Exercise Set 9
UTILITY MAXIMIZATION

I. Objectives

II. Data

III. Questions

  1. Select a value for P1. Sketch the budget constraint. Sketch the indifference curve and indicate the optimal bundle on the graph. [Obtain the optimal values from the calculator above.]

  2. Increase P1 by 10%. The quantity demanded of coconuts will [ increase / decrease ] to ________. Sketch the new budget constraint and indifference curve. Indicate the new bundle on the graph. Has the consumer's utility increased? Explain.

    [Note a peculiar thing here: The quantity demanded of muffins has not changed. This result is unusual, and it is due to the choice of the utility function in the exercise. In a typical case, the quantity of muffins too would have changed as a result of the increase in the price of coconuts.]

  3. Consider the case where coconuts become cheaper. Since a decrease in P1 leads to [ more / less ] consumption of coconuts, we may conclude that the substitution effect is [ greater / less ] than the income effect. Explain.

  4. Consider the effect of a decrease in P1 on the quantity demanded of muffins. According to the substitution effect, the consumer will buy [ more / fewer ] muffins, while the income effect leads the consumer to buy [ more / fewer ] muffins. [Since the quantity of muffins has remained unchanged in this exercise (see table above), we may conclude that the two effects have exactly offset each other. As I said earlier, highly unusual.]

  5. Change P1 a few more times. Obtain the corresponding quantity of coconuts in each case. Sketch a demand curve for coconuts.

IV. Additional questions

  1. Sly Stallone, the consumer, seeks to maximize his utility by consuming certain amounts of chips (Good 1) and iced tea (Good 2). The price of a pound of chips is $4; that of a gallon of iced tea is $2. Stallone's income is $12.
    1. Write the equation for Stallone's budget constraint. Sketch the constraint, and indicate the intercepts and the slope.
    2. Using indifference curves, indicate Stallone's optimal consumption bundle on the graph in (a).
    3. If Stallone's income increases, what happens to the optimal bundle? What happens to his consumption of chips and iced tea? Is his utility higher than that in (b)? Why?

  2. Reggie White likes to consume two goods - beef and chicken. The price of beef is $3/lb; chicken $2/lb. Reggie White's income is $24.
    1. Sketch Mr. White's budget constraint. Indicate the intercepts and slope.
    2. Using indifference curves, indicate Reggie's optimal consumption bundle.
    3. Explain, intuitively, why some other point on the budget constraint is not optimal. Be very clear.
    4. If beef become more expensive, what will happen to Mr. White's consumption of beef and chicken, and his utility? Explain using graphs.
    5. If Reggie's income rises to $30 and prices remain the same as in (a), how is his consumption of beef and chicken affected? Provide a sketch to explain your answer.
    6. Based on your answer in the last question, is chicken an inferior good? Why?

  3. Lamar Alexander consumes two goods - potato chips and eggs. The price of a pound of potato chips is $3, while the price of an egg is $2. Lamar's income is $24.
    1. Sketch Lamar's budget constraint. Indicate the intercepts and the slope.
    2. Using indifference curves, obtain Lamar's optimal consumption bundle. Denote the optimal quantity of potato chips by QP and that of eggs by QE. Use the graph above.
    3. At the optimal point, what is Lamar's marginal rate of substitution?
    4. Lamar gets a salary raise. What are the effects of the increase in his income on his consumption of potato chips and eggs, and his utility? (Provide a sketch along with an explanation.)
    5. Based on your graph in (d), explain whether Lamar regards eggs as an inferior good or a normal good.

  4. Tina Turner consumes two goods. At the point where her total utility is maximized, which of the following is true?
    1. The marginal rate of substitution (MRS) is greater than the slope of the indifference curve
    2. The indifference curve has the same slope as the budget constraint
    3. MRS equals the ratio of prices of the two goods
    4. Both (a) and (b) are true (e) Both (b) and (c) are true

  5. Phil Gramm considers potatoes to be an inferior good. This means that
    1. Gramm's consumption of potatoes will fall if his income goes down
    2. Gramm's consumption of potatoes will fall if the price of potatoes increases
    3. His income elasticity of demand for potatoes is negative
    4. His income elasticity of demand for potatoes is positive
    5. Both (a) and (d) are correct

  6. At the point of tangency between the budget constraint and an indifference curve, which of the following is true?
    1. The consumer's optimal bundle is obtained.
    2. The marginal rate of substitution (MRS) is greater than the slope of the indifference curve.
    3. The bundle is not within the set of feasible choices.
    4. Both (a) and (b) are true.
    5. Both (b) and (c) are true.

  7. Bill Clinton buys two goods - hamburgers and milk. The price of milk decreases. If the substitution effect outweighs the income effect, we may conclude that, ceteris paribus,
    1. Bill will buy more milk and hamburgers
    2. Bill will buy more milk and fewer hamburgers
    3. Bill will buy less milk and more hamburgers
    4. Bill will buy less of both goods
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