Question 1

Suppose a consumer has a utility function $$U(x, y) = x$$^{0.5}$$y^{0.5}$$, where $$x is $$the quantity of good X and $$y is $$the quantity of good Y. If the price of X is $$4, the price of Y is 2$$, and the consumer's income is $$40, how many units of good X will the consumer purchase to maximize utility?

Accepted Answer

$$x = 6$$

Question 2

If a consumer's marginal rate of substitution (MRS) between apples and oranges is $$MRS_{A,O} = 2$$, what does this imply about the consumer's willingness to trade?

Accepted Answer

The consumer is willing to give up 2 oranges for 1 apple.

Question 3

Given the budget constraint $$4x + 2y = 40$$, which of the following bundles is affordable for the consumer?

Accepted Answer

$$(x, y) = (6, 4)$$

Question 4

If a consumer's utility function is $$U(x, y) = x + 2y$$, what is the marginal utility of good y?

Accepted Answer

$$MU_y = 2$$

Question 5

A 50% increase in a consumer's income will have what effect on the budget line and opportunity set?

Accepted Answer

Shifts the budget line outward, increasing the opportunity set.

Question 6

If the marginal rate of transformation (MRT) between two goods is $$MRT = 2$$, what does this mean in terms of opportunity cost?

Accepted Answer

The opportunity cost of 1 unit of good 2 is 0.5 units of good 1.

Question 7

Given the utility function $$U(x, y) = x^2$y$$, what is the marginal utility of $$x$$?

Accepted Answer

$$MU_x = 2xy$$

Question 8

If a consumer's indifference curve is steeper than the budget line at the current consumption bundle, what should the consumer do to maximize utility?

Accepted Answer

Consume more of the good on the vertical axis.

Question 9

Suppose a consumer has $$U(x, y) = x + y$$ and faces prices $$P_x = 2$$, $$P_y = 1$$, and income $$I = 10. $$What is the optimal consumption bundle?

Accepted Answer

$$(x, y) = (0, 10)$$

Question 10

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 11

Given the utility function $$U(x, y) = x$$^{0.5}$$y^{0.5}$$, if the consumer is currently consuming $$(x, y) = (4, 16)$, what is the marginal rate of substitution (MRS) at this point?

Accepted Answer

$$MRS = 1$$

Question 12

If the price of good X increases while the price of good Y and income remain constant, what happens to the consumer's budget line?

Accepted Answer

The budget line rotates inward around the Y-intercept.

Question 13

If a consumer's utility function is $$U(x, y) = x + 2y$$ and the consumer has $$x = 2$$ and $$y = 3$$, what is the total utility?

Accepted Answer

$$U = 8$$

Question 14

If a consumer's marginal utility per dollar spent on good X is greater than that for good Y, what should the consumer do to maximize utility?

Accepted Answer

Buy more of good X and less of good Y.

Question 15

If a consumer's utility function is $$U(x, y) = x^2$ + y^2$, and the consumer is currently consuming (x$$, y) = (3, 4)$$, what is the marginal utility of y$?

Accepted Answer

$$MU_y = 8$$

Question 16

If the opportunity cost of good X in terms of good Y increases, what happens to the slope of the budget line?

Accepted Answer

The slope becomes steeper.

Question 17

If a consumer's utility function is $$U(x, y) = x$$^{0.5}$$y^{0.5}$, and the consumer's income doubles, what happens to the optimal consumption bundle?

Accepted Answer

Both $$x$$ and $$y$$ double.

Question 18

If a consumer's indifference curve is tangent to the budget line, what does this indicate?

Accepted Answer

The consumer is maximizing utility.

Question 19

If a consumer's utility function is $$U(x, y) = x + y$$, what is the shape of the indifference curves?

Accepted Answer

Straight lines with a slope of -1.

Question 20

If a consumer's utility function is $$U(x, y) = \min(2x, y)$$, and the consumer has $$x = 3$$ and $$y = 8$$, what is the utility?

Accepted Answer

$$U = 6$$

Intermediate Microeconomics: Chapter 3 Homework Study Guide

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