Q: Suppose a consumer's utility function is $$U(x_1$, x_2$) = x_1$^{0.3} x_2$^{0.7}. If $$the consumer currently consumes $$x_1 = 2$ and x_2$ = 4$$, what is their utility?

$$U = 2$$^{0.3}$$ \times 4$$^{0.7}$$

Question 1

Suppose a consumer's preferences over goods 1 and 2 are represented by the utility function $$U(x_1$, x_2$) = x_1$ + 2x_2. $$Which of the following statements is true about the consumer's indifference curves?

Accepted Answer

They are straight lines with slope $$-1/2$$, indicating perfect substitutes.

Question 2

Given the Cobb-Douglas utility function $$U(x_1$, x_2$) = x_1$^{0.5} x_2$^{0.5}$$, what is the Marginal Rate of Substitution (MRS) at the bundle $$(x_1$, x_2$)$$?

Accepted Answer

$$MRS = \frac{x_2$}{x_1$}$$

Question 3

A consumer has the utility function $$U(x_1$, x_2$) = \min\{x_1$, 2x_2\}. If $$the consumer has 4 units of good 1 and 3 units of good 2, what is their utility?

Accepted Answer

Question 4

Which of the following best describes a 'boundary bundle' in the context of consumer theory?

Accepted Answer

A bundle where at least one good is consumed in zero quantity.

Question 5

If a consumer's indifference curves are convex to the origin, what does this imply about their preferences?

Accepted Answer

The consumer has a strong taste for variety.

Question 6

Suppose a consumer's utility function is $$U(x_1$, x_2$) = x_1$^{a} x_2$^{1-a}$$, with $$0 \u003c a \u003c 1. $$What is the equation for the indifference curve at utility level $$U_0$$?

Accepted Answer

$$x_2$$ = \left(\frac{$$U_0$$}{$$x_1^a$$}\$$right)^{\frac{1}$${1-a}}$$

Question 7

A consumer's preferences are represented by $$U(x_1$, x_2$) = x_1$ + x_2$. What is the slope of the indifference curve at any point?

Accepted Answer

$$-1$$

Question 8

Which utility function represents perfect complements?

Accepted Answer

$$U(x_1$, x_2$) = \min\{x_1$, x_2$\}$$

Question 9

If a consumer's Marginal Rate of Substitution (MRS) between goods 1 and 2 is constant, what does this imply about their preferences?

Accepted Answer

The consumer views the goods as perfect substitutes.

Question 10

Suppose a consumer's utility function is $$U(x_1$, x_2$) = x_1$^{0.3} x_2$^{0.7}. If $$the consumer currently consumes $$x_1 = 2$ and x_2$ = 4$$, what is their utility?

Accepted Answer

$$U = 2$$^{0.3}$$ 	imes 4$$^{0.7}$$

Question 11

Which of the following statements about the Marginal Rate of Substitution (MRS) is correct?

Accepted Answer

MRS is the ratio of the marginal utilities of the two goods.

Question 12

Consider the utility function $$U(x_1$, x_2$) = \min\{x_1$, 2x_2\}. $$What is the equation for the 'corner' of the L-shaped indifference curve?

Accepted Answer

$$x_1 = 2x_2$

Question 13

If a consumer's preferences are represented by $$U(x_1$, x_2$) = x_1$^{0.5} x_2$^{0.5}$$, what happens to the MRS as the consumer increases $$x_1$$ while holding $$x_2$$ constant?

Accepted Answer

MRS decreases.

Question 14

Which of the following is true about a consumer with strictly convex preferences?

Accepted Answer

The consumer prefers mixtures of goods to extremes.

Question 15

Suppose a consumer's utility function is $$U(x_1$, x_2$) = x_1$ x_2$. If the consumer has 3 units of good 1 and 5 units of good 2, what is their utility?

Accepted Answer

$$U = 15$$

Question 16

Which of the following utility functions exhibits a constant elasticity of substitution (CES)?

Accepted Answer

$$U(x_1$, x_2$) = (x_1$^{\rho} + x_2$^{\rho}$$)^{1/\rho}$$

Question 17

If a consumer's indifference curve for goods 1 and 2 is vertical, what does this imply about their preferences?

Accepted Answer

The consumer only cares about good 2.

Question 18

Suppose a consumer's utility function is $$U(x_1$, x_2$) = x_1$^{0.5} + x_2$^{0.5}. $$What is the MRS at the bundle $$(x_1$, x_2$)$$?

Accepted Answer

$$MRS = \frac{x_1$^{-0.5}}{x_2$^{-0.5}}$$

Question 19

Which of the following statements is true about the slope of the indifference curve at an interior bundle for normal goods?

Accepted Answer

The slope is equal to the negative of the MRS.

Consumer Theory: Preferences, Utility Functions, and Indifference Curves

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