Question 1

Given the utility function $$u(x, y) = x$$^{1/2}$$ y$$^{1/2}$$, which of the following bundles provides the highest utility?

Accepted Answer

Bundle (2, 2)

Question 2

If the budget constraint is $$8x + 4y = 24$$, what is the opportunity cost of one unit of $$x$$?

Accepted Answer

$$2$$

Question 3

The Marginal Rate of Substitution (MRS) for $$u(x, y) = x$$^{1/2}$$ y$$^{1/2}$$ is given by:

Accepted Answer

$$\frac{y}{x}$$

Question 4

Suppose $$m = 24$$, $$p_x = 8$$, and $$p_y = 4. $$What is the optimal bundle for perfect substitutes $$u(x, y) = x + y$$?

Accepted Answer

$$(x, y) = (3, 0)$$

Question 5

For perfect complements $$u(x, y) = \min(x, y)$$ with $$m = 24$$, $$p_x = 8$$, $$p_y = 4$$, what is the optimal consumption bundle?

Accepted Answer

$$(x, y) = (2, 2)$$

Question 6

If the price of $$x$$ falls, which effect describes the change in quantity demanded due to the change in relative price, holding utility constant?

Accepted Answer

Substitution effect

Question 7

Given $$u(x, y) = x$$^{1/2}$$ y$$^{1/2}$$, m = 24$, p_x = 2$, p_y = 4$, what is the demand for x$?

Accepted Answer

$$x = 6$$

Question 8

If a consumer faces a membership fee $$f$$ and per-unit prices $$p_x$$ and $$p_y$$, how does the budget constraint change?

Accepted Answer

$$p_x x + p_y y = m - f$$

Question 9

If $$u(x, y) = x$$^{1/2}$$ y$$^{1/2}$$, m = 120$, p_x = 1$, p_y = 1$, what is the optimal bundle?

Accepted Answer

$$(x, y) = (60, 60)$$

Question 10

Which of the following best describes the tangency condition for utility maximization?

Accepted Answer

$$\frac{MU_x}{MU_y} = \frac{p_x}{p_y}$$

Question 11

If the government imposes a per-unit tax $$t_x on $$good $$x$$, how does the budget line change?

Accepted Answer

$$(p_x + t_x)x + p_y y = m$$

Question 12

For the utility function $$u(x, y) = x + y$$, the indifference curves are:

Accepted Answer

Straight lines

Question 13

For the utility function $$u(x, y) = \min(x, y)$$, the indifference curves are:

Accepted Answer

L-shaped

Question 14

If $$p_x$$ increases and $$p_y$$ remains constant, what happens to the budget line?

Accepted Answer

It becomes steeper

Question 15

Suppose $$u(x, y) = x$$^{1/2}$$ y$$^{1/2}$$, m = 24$, p_x = 2$, p_y = 4$. If p_x$ increases to 4$, what happens to the demand for x$?

Accepted Answer

It decreases

Question 16

If a consumer faces a budget constraint $$p_x x + p_y y = m$$ and chooses $$(x^*, y^*)$$ such that $$\frac{MU_x}{MU_y} \u003e \frac{p_x}{p_y}$$, what should the consumer do?

Accepted Answer

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

Question 17

If $$u(x, y) = x$$^{1/2}$$ y$$^{1/2}$$, m = 12$, p_x = 2$, p_y = 2$, what is the optimal bundle?

Accepted Answer

$$(x, y) = (3, 3)$$

Question 18

If a consumer's income increases, what happens to the budget line?

Accepted Answer

It shifts outward

Question 19

Which of the following is true for economic bads, such as $$u(x, y) = (16 - x$$^{1/2}$$ y$$^{1/2}$$)$$?

Accepted Answer

The consumer prefers less of the bad and more of the good

Microeconomics Study Notes: Utility Maximization, Indifference Curves, and Consumer Choice

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