Q: The budget constraint $$p_1x_1 + p_2x_2 = m$$ can be rewritten in terms of $$x_2 as$$:

$$x_2$$ = \\frac{m - p_1x_1}{$$p_2$$}$$

Q: Suppose a consumer faces the budget constraint $$p_1x_1 + p_2x_2 = m$$ and has a utility function $$u(x_1$, x_2$) = x_1x_2. $$What is the condition for optimal consumption?

$$\\frac{p_1$}{p_2$} = \\frac{x_2$}{x_1$}$$

Question 1

Which of the following is NOT one of the four elements of a consumer model as described in microeconomics?

Accepted Answer

Production function

Question 2

Suppose a consumer faces the budget constraint $$p_1x_1 + p_2x_2 \leq m. If$$ $$p_1$$ increases while $$m$$ and $$p_2$$ remain constant, what happens to the consumer's feasible set?

Accepted Answer

It shrinks

Question 3

Which property of consumer preferences is illustrated by the statement: 'If $$A \succ B$$ and $$B \succ C$$, then $$A \succ C$$'?

Accepted Answer

Transitivity

Question 4

Given the utility function $$u(x_1$, x_2$) = x_1$ + 2x_2$$, what is the marginal rate of substitution (MRS) between $$x_1$$ and $$x_2$$?

Accepted Answer

$$MRS = 1/2$$

Question 5

If a consumer's utility function is $$u(x_1$, x_2$) = x_1x_2$$, and their budget constraint is $$2x_1 + 4x_2 = 24$$, what is the optimal bundle $$(x_1$^*, x_2$^*)$$?

Accepted Answer

$$(x_1$^*, x_2$^*) = (6, 3)$$

Question 6

Which of the following statements about indifference curves is TRUE?

Accepted Answer

Indifference curves are downward sloping and convex to the origin

Question 7

A utility function $$u(x_1$, x_2$) is $$said to be monotonic if:

Accepted Answer

Increasing $$x_1 or$$ $$x_2$$ always increases utility

Question 8

If a consumer has a Cobb-Douglas utility function $$u(x_1$, x_2$) = x_1$^{0.5}x_2$^{0.5}$$ and faces prices $$p_1 = 2$, p_2$ = 4$$, and income $$m = 24$$, what is the optimal consumption of $$x_1$$?

Accepted Answer

$$x_1^* = 6$

Question 9

Which of the following is a valid interpretation of the concept of 'utility' in microeconomics?

Accepted Answer

Utility is a numerical representation of consumer satisfaction

Question 10

Suppose a consumer's preferences are represented by the utility function $$u(x_1$, x_2$) = x_1$ + x_2$. If the consumer chooses $$($$x_1$$, $$x_2) = (3$$, 5)$$, what is their utility?

Accepted Answer

$$u = 8$$

Question 11

Which axiom of consumer theory ensures that a consumer can always compare any two bundles of goods?

Accepted Answer

Completeness

Question 12

If a consumer's utility function is $$u(x_1$, x_2$) = x_1$^2 + x_2$^2$$, which of the following bundles $$(x_1$, x_2$)$$ gives the highest utility?

Accepted Answer

$$(2, 3)$$

Question 13

The budget constraint $$p_1x_1 + p_2x_2 = m$$ can be rewritten in terms of $$x_2 as$$:

Accepted Answer

$$x_2$$ = \frac{m - p_1x_1}{$$p_2$$}$$

Question 14

Which of the following is NOT a property of a utility function that represents rational preferences?

Accepted Answer

Intersection of indifference curves

Question 15

If a consumer's utility function is $$u(x_1$, x_2$) = \min\{x_1$, x_2$\}$$, what type of goods does this utility function represent?

Accepted Answer

Perfect complements

Question 16

Suppose a consumer faces the budget constraint $$p_1x_1 + p_2x_2 = m$$ and has a utility function $$u(x_1$, x_2$) = x_1x_2. $$What is the condition for optimal consumption?

Accepted Answer

$$\frac{p_1$}{p_2$} = \frac{x_2$}{x_1$}$$

Question 17

Which of the following statements about the expenditure function $$e(p_1$, p_2$, u) is $$correct?

Accepted Answer

It gives the minimum expenditure needed to achieve utility $$u at $$prices $$p_1$$ and $$p_2$$

Question 18

If a consumer's utility function is $$u(x_1$, x_2$) = x_1$ + x_2$, and prices are p_1$ = 1$$, $$p_2 = 2$, with income m = 10$, what is the optimal bundle?

Accepted Answer

$$(x_1$^*, x_2$^*) = (0, 5)$$

Question 19

Which of the following is a consequence of the convexity of preferences?

Accepted Answer

Consumers prefer averages to extremes

Consumer Theory in Microeconomics: Foundations and Applications

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