10) A worker views leisure and income as "goods" and has an opportunity to work at an hourly wage of $15 per hour.
a Illustrate the worker's opportunity set in a given 24-hour period.
b Suppose the worker is always willing to give up $11 of income for each hour of leisure. Do her preferences exhibit a diminishing marginal rate of substitution? How many hours per day will she choose to work?

11) 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?

Assume that this consumer has $24 of income to spend on sugar, and the price of a store-brand sugar is $1 per pound and the price or producer-brand sugar is $3 per pound. How much of each type of sugar will be purchased?

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?

Solution Preview

#10
Question a) Illustrate the worker's opportunity set in a given 24-hour period.

Answer) Put Leisure (hours) along the horizontal axis and Income ($) along the vertical axis. The maximum number of leisure hours she can have per day is 24 hours, so the Leisure axis intercept is 24. The Income axis intercept is

The shaded triangle in the pdf file below shows the opportunity set.

Question b) Suppose the worker is always willing to give up $11 of income for each hour of leisure. Do her preferences exhibit a diminishing marginal rate of substitution? How many hours per day will she choose to work?

Answer) Her preferences do not exhibit a diminishing marginal rate ...

Solution Summary

Detailed explanations to the two problems are provided. The solution to #10 contains a graphical explanation, and approximately 150 words. The solution to #11 explains the solution to each question and contains approximately 250 words.

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