Question 1

A consumer has strictly convex preferences and is indifferent between baskets $$x_1 = (1$$,3)$$ and x_2$ = (5,1). $$Which of the following statements best describes the consumer's preference between $$x_1$$ and $$x_7 = (2$$,2)$$?

Accepted Answer

The consumer strictly prefers $$x_7 to$$ $$x_1.$$

Question 2

Given the utility function $$u(x_1$, x_2$) = x_1$^{1/2} x_2$^{1/2}$$, what is the Hicksian (compensated) demand function for good 1?

Accepted Answer

$$x_1^h = u$$ \frac{$$p_2$$^{1/2}}{$$p_1$$^{1/2}}$$

Question 3

For the utility function $$u(x_1$, x_2$) = x_1$^{1/2} x_2$^{1/2}$$, what is the expenditure function $$e(p_1$, p_2$, u)$$?

Accepted Answer

$$e(p_1$, p_2$, u) = 2u \sqrt{p_1$ p_2$}$$

Question 4

A consumer with utility $$u(x_1$, x_2$) = x_1$ x_2$ faces prices p_1$ = 8$$, $$p_2 = 2$, and income M = 20$. If a unit tax t = 6$ is imposed on good 2, what is the minimum lump-sum subsidy required to keep the consumer at least as well off as before?

Accepted Answer

$$10$$

Question 5

Given the market demand $$Y^d(p) = 4400 - 200p$$ and the short-run average cost $$SAC(y, K) = \frac{2}{3}y + \frac{23}{4}y + 40 - K + \frac{K^2$}{y}$$, what is the long-run equilibrium price in a perfectly competitive industry with constant costs?

Accepted Answer

$$p = 20$$

Question 6

For the same market as above, what is the equilibrium number of firms in the long run if each firm produces $$y^* = 20$$ units at the minimum average cost?

Accepted Answer

$$220$$

Question 7

Suppose the inverse market demand is $$p = 100 - Y$$ and both firms have cost functions $$c(y) = 28y. In $$Cournot equilibrium, what is the output of each firm?

Accepted Answer

$$y_1$$ = $$y_2 = 24$

Question 8

In the Stackelberg duopoly with the same demand and cost as above, if firm 1 is the leader, what is its optimal output?

Accepted Answer

$$y_1 = 36$

Question 9

For the same market, what is the total output in the collusive (joint profit-maximizing) equilibrium?

Accepted Answer

$$Y = 28$$

Question 10

In the long-run perfectly competitive equilibrium for the market with $$p = 100 - Y$$ and $$c(y) = 28y$$, what is the equilibrium price?

Accepted Answer

$$p = 28$$

Question 11

If a consumer's preferences are strictly convex and they are indifferent between $$x_1 = (1$$,3)$$ and x_2$ = (5,1)$$, which of the following baskets is strictly preferred to $$x_1$$?

Accepted Answer

$$x_7 = (2$$,2)$$

Question 12

Given the utility function $$u(x_1$, x_2$) = x_1$ x_2$ and prices p_1$ = 8$$, $$p_2 = 2$, what is the Marshallian demand for x_1$ if income M = 20$?

Accepted Answer

$$x_1 = 5$

Question 13

If the government imposes a unit tax $$t on $$good 2, how does the compensated (Hicksian) demand for good 2 change, holding utility constant?

Accepted Answer

It decreases because the effective price of good 2 increases.

Question 14

In a perfectly competitive industry with constant costs, what happens to the number of firms in the long run if market demand increases?

Accepted Answer

The number of firms increases, but the price remains unchanged.

Question 15

Suppose two firms collude to maximize joint profits in a market with $$p = 100 - Y$$ and $$c(y) = 28y. $$What is the profit-maximizing total output $$Y^*$$?

Accepted Answer

$$Y^* = 28$$

Question 16

If a consumer's utility function is $$u(x_1$, x_2$) = x_1$^{1/2} x_2$^{1/2}$$, and prices double while income also doubles, what happens to the consumer's optimal bundle?

Accepted Answer

The optimal bundle remains unchanged.

Question 17

In the Cournot duopoly with $$p = 100 - Y$$ and $$c(y) = 28y$$, what is the market price in equilibrium?

Accepted Answer

$$p = 52$$

Question 18

Which of the following best describes the Stackelberg leader's advantage in the duopoly model?

Accepted Answer

The leader can commit to a higher output, forcing the follower to accept a lower profit.

Question 19

If the expenditure function for a utility function is $$e(p_1$, p_2$, u) = 2u \sqrt{p_1$ p_2$}$$, what is the minimum expenditure required to achieve utility $$u = 10$$ when $$p_1 = 4$ and p_2$ = 9$$?

Accepted Answer

$$e = 120$$

Question 20

A consumer with utility $$u(x_1$, x_2$) = x_1$ x_2$ faces prices p_1$ = 8$$, $$p_2 = 2$, and income M = 20$. What is the utility at the optimal bundle?

Accepted Answer

$$u = 25$$

Microeconomics Exam Study Guide: Consumer Preferences, Utility, Subsidies, Market Equilibrium, and Oligopoly Models

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