Q: Suppose a consumer's income is $$200, the price of x$ is 20$, and the price of y$ is 2$. If there is a quantity discount so that after 3 units of x$, the price drops to 10$ per unit, what is the equation for the budget constraint when x$$ \u003e 3$?

$$(20 \times 3) + 10(x-3) + 2y = 200$$

Question 1

Suppose a consumer has an income of $$120, the price of good x$ is 20$$, and the price of good $$y is$$ $10. What is the equation for the consumer's budget constraint?

Accepted Answer

$$20x + 10y = 120$$

Question 2

If a consumer's income doubles while the prices of both goods remain unchanged, what happens to the slope and intercepts of the budget constraint?

Accepted Answer

Both intercepts double, but the slope remains unchanged.

Question 3

Given the budget constraint $$5b + 10m = 100$$, where $$b is $$baseball games and $$m is $$movies, what is the maximum number of baseball games the consumer can buy if they buy no movies?

Accepted Answer

$$\frac{100}{5} = 20$$

Question 4

If the price of good $$y$$ increases while income and the price of good $$x$$ remain constant, what happens to the budget constraint?

Accepted Answer

The $$y-$$intercept decreases, the $$x-$$intercept stays the same, and the slope becomes less steep (closer to zero).

Question 5

A consumer faces the following budget constraint: $$2x + 10y = 100. $$What is the slope of the budget line?

Accepted Answer

$$-\frac{2}{10} = -0.2$$

Question 6

Suppose a consumer's income is $$200, the price of x$ is 20$, and the price of y$ is 2$. If there is a quantity discount so that after 3 units of x$, the price drops to 10$ per unit, what is the equation for the budget constraint when x$$ \u003e 3$?

Accepted Answer

$$(20 	imes 3) + 10(x-3) + 2y = 200$$

Question 7

What does the slope of the budget line $$-\frac{p_x}{p_y}$$ represent in economic terms?

Accepted Answer

The opportunity cost of good $$x in $$terms of good $$y$$

Question 8

If a consumer's budget constraint is $$40x + 20y = 400$$, and the price of $$y$$ increases to $$40$$, what is the new $$y-$$intercept?

Accepted Answer

$$\frac{400}{40} = 10$$

Question 9

Which of the following statements is TRUE regarding the effect of a decrease in income on the budget constraint, holding prices constant?

Accepted Answer

Both the $$x- $$and $$y-$$intercepts decrease, but the slope remains unchanged.

Question 10

A consumer has a budget constraint $$p_x x + p_y y = I. If$$ $$p_x$$ increases while $$p_y$$ and $$I$$ remain constant, what happens to the $$x-$$intercept and the slope?

Accepted Answer

The $$x-$$intercept decreases and the slope becomes steeper (more negative).

Question 11

Suppose a consumer can spend their income on only two goods, $$x$$ and $$y. If $$the price of $$x is$$ $$10$$, the price of $$y is$$ $$5$$, and income is $$50$$, what is the $$y-$$intercept of the budget constraint?

Accepted Answer

$$\frac{50}{5} = 10$$

Question 12

Which of the following best describes a kinked budget constraint?

Accepted Answer

A budget constraint where the slope changes at a certain quantity due to a price discount or surcharge.

Question 13

If a consumer spends all their income on good $$y$$, what is the formula for the maximum amount of $$y$$ they can buy?

Accepted Answer

$$\frac{I}{p_y}$$

Question 14

A student has $$60 to $$spend on coffee ($$p_c = 3) $$and bagels ($$p_b = 6). $$What is the equation for their budget constraint?

Accepted Answer

$$3c + 6b = 60$$

Question 15

If the price of baseball tickets increases from $$5 to$$ $$10$$ while the price of movies and income remain unchanged, what happens to the slope of the budget constraint ($$b on$$ $$x-$$axis, $$m on$$ $$y-$$axis)?

Accepted Answer

The slope changes from $$-\frac{5}{10} = -0.5 to$$ $$-\frac{10}{10} = -1$$

Question 16

Which of the following is NOT an assumption of the basic two-good consumption model discussed in the lecture?

Accepted Answer

Consumers can borrow or lend across periods.

Question 17

If a consumer's budget constraint is $$p_x x + p_y y = I$$, and both $$p_x$$ and $$p_y$$ double while $$I$$ remains constant, what happens to the budget constraint?

Accepted Answer

Both intercepts are halved, but the slope remains unchanged.

Question 18

Which of the following statements is TRUE about the relationship between budget constraints and consumer preferences?

Accepted Answer

Budget constraints are determined by prices and income, not by preferences.

Question 19

A consumer has $$I = 100$$, $$p_x = 4$$, and $$p_y = 20. $$What is the $$x-$$intercept of the budget constraint?

Accepted Answer

$$\frac{100}{4} = 25$$

Budget Constraints in the Two-Good Model: Mathematical and Graphical Analysis

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