Question 1

Suppose a consumer has the utility function $$U(x, y) = x$$^{1/2}$$ y$$^{1/2}$$, faces prices P_x = 2$ and P_y = 4$, and has an income I = 40$. What is the consumer's optimal bundle (x$$^*, y^*)$$?

Accepted Answer

$$(x^*, y^*) = (10, 5)$$

Question 2

Given the utility function $$U(x, y) = x$$^{1/2}$$ y$$^{1/2}$$, what is the marginal rate of substitution (MRS) between x$ and y$?

Accepted Answer

$$MRS = \frac{y}{x}$$

Question 3

If a consumer's utility function is $$U(x, y) = \min[x, y]$$, which of the following best describes their preferences?

Accepted Answer

The consumer views $$x$$ and $$y as $$perfect complements.

Question 4

For the utility function $$U(x, y) = \min[x, y]$$, if the consumer has an income $$I$$ and prices $$P_x$$ and $$P_y$$, what is the optimal demand for $$x$$?

Accepted Answer

$$x^* = \frac{I}{P_x + P_y}$$

Question 5

A consumer faces $$P_x = 3$$, $$P_y = 6$$, and $$I = 36. If $$their utility function is $$U(x, y) = x + y$$, what is the optimal bundle if $$x$$ and $$y$$ are perfect substitutes?

Accepted Answer

$$(x^*, y^*) = (12, 0)$$

Question 6

If the marginal utility per dollar spent on $$x is $$greater than that on $$y$$, what should the consumer do to maximize utility?

Accepted Answer

Buy more $$x$$ and less $$y.$$

Question 7

Given the budget constraint $$P_x x + P_y y = I$$, if $$P_x$$ increases while $$P_y$$ and $$I$$ remain constant, what happens to the consumer's opportunity set?

Accepted Answer

It rotates inward along the $$x-$$axis.

Question 8

If a consumer's indifference curves are L-shaped, which of the following is true?

Accepted Answer

The goods are perfect complements.

Question 9

Suppose a consumer always uses one unit of cream with one unit of sugar. If cream costs $$P_x$$ and sugar costs $$P_y$$, and income is $$I$$, what is the maximum number of cups of coffee the consumer can make?

Accepted Answer

$$\frac{I}{P_x + P_y}$$

Question 10

If a consumer's utility function is $$U(x, y) = x + 2y$$, and $$P_x = 1$$, $$P_y = 2$$, $$I = 10$$, what is the optimal bundle?

Accepted Answer

$$(x^*, y^*) = (0, 5)$$

Question 11

Which of the following best describes the budget constraint equation?

Accepted Answer

$$P_x x + P_y y = I$$

Question 12

If a consumer's marginal rate of substitution (MRS) is greater than the price ratio $$\frac{P_x}{P_y}$$, what should the consumer do?

Accepted Answer

Buy more $$y$$ and less $$x.$$

Question 13

For perfect substitutes, which utility function best represents the consumer's preferences?

Accepted Answer

$$U(x, y) = x + y$$

Question 14

If a consumer is always willing to trade 2 nickels for 1 dime, what is the marginal rate of substitution (MRS) between nickels and dimes?

Accepted Answer

$$MRS = 0.5$$

Question 15

If a consumer's utility function is $$U(x, y) = x + y$$ and $$P_x = P_y$$, what is true about the consumer's optimal choice?

Accepted Answer

The consumer is indifferent between all combinations on the budget line.

Question 16

Which of the following is NOT a property of indifference curves for perfect complements?

Accepted Answer

They are downward sloping straight lines.

Question 17

If a consumer's utility function is $$U(x, y) = x$$^{1/2}$$ y$$^{1/2}$$, and P_x = 1$, P_y = 2$, I = 12$, what is the optimal consumption of y$?

Accepted Answer

$$y^* = 4$$

Question 18

If a consumer's utility function is $$U(x, y) = \min[2x, y]$$, and $$P_x = 1$$, $$P_y = 1$$, $$I = 12$$, what is the optimal bundle?

Accepted Answer

$$(x^*, y^*) = (4, 8)$$

Utility Maximization and Consumer Choice: Indifference Curves, Perfect Complements, and Perfect Substitutes

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