Question

It is common for supermarkets to carry both generic (store-label) and brand-name (producer-label) 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 who is always willing to substitute four pounds of a generic store-brand sugar for two pounds of a brand-name sugar. Do these preferences exhibit a diminishing marginal rate of substitution between store-brand and producer-brand sugar.

Required:
a. Do these preferences exhibit a diminishing marginal rate of substitution? Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound.
b. How much of each type of sugar will be purchased?
c. How would your answer change if the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per pound?

Answer 1

a. Do these preferences exhibit a diminishing marginal rate of substitution?

• no, because the consumer is actually purchasing a higher amount of goods, the only difference is that they are paying a lower price.

Assume that this consumer has $24 of income to spend on sugar, and the price of store-brand sugar is $1 per pound and the price of producer-brand sugar is $3 per pound.

• The consumer will purchase 24 pounds of price of store sugar simply because the price is much lower, not because he/she wants to consume less. Actually a lower price might result in an increase of consumption.

b. How much of each type of sugar will be purchased?

• If the consumer is willing to spend the whole $24 on sugar, he/she will purchase 24 pounds of store brand sugar. The alternative is to buy 8 pounds of producer brand sugar, and that is not a good deal.

c. How would your answer change if the price of store-brand sugar was $2 per pound and the price of producer-brand sugar was $3 per pound?

• The consumer would purchase 12 pounds of store brand sugar instead of 24, but he/she will still not purchase producer brand sugar since the difference in price is still too high. Remember that consumers view both types of sugar as perfect substitutes, so they will purchase the brand with the lower price.