price, how much additional income is required to keep the consumer on the same indifference curve as in part (b)? (5 points)

e) Consider quantities of G consumed in part (b) and in part (c). What is the amount of the change due to the substitution effect? What is the amount of the change due to the income effect? (5 points)

f) Given PB = $3 and m = $24, plot the consumer’s demand curve for G. Put PG on the vertical axis. Label everything clearly. (5 point)

Answer 1

The first three sub-parts have been worked out.