Problem Set 14



Problem Set 7

Econ 202 (03, 04, and 05) Spring 2003

(Dr. Tin-Chun Lin)

1. If two goods are perfect substitutes, then their

A) Indifference curves are positively sloped straight lines.

B) Indifference curves are negatively sloped straight lines.

C) Indifference curves are L-shaped.

D) Marginal rate of substitution is zero.

E) Indifference curves are bowed inward.

(Answer: (B))

2. When the price of a good changes, we call the change in consumption that leaves the consumer indifferent, the

A) Substitution effect.

B) Utility effect.

C) Income effect.

D) Price effect.

E) Wealth effect.

(Answer: (A))

3. If the price of a normal good rises, then

A) The income effect will increase consumption of the good and the substitution effect will decrease consumption.

B) The income effect will decrease consumption of the good and the substitution effect will increase consumption.

C) The income effect and the substitution effect will both increase consumption of the good.

D) The income effect and the substitution effect will both decrease consumption of the good.

E) The income effect and the substitution effect will not change consumption of the good.

(Answer: (D))

4. Sara has an income of $9 a week. Popcorn costs $1 a bag, and cola costs $1.50 a can.

a. What is Sara’s real income in terms of cola? (Answer: 6 cans of cola)

b. What is her real income in terms of popcorn? (Answer: 9 bags of popcorn)

c. What is the relative price of cola in terms of popcorn? (Answer: 1.5 popcorns per cola)

d. What is opportunity cost of a can of cola? (Answer: 1.5 popcorns per cola)

e. What is Sara’s budget equation? (Answer: you can do it by yourself)

f. Draw a graph of Sara’s budget line with popcorn on the x-axis. (Answer: you can do it by yourself)

g. In part (f), what is the slope of Sara’s budget line? What is it equal to? (Answer: The absolute value of the budget line equals 0.67 cola per popcorn. The slope of budget line equals the relative price of popcorn.)

5. Suppose that an individual owed no taxes on the first $10,000 she earned and 15 percent of any income she earned over $10,000. Now suppose that Congress is considering two ways to reduce the tax burden: a reduction in the tax rate and an increase in the amount on which no tax is owed.

a. What effect would a reduction in the tax rate have on the individual’s labor supply if she earned $30,000 to start? Explain in words using the income and substitution effects. (Answer: A lower tax rate would give rise to income and substitution effects on a person’s choice of consumption and leisure. The income effect would increase both consumption and leisure, if both are normal goods, since the reduction in the tax rate leaves more after-tax income. The lower tax rate would increase the slope of the budget constraint, so the substitution effect would increase consumption and decrease leisure. The net result is an increase in consumption and an ambiguous effect on leisure, and thus an ambiguous effect on labor supply).

b. What effect would an increase in the amount on which no tax is owed have on the individual’s labor supply? Explain in words using the income and substitution effects. (Answer: An increase in the amount on which no tax is owed would be a pure income effect. If both consumption and leisure are normal goods, both would increase, so labor supply would decrease.)

6. Mr. A consumes both X and Y. The price of X is $1 per unit and the price of Y is $1.5 per unit. Mr. A’s income is $12.

a. What is the relative price of X? (Answer: the relative price of X is the price of X divided by the price of Y: 2 ∕3 )

b. Derive Mr. A’s budget equation and draw her budget line in a graph. Measure X on the horizontal axis. (Answer: You can do it by yourself.)

c. On your graph, draw an indifference curve so that the best affordable point c corresponds to 6 units of X and 4 units of Y. (Answer: You can do it by yourself)

d. What is marginal rate of substitution of X for Y at this point c? (Answer: 2 ∕3)

e. Show that any other point on the budget line is inferior. (Answer: every other point on the budget line is inferior to the point c.)

7. If the price of good X rises, the _______ effect will always imply that less of X will be consumed, while the _______ effect reinforces this only if X is a normal good.

(Answer: substitution, income)

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