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POST UTME AAUA 2020 Economics | Objective

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Question 1

Consider a production function given by $ Q = 100K^{\frac{1}{2}}L^{\frac{1}{2}} $, where ( Q ) is output, ( K ) is capital, and ( L ) is labor. If the marginal product of labor is 10, and the marginal product of capital is 5, what is the value of $ \frac{dQ}{dL} $ when $ K = 100 $ and $ L = 100 $?

Correct A. 20

B. 30

C. 40

D. 50

Correct Answer: A

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Question 2

A monopolist faces a demand curve given by $ P = 100 - 2Q $ and a \cost function given by $ C = 50 + 10Q $. If the firm's profit-maximizing output is 20 units, what is the value of the price elasticity of demand at this output level?

Correct A. -2

B. -1

C. 0

D. 1

Correct Answer: A

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Question 3

Consider the following diagram:

A. The demand curve is downward-sloping.

B. The supply curve is upward-sloping.

Correct C. The equilibrium price is $10.

D. The equilibrium quantity is 10 units.

Correct Answer: C

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Question 4

A country's GDP is given by $ Y = C + I + G $, where ( C ) is consumption, ( I ) is investment, and ( G ) is government sp\ending. If the country's GDP is $100 billion, and the government sp\ending is $20 billion, what is the value of the marginal propensity to consume?

Correct A. 0.2

B. 0.3

C. 0.4

D. 0.5

Correct Answer: A

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Question 5

Consider a firm that produces a good u\sing a production function given by $ Q = 100K^{\frac{1}{2}}L^{\frac{1}{2}} $, where ( Q ) is output, ( K ) is capital, and ( L ) is labor. If the firm's marginal product of labor is 10, and the marginal product of capital is 5, what is the value of the elasticity of substitution between labor and capital?

A. 0.5

Correct B. 1

C. 2

D. 3

Correct Answer: B

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Question 6

The opportunity \cost of producing one more unit of a good is measured by the

Correct A. marginal \cost

B. marginal revenue

C. marginal benefit

D. marginal utility

Correct Answer: A

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Question 7

The law of diminishing returns states that as the quantity of a variable input is increased, while the quantity of a fixed input is held cons\tant, the marginal product of the variable input will eventually

A. increase

Correct B. decrease

C. remain cons\tant

D. become negative

Correct Answer: B

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Question 8

The concept of comparative advantage suggests that a country should specialize in producing goods for which it has a

A. absolute advantage

Correct B. comparative advantage

C. opportunity \cost

D. marginal benefit

Correct Answer: B

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Question 9

The production function is given by Q = 2L^0.5K^0.5, where Q is the output, L is the labor, and K is the capital. If the labor and capital are increased by 10% and 20% respectively, the new output will be

A. 1.2Q

B. 1.4Q

Correct C. 1.6Q

D. 2Q

Correct Answer: C

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Question 10

The diagram below shows the production isoquant and the budget constraint. If the price of labor is 10 and the price of capital is 20, the optimal combination of labor and capital is

Correct A. (10,20)

B. (20,10)

C. (15,15)

D. (20,20)

Correct Answer: A

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Question 11

A monopolist faces a demand curve given by Q = 100 - 2P and a \cost function C(Q) = 2Q^2 + 10Q. Find the profit-maximizing price and quantity.

A. ₦250

Correct B. ₦300

C. ₦350

D. ₦400

Correct Answer: B

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Question 12

A firm's production function is given by Q = 2L^2 + 5L. If the wage rate is ₦50 per hour, find the profit-maximizing level of labor.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 13

A firm faces a demand curve given by Q = 100 - 2P and a \cost function C(Q) = 2Q^2 + 10Q. Find the profit-maximizing price and quantity u\sing the Lagrange method.

A. ₦250

Correct B. ₦300

C. ₦350

D. ₦400

Correct Answer: B

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Question 14

A firm's production function is given by Q = 2L^2 + 5L. If the wage rate is ₦50 per hour, find the profit-maximizing level of labor u\sing the Kuhn-Tucker method.

A. 10

Correct B. 15

C. 20

D. 25

Correct Answer: B

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Question 15

A monopolist faces a demand curve given by Q = 100 - 2P and a \cost function C(Q) = 2Q^2 + 10Q. Find the profit-maximizing price and quantity u\sing the Hotelling's rule.

A. ₦250

Correct B. ₦300

C. ₦350

D. ₦400

Correct Answer: B

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Question 16

The demand for a product is given by the equation Qd = 100 - 2P, where Qd is the quantity demanded and P is the price. If the price elasticity of demand is -2, what is the percentage change in quantity demanded when the price increases by 10%?

Correct A. 20%

B. 30%

C. 40%

D. 50%

Correct Answer: A

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Question 17

A firm produces two goods, X and Y, u\sing two inputs, labor (L) and capital (K). The production functions are given by Qx = 2L + 3K and Qy = 4L + 2K. If the firm has 10 units of labor and 5 units of capital, what is the total output of the firm?

A. 30

B. 40

Correct C. 50

D. 60

Correct Answer: C

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Question 18

The following diagram shows the supply and demand curves for a product. If the price elasticity of supply is 2 and the price elasticity of demand is -3, what is the equilibrium price and quantity?

A. P = 10, Q = 20

B. P = 15, Q = 30

Correct C. P = 20, Q = 40

D. P = 25, Q = 50

Correct Answer: C

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Question 19

A country's balance of payments is given by the following equation: BOP = X - M, where X is the value of exports and M is the value of imports. If the value of exports is 100 and the value of imports is 80, what is the balance of payments?

Correct A. 10

B. 20

C. 30

D. 40

Correct Answer: A

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Question 20

The following table shows the demand for a product at different prices. If the price elasticity of demand is -2, what is the percentage change in quantity demanded when the price increases by 10%?

Correct A. 20%

B. 30%

C. 40%

D. 50%

Correct Answer: A

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Question 21

A consumer's indifference curve is represented by the equation u(x,y) = 2x + 3y. If the consumer's income is ₦1000 and the prices of x and y are ₦5 and ₦3 respectively, what is the consumer's optimal bundle?

Correct A. x = 40, y = 20

B. x = 30, y = 30

C. x = 20, y = 40

D. x = 10, y = 50

Correct Answer: A

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Question 22

A firm's production function is given by Q = 2L^0.5K^0.5. If the firm's output is 100 units and the price of labor is ₦10 per unit, what is the minimum \cost of production?

A. ₦1000

Correct B. ₦2000

C. ₦3000

D. ₦4000

Correct Answer: B

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Question 23

A country's GDP is ₦100 billion and its population is 20 million. If the country's GDP per capita is ₦5000, what is the country's economic growth rate?

A. 5%

Correct B. 10%

C. 15%

D. 20%

Correct Answer: B

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Question 24

A firm's demand function is given by Q = 100 - 2P. If the firm's output is 50 units, what is the firm's revenue?

A. ₦1000

Correct B. ₦2000

C. ₦3000

D. ₦4000

Correct Answer: B

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Question 25

A consumer's indifference curve is represented by the equation u(x,y) = 3x + 2y. If the consumer's income is ₦2000 and the prices of x and y are ₦10 and ₦5 respectively, what is the consumer's optimal bundle?

A. x = 40, y = 20

B. x = 30, y = 30

Correct C. x = 20, y = 40

D. x = 10, y = 50

Correct Answer: C

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