Question 1

Suppose a consumer has a utility function $$u(x, y) = x$$^{0.5}$$y^{0.5}$$, a budget of $$24$$, and faces prices $$p_x = 2$$ and $$p_y = 4. $$What is the optimal consumption bundle $$(x^*, y^*)$?

Accepted Answer

$$x^* = 6, y^* = 3$$

Question 2

The Marginal Rate of Substitution (MRS) between goods $$x$$ and $$y$$ for the utility function $$u(x, y) = x$$^{0.5}$$y^{0.5}$ is given by:

Accepted Answer

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

Question 3

If the price of good $$x$$ decreases, holding income and the price of $$y$$ constant, what happens to the budget line?

Accepted Answer

It rotates outward from the $$y-$$axis, increasing the maximum affordable $$x$$

Question 4

For perfect complements, the indifference curves are:

Accepted Answer

L-shaped

Question 5

A consumer faces $$p_x = 2$$, $$p_y = 4$$, and has income $$I = 24. If $$the price of $$y$$ falls to $$p_y = 2$$, what is the new maximum quantity of $$y$$ the consumer can afford if all income is spent on $$y$$?

Accepted Answer

$$12$$

Question 6

The opportunity cost of good $$x in $$terms of good $$y is $$represented by the slope of the budget line. If $$p_x = 2$$ and $$p_y = 4$$, what is the opportunity cost of $$x$$?

Accepted Answer

$$0.5$$

Question 7

If a consumer’s utility function is $$u(x, y) = x + y$$, what type of goods are $$x$$ and $$y$$?

Accepted Answer

Perfect substitutes

Question 8

Which of the following best describes the income effect?

Accepted Answer

The change in quantity demanded resulting from a change in real income due to a price change

Question 9

Suppose a consumer’s utility function is $$u(x, y) = x$$^{0.5}$$y^{0.5}$$, $$p_x = 2$$, $$p_y = 4$$, and $$I = 24. If $$the price of $$x$$ increases to $$p_x = 4$, what is the substitution effect?

Accepted Answer

The consumer buys less $$x$$ and more $$y$$

Question 10

If a consumer’s indifference curves are straight lines, what does this imply about the goods?

Accepted Answer

They are perfect substitutes

Question 11

Given the utility function $$u(x, y) = x$$^{0.5}$$y^{0.5}$, what is the condition for utility maximization with respect to the budget constraint?

Accepted Answer

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

Question 12

If the price of good $$x$$ increases and good $$y is a $$substitute, what is the likely response of the consumer?

Accepted Answer

Purchase more of good $$y$$

Question 13

Which of the following is true about the slope of an indifference curve for $$u(x, y) = x$$^{0.5}$$y^{0.5}$?

Accepted Answer

It is diminishing as $$x$$ increases

Question 14

If a consumer’s utility function is $$u(x, y) = \min(x, y)$$, what type of goods are $$x$$ and $$y$$?

Accepted Answer

Perfect complements

Question 15

Suppose a consumer’s budget constraint is $$2x + 4y = 24. If $$the consumer spends all income on $$x$$, how many units of $$x$$ can be purchased?

Accepted Answer

$$12$$

Question 16

If the utility function is $$u(x, y) = x + y$$ and the budget constraint is $$2x + 4y = 24$$, what is the optimal bundle?

Accepted Answer

$$x = 12, y = 0$$

Question 17

Which of the following best describes the substitution effect?

Accepted Answer

The change in quantity demanded resulting from a change in relative prices, holding utility constant

Question 18

If a consumer’s utility function is $$u(x, y) = x$$^{0.5}$$y^{0.5}$$, $$p_x = 2$$, $$p_y = 4$$, and $$I = 24$$, what is the marginal utility of $$x at$$ $$x = 6$$, $$y = 3$?

Accepted Answer

$$MU_x = 0.25$$

Question 19

If the indifference curves for two goods are convex to the origin, what does this imply about the consumer’s preferences?

Accepted Answer

The consumer prefers balanced combinations of the two goods

Question 20

If a consumer’s utility function is $$u(x, y) = x$$^{0.5}$$y^{0.5}$$ and the budget constraint is $$2x + 4y = 24$, what is the utility at the optimal bundle?

Accepted Answer

$$u^* = 6$$

Household Demand and Utility Maximization: Microeconomics Study Notes

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