microeconomic problem solve.

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Problem Set 1

Professor: Miguel A. Iraola Spring 2016 Due date: February 8th.

1. Decide whether the following statements are true or false and provide a brief explanation:

a. The slope of the budget constraint is -p1/p2. b. A decrease in wage taxes causes the opportunity cost of

leisure to increase. c. The effect of an increase in the interest rate is an increase in

the opportunity cost of consuming in the future. d. A bond that promises to pay $X in 10 years must be worth less

than $X now. e. Bundles of goods at higher indifference curves are more

desirable. f. Complete tastes are tastes that make people desire at least

some of every good. g. If you observe me choosing bundle A over bundle B on Monday,

bundle B over bundle C on Tuesday and bundle C over bundle A on Wednesday, it must be that my tastes violate transitivity.

h. Indifference curves cannot be increasing.

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i. The Marginal Rate of Substitution 𝑀𝑅𝑆!,! is -5 at any point in the following indifference curve:

j. The Marginal Rate of Substitution 𝑀𝑅𝑆!,! is -1 at point A in the following indifference curve:

Tangent line to the indifference curve at A

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2. Each year, Betty spends $1,000 on T-shirts, which she buys either at A or at B. She does not purchase anything else from these two retailers. Her preferences over T-shirts from these two retailers are convex. One of Betty’s indifference curves is shown on the graph below.

T-shirts from A cost $10 each. T-shirts from B cost $20 each. However, customers who open a B credit card account get B T-shirts at the discounted price of $10 each. There is a $100 per year membership fee to open a B credit card account. A. Based on the information given, and assuming that Betty maximizes her utility, should Betty open a B credit card account?

B. Briefly describe how (if at all) your answer to A would change if Betty viewed both T-shirts as perfect substitutes: one A T-shirt is indifferent to two B Tshirt. If your answer changes, explain why.

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B T-shirts

A T-shirts

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3. Suppose a worker gets a weekly check equal to $1,000 from a risk- free investment, has 60 hours of weekly leisure that can be devoted to work and can earn a wage of $40 per hour a. Illustrate this worker’s budget constraint, with weekly leisure

hours on the horizontal and weekly consumption (in dollars) on the vertical.

b. Illustrate what happens to this worker’s budget constraint when the weekly investment check increases to $1,500.

c. Illustrate what happens to this worker’s budget constraint when instead the wage increases to $50 per hour.

4. Sandra declares that she is always willing to give up 3 unit of pepsi

for 1 units of coke (Perfect Substitutes). Her income is $12,000, the price of pepsi is 1 and the price of coke is 4. What is her optimal consumption bundle? What would be her optimal consumption bundle if the price of pepsi were 10 instead?

5. Peter consumes wine and food in a fixed proportion: 1 glass of wine

with 2 units of food (Perfect Complements). His income is $2,000, the price of wine is 3 and the price of food is 1. What is his optimal consumption bundle? What would be his optimal consumption bundle if the price of wine were 8 instead?

6. Clarisse consumes soccer and cinema tickets. Her preferences over

the monthly consumption of these goods are represented by the following Cobb-Douglas utility function:

𝑈 𝑆,𝐶 = 𝑆!/!𝐶!/!. Her income is $4,000, the price of a soccer ticket is 1 and the price of a cinema ticket is 10. Compute her optimal consumption of soccer and cinema tickets.