B Practice Tests

Question 1

A consumer has a monthly income of €1200 to spend on two goods: food (F) and clothing (C). The price of food is €15 per unit, and the price of clothing is €30 per unit. Write the equation for the budget constraint.

Accepted Answer

15F + 30C = 1200

Question 2

Suppose a consumer's utility function is given by $U(x_1, x_2) = x_1^{0.4}x_2^{0.6}$. If the prices of the goods are $p_1 = 2$ and $p_2 = 3$, and the consumer's income is $m = 60$, what are the optimal quantities of $x_1$ and $x_2$?

Accepted Answer

A. x1 = 12, x2 = 12

Answer

B. x1 = 15, x2 = 10

Answer

C. x1 = 10, x2 = 15

Answer

D. x1 = 20, x2 = 5

Question 3

If a consumer's preferences are complete and transitive, then the consumer is considered to be rational.

Accepted Answer

True

Answer

False

Question 4

A consumer's utility function is given by $U(x, y) = \sqrt{x} + \sqrt{y}$. Calculate the Marginal Rate of Substitution (MRS) of x for y.

Accepted Answer

MRS = $\sqrt{y} / \sqrt{x}$

Question 5

Which of the following changes would cause a parallel shift in the budget line?

Answer

A. An increase in income

Answer

B. A decrease in income

Answer

C. An increase in the price of good 1

Answer

D. A decrease in the price of good 2

Question 6

Suppose a consumer has a utility function $U(x_1, x_2) = min(2x_1, x_2)$. If the prices are $p_1 = 4$ and $p_2 = 5$, and the consumer's income is $m = 60$, what are the optimal quantities of $x_1$ and $x_2$?

Accepted Answer

x1 = 5, x2 = 10

Question 7

Consider a consumer with a Cobb-Douglas utility function $U(x_1, x_2) = x_1^{0.4}x_2^{0.6}$. If the prices are $p_1 = 2$ and $p_2 = 3$, and the consumer's income is $m = 60$, calculate the optimal consumption bundle $(x_1^*, x_2^*)$.

Accepted Answer

(12, 12)

Question 8

A consumer has a utility function $U(x_1, x_2) = 5x_1 + x_2$. If $p_1 = 2$, $p_2 = 1$, and $m = 10$, what is the optimal consumption of $x_1$?

Accepted Answer

A. 5

Answer

B. 0

Answer

C. 2

Answer

D. 10

Question 9

A consumer's utility function is given by $U(x, y) = \sqrt{x} + y$. The prices of the goods are $p_x = 4$ and $p_y = 1$, and the consumer's income is $M = 20$. Use the Lagrangian method to find the optimal consumption bundle $(x^*, y^*)$.

Accepted Answer

(1/4, 19)

Question 10

For perfect complements, the optimal consumption bundle always lies at a corner solution.

Accepted Answer

False

Answer

True

Question 11

Given the utility function $U(x_1, x_2) = x_1^{0.5}x_2^{0.5}$, derive the demand function for good $x_1$ as a function of prices $p_1$, $p_2$ and income $m$.

Accepted Answer

x_1(p_1, p_2, m) = m / (2p_1)

Question 12

Which of the following statements are true regarding Engel curves?

Answer

An Engel curve graphs the demand for one good as a function of income.

Answer

An Engel curve graphs the demand for one good as a function of price.

Answer

For a normal good, the Engel curve has a positive slope.

Answer

For an inferior good, the Engel curve has a positive slope.

Question 13

Suppose the demand function for a good is given by $x(p, m) = 10 - 2p + 0.01m$. Initially, $p = 5$ and $m = 1000$. If the price increases to $p' = 6$, calculate the total change in demand. Then, assuming this good is a normal good, explain how you would decompose the total effect into substitution and income effects.

Accepted Answer

-2

Question 14

A consumer has an initial endowment of $\omega_1 = 10$ units of good 1 and $\omega_2 = 5$ units of good 2. The prices are $p_1 = 2$ and $p_2 = 4$. The consumer's utility function is $U(x_1, x_2) = x_1x_2$. Calculate the consumer's optimal consumption of good 1 ($x_1^*$).

Accepted Answer

8.75

Question 15

Suppose a consumer's utility function is given by $U(C, L) = C^{0.6}L^{0.4}$, where $C$ is consumption and $L$ is leisure. The wage rate is €20 per hour, and the consumer has 24 hours to allocate between labor and leisure. There is no non-labor income. What is the optimal amount of leisure the consumer will choose?

Accepted Answer

B. 9.6 hours

Answer

A. 14.4 hours

Answer

C. 12 hours

Answer

D. 8 hours

Question 16

A lump-sum tax causes both income and substitution effects, while a per-unit tax only causes an income effect.

Accepted Answer

True

Answer

False

Question 17

A consumer has an income of $m_1 = €50,000$ in period 1 and $m_2 = €60,000$ in period 2. The interest rate is 10% (r = 0.10). The consumer's utility function is $U(c_1, c_2) = \ln(c_1) + 0.9\ln(c_2)$, where $c_1$ and $c_2$ are consumption in periods 1 and 2, respectively. Calculate the optimal consumption in period 1 ($c_1^*$).

Accepted Answer

49545.45

Question 18

Consider an Edgeworth box representing two consumers, A and B, and two goods, X and Y. Consumer A's initial endowment is (10, 2) and Consumer B's initial endowment is (2, 10). Their utility functions are given by $U_A(X, Y) = X^{0.5}Y^{0.5}$ and $U_B(X, Y) = XY$, respectively. Find the equation of the contract curve.

Accepted Answer

Y = X

Question 19

In a two-person, two-good exchange economy, suppose the aggregate excess demand function for good X is given by $E_X(p_X, p_Y) = 2p_X - p_Y$. According to Walras' Law, what must be the aggregate excess demand function for good Y, $E_Y(p_X, p_Y)$?

Accepted Answer

C. $E_Y(p_X, p_Y) = p_Y - 2p_X$

Answer

A. $E_Y(p_X, p_Y) = 2p_X + p_Y$

Answer

B. $E_Y(p_X, p_Y) = -2p_X - p_Y$

Answer

D. $E_Y(p_X, p_Y) = -p_Y + 2p_X$

Question 20

The Second Fundamental Theorem of Welfare Economics implies that any Pareto-optimal allocation can be achieved as a competitive equilibrium without requiring any lump-sum transfers.

Accepted Answer

True

Answer

False

B Practice Tests

Practice Tests

Consumer Choice and General Equilibrium: Practice Problems

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