Economics 301 Problem Set 4 5 October 2007

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1 Economics 301 Name Problem Set 4 5 October 2007 Budget Lines and Indifference Curves and the Consumer Optimum 1. Parvez, a pharmacology student, has allocated $120 per month to spend on paperback novels and used CDs. Novels cost $8 each; CDs cost $6 each. Draw his budget line. a. Draw and label a second budget line that shows what happens when the price of a CD rises to $10. b. Draw and label a third budget line that shows what happens when the price of a CD rises to $10 and Parvez's income rises to $ What happens to a consumer's equilibrium if all prices and income double? [Hint: What happens to the intercepts of the budget line?]

Draw his budget line. a. Draw and label a second budget line that shows what happens when the price of a CD rises to $10. b. Draw and label a third budget line that shows what happens when the price of a CD rises to $10 and Parvez's income rises to $240.

2 3. Continental Long Distance Telephone Service offers an optional package for in-state calling whereby each month the subscriber gets the first 50 minutes of in-state calls free, the next 100 minutes at $0.25/min, and any additional time at the normal rate of $0.50/min. Draw the budget constraint for instate phone calls and a composite good (whose price equals $1) for a subscriber with an income of $400/month. 4. Suppose Carmela s income is $100 per week, which she allocates between sandwiches and books. Sandwiches cost $2 each. Books cost $10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to $5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Carmela might have more than one utility-maximizing solution?

Draw the budget constraint for instate phone calls and a composite good (whose price equals $1) for a subscriber with an income of $400/month. 4.

3 5. In Larry's state, a sales tax of 10% is applied to clothing but not to food. Show the effect of this tax on Larry's choice between food and clothing using indifference curves and budget lines. 6. Lauren buys pizza slices for $3 a slice and "all other goods" at a price of $1 per unit. Her optimal bundle is 10 slices of pizza per week and 30 units of other goods per week. Draw her budget constraint. Label her optimal bundle A and show the relevant indifference curve. The pizzeria raises its price to $4 a slice. Her parents give her enough extra money that she can buy her original bundle, A. Draw Lauren's new budget constraint. Can you tell how her new bundle, B, compares to the original one, A?

Lauren buys pizza slices for $3 a slice and "all other goods" at a price of $1 per unit. Her optimal bundle is 10 slices of pizza per week and 30 units of other goods per week.

4 7. Ann's only income is her annual college scholarship, which she spends exclusively on gallons of ice cream and books. Last year when ice cream cost $10 and used books cost $20, Ann spent her $250 scholarship on 5 gallons of ice cream and 10 books. This year, the price of ice cream rose to $15 and the price of books increased to $25. So that Ann can afford the same bundle of ice cream and books that she bought last year, her college raised her scholarship to $325. Ann has the usual-shaped indifference curves. Will Ann change the amount of ice cream and books that she buys this year? If so, explain how and why. Will Ann be better off, as well off, or worse off this year than last year? Why? 8. Under a welfare plan, poor people are given a lump-sum payment of $L. If they accept this welfare payment, they must pay half of anything they earn to the government as a tax. If they do not accept the welfare payment, they do not have to pay a tax on their earnings. Show that whether an individual accepts welfare depends on the individual's tastes.

This year, the price of ice cream rose to $15 and the price of books increased to $25.

5 9. Suppose that Samantha and Jason both spend $24 per week on video and movie entertainment. When the prices of videos and movies are both $4, they both rent 3 videos and buy 3 movie tickets. Following a video price war and an increased cost of movie tickets, the video price falls to $2 and the movie ticket increases to $6. Samantha now rents 6 videos and buys 2 movie tickets; Jason, however, buys 1 movie ticket and rents 9 videos. a. Is Samantha better off or worse off after the price change? b. Is Jason better off or worse off? 10. Last year, the price of heating oil was $4 per gallon, and Jonetta purchased 100 gallons of heating oil. This year, the price of heating oil falls to $3 per gallon while Jonetta's income is unchanged. Jonetta decides to share her good fortune by giving her retired father a gift of $100. Consider an indifference curve-budget line diagram with heating oil on the horizontal axis and "all other goods" on the vertical axis. a. Does the price change make Jonetta's budget line flatter or steeper? Justify your choice. b. After Jonetta gives the $100 gift, will her new budget line lie above, lie below, or pass through her initial optimum? Justify your choice. c. Sketch an indifference curve-budget line diagram that illustrates this situation. This year, will Jonetta be better or worse off than she was last year?

Samantha now rents 6 videos and buys 2 movie tickets; Jason, however, buys 1 movie ticket and rents 9 videos. a. Is Samantha better off or worse off after the price change? b. Is Jason better off or worse off?

6 11. The Simpsons, a family of four, have a meager annual income of $ a. Draw their budget line on a graph on which the vertical axis shows their quantity consumed of food, measured in dollars, and the horizontal axis shows their quantity consumed of other goods, also measured in dollars. b. Suppose that the Simpsons spend $4000 each year on food. Assuming that the Simpsons are utility maximizers, draw an indifference curve at their consumption point.

7 A governmental agency decides that $6000 is the minimum annual expenditure on food needed to provide proper nutrition for a family of four. Noting that the Simpsons spend less than this minimum amount, the agency gives them an annual allotment of $2000 worth of food stamps, which can be used only to buy food. Suppose in addition that the Simpsons' income elasticity of demand for food equals one. c. On a new diagram, draw their new budget set. Determine how much the Simpsons will now spend on food each year. Draw an indifference curve at their new consumption point. Does the government succeed in its objective of raising their food consumption to the minimum standard? d. Repeat part (c), but assume instead that the agency increases its aid to the Simpsons to $6000 per year in food stamps. e. Would the Simpsons prefer to receive the $6000 in cash instead? Would the agency succeed in its objective in that case? Draw a new diagram to support your answers.

Suppose in addition that the Simpsons' income elasticity of demand for food equals one. c. On a new diagram, draw their new budget set.

8 12. Since 1979, recipients have been given food stamps. Before 1979, however, people bought food stamps at a subsidized rate. For example, to get $1 worth of food stamps, a household paid about $0.25 (the exact amount varied by household characteristics and other factors). What is the budget constraint facing an individual if that individual may buy up to $100 per month in food stamps at $0.25 per each $1 coupon?

For example, to get $1 worth of food stamps, a household paid about $0.

CHAPTER 3 CONSUMER BEHAVIOR

CHAPTER 3 CONSUMER BEHAVIOR EXERCISES 2. Draw the indifference curves for the following individuals preferences for two goods: hamburgers and beer. a. Al likes beer but hates hamburgers. He always prefers