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1. A consumer has \$400 to spend on goods X and Y. The market prices of these two goods are Px=\$10 and Py=\$40.
a. What is the market rate of substitution between goods X and Y?
b. Illustrate the consumer’s opportunity set in a carefully labeled diagram.
c. Show how the consumer’s opportunity set changes if income increases by \$400. How does the \$400 increase in income alter the market rate of substitution between goods X and Y?

5. Provide an intuitive explanation for why a “buy one, get one free” deal is not the same as a “half-price” sale.

7. A consumer must spend all of her income on two goods (X and Y). In each of the following scenarios, indicate whether the equilibrium consumption of goods X and Y will increase or decrease. Assume good X is an inferior good and good Y is a normal good.
a. Income doubles.
b. Income quadruples and all prices double.
c. Income and all prices quadruple.
d. Income is halved and all prices double.

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 willing to substitute three 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 \$10 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 \$2 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 \$1 per pound?

13. A recent newspaper circular advertised the following special on tires: “Buy three, get the fourth tire for free-limit one free tire per customer.” If a consumer has \$500 to spend on tires and other goods and each tire usually sells for \$50 how does this deal impact the consumer’s opportunity set?

3. A consumer must divide \$250 between the consumption of product X and product Y. The relevant market prices are Px = \$5 and Py = \$10.
a. Write the equation for the consumer’s budget line.
b. Illustrate the consumer’s opportunity set in a carefully labeled diagram.
c. Show how the consumer’s opportunity set changes when the price of good X increases to \$10. How does this change alter the market rate of substitution between goods X and Y?
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