Problem 1: 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?
Problem 2: 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?