Question 1

Which of the following best explains why the demand curve can be interpreted as a reservation-price or willingness-to-pay curve?

Accepted Answer

Because each point on the demand curve shows the maximum price a consumer is willing to pay for an additional unit of the good.

Question 2

In the short run, the supply of apartments is ______, and the reason for this is ______.

Accepted Answer

perfectly inelastic; the number of apartments cannot be changed quickly

Question 3

Which of the following is NOT a characteristic of a perfectly competitive market equilibrium?

Accepted Answer

Firms can influence the market price.

Question 4

Which statement about Pareto Efficiency is correct?

Accepted Answer

A Pareto-efficient allocation is one where no individual can be made better off without making someone else worse off.

Question 5

Suppose 25 people have a reservation price of $$500 for an apartment, while the 26th person has a reservation price of 200. $$What does the demand curve look like in this scenario?

Accepted Answer

It is flat at $$500 for the first 25 apartments, then drops vertically to 200 $$for the 26th apartment.

Question 6

Given the demand curve $$D(p) = 100 - 2p$$, if a monopolist has 60 apartments, what price will the monopolist charge?

Accepted Answer

$$p = 20$$

Question 7

What is the economic meaning of the slope of the budget constraint?

Accepted Answer

It represents the opportunity cost of one good in terms of the other, or the rate at which the market allows the consumer to trade one good for another.

Question 8

Given the budget constraint $$p_1$$ $$x_1$$ + $$p_2$$ $$x_2 = m$ with p_1$ = 8$$, $$p_2 = 4$, m = 64$, and making good 2 the numeraire, what is the normalized form of the budget constraint?

Accepted Answer

$$2x_1 + x_2$ = 16$$

Question 9

If the government imposes a tax of 15 cents per gallon of gasoline and then introduces a subsidy of 7 cents per gallon, what is the equivalent net tax per gallon?

Accepted Answer

8 cents per gallon

Question 10

Suppose both pepperoni and anchovies are 'bads' for a consumer. What is the slope of the indifference curves between these two goods?

Accepted Answer

Positive, because the consumer requires more of one bad to compensate for more of the other.

Question 11

Why are convex preferences often summarized by the phrase 'averages are preferred to extremes'? Use the bundles $$x$$ and $$y$$ and the average $$z = t x + (1-t) y$$, $$0 \u003c t \u003c 1.$$

Accepted Answer

Because $$z is at $$least as preferred as $$x or$$ $$y$$, i.e., $$z \succsim x$$ and $$z \succsim y.$$

Question 12

For the Cobb–Douglas utility function $$u(x_1$, x_2$) = c \ln x_1$ + d \ln x_2$, what is the marginal rate of substitution (MRS) of good 1 for good 2?

Accepted Answer

$$\frac{c}{d} \cdot \frac{x_2$}{x_1$}$$

Question 13

Suppose a consumer has the utility function $$u(x_1$, x_2$) = x_1$ x_2$^4. $$What fraction of income will the consumer spend on good 2?

Accepted Answer

$$\frac{4}{5}$$

Question 14

If two goods are perfect substitutes, what is the demand function for good 2 when $$p_2$$ \u003c $$p_1$$?

Accepted Answer

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

Question 15

A consumer always uses 2 spoonfuls of sugar with each cup of coffee. If $$p_1 is $$the price of sugar, $$p_2 is $$the price of coffee, and $$m is $$income, how many spoonfuls of sugar and cups of coffee will the consumer purchase?

Accepted Answer

$$x_1 = 2x_2$, where x_2$ = \frac{m}{p_1$ \cdot 2 + p_2$}$$

Question 16

Which of the following statements about Cobb–Douglas preferences is correct?

Accepted Answer

They are homothetic, meaning that if income doubles, the demand for each good also doubles.

Question 17

Suppose a consumer's marginal rate of substitution (MRS) is $$-\frac{1}{2}$$ and the market rate of exchange is $$-\frac{p_1$}{p_2$} = -1. $$What should the consumer do to improve welfare while staying within the budget constraint?

Accepted Answer

Reallocate spending to buy more of good 2 and less of good 1.

Question 18

If a consumer's utility function is $$u(x_1$, x_2$) = x_1$ + \sqrt{x_2$}$$, what kind of preferences does this represent?

Accepted Answer

Quasi-linear preferences

Question 19

Why does applying a strictly increasing monotonic transformation to a utility function not change the marginal rate of substitution (MRS)?

Accepted Answer

Because the transformation preserves the order of preferences and the MRS depends only on the shape of indifference curves, not their numerical values.

Question 20

For perfect complements, if the direct demand function for good 1 is $$x_1$$ = \frac{m}{$$p_1$$ + $$p_2$$}$$, what is the form of the inverse demand function for good 1?

Accepted Answer

$$p_1$$ = \frac{m}{$$x_1$$} - $$p_2$$

Step-by-Step Guidance for Intermediate Microeconomics Homework

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