Principles of Microeconomics hw

Problem Set 4

Principles of Microeconomics

Matthew Weinberg

Due: May 15, 2014

1. Bonnie and Clyde each have the same income of $100, which they can spend on cigarettes and guns. Assume that their indifference curves are downward-sloping and convex. Suppose Bonnie has a stronger preference for guns over cigarettes, while Clyde has a stronger preference for cigarettes over guns.

(a) On the same graph, draw Bonnie’s indifference curves, and Clyde’s indifference curves. Briefly explain how you derived their shapes.

(b) Which person will buy more guns than the other, Bonnie or Clyde? Which person will buy more cigarettes than the other, Bonnie or Clyde? Show this graphically.

2. Lizzy has an income of $50, which she can spend on two (normal) goods: books and oranges. Each book costs $10 and each pound of oranges costs $2. For each of the following situations, is the proposed bundle Lizzy’s optimal consumption bundle? If not, how should Lizzy change her consumption of oranges and books to increase her utility?

(a) Lizzy is considering buying 1 book and 10 pounds of oranges. At that bundle, her marginal rate of substitution is 5 pounds of oranges for 1 book.

(b) Lizzy is considering buying 4 books and 5 pounds of oranges. At that bundle, she is willing to forgo 1 book to acquire 1 pound of oranges (and maintain the same utility).

(c) Lizzy is considering buying 2 books and 15 pounds of oranges. Lizzy’s marginal utility of the second book is 25, and her marginal utility of the 15th pound of oranges is 5.

(d) Lizzy is considering buying 1 book and 20 pounds of oranges. Lizzy’s marginal utility of the first book is 40, and her marginal utility of the 20th pound of oranges is 2.

3. Jane derives utility only from her caffeine intake. She can consume coffee or tea, and a cup of coffee contains four times as much caffeine as a cup of tea.

(a) Draw a graph containing Jane’s indifference curves, and explain how you obtained them. Be sure to label and number the axes of your diagram.

(b) Suppose Jane’s income is $10. The price of tea is $0.50/cup, and the price of coffee is $1/cup. Write the equation for Jane’s budget constraint. On the same graph as in part (a), draw Jane’s budget constraint.

(c) How many cups of tea and coffee will Jane consume? Explain intuitively and mark the optimal bundle on your graph.

4. Jim buys only bananas and CDs. Suppose that Jim’s income is $40, bananas cost $0.80 per pound, and CDs cost $8 each.

(a) Write the equation for Jim’s budget constraint and graph it.

(b) Suppose that Jim’s optimal consumption bundle is 10 pounds of bananas and 4 CDs. Verify that he spends all of his income on this bundle. Illustrate this consumption choice on your graph for part (a), assuming that Jim’s indifference curves are downward-sloping and convex.

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(c) Suppose the price of CD’s decreases to $5. Write the equation for Jim’s new budget constraint. On a new graph, illustrate the impact of this price change on Jim’s budget constraint (by drawing Jim’s old and new budget constraints).

(d) Assuming that (1) bananas are a normal good, and (2) the income effect dominates for banana consumption, what is the effect of the price decrease of CDs on Jim’s consumption of bananas? Explain why. On your graph from part (c), show the impact of the change in the price of CDs on Jim’s consumption bundle, by decomposing it into the income and substitution effects. Carefully label the income effect, substitution effect and total effect on banana consumption on your graph (label the relevant consumption bundles, mark the sizes of each effect along the relevant axis, and use arrows to indicate the direction of each effect).

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