POST UTME ACHIEVERS UNIVERSITY 2018 Economics | Objective
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Question 1
Consider a perfectly competitive market with n firms, each producing a homogeneous product. If the market price is P = 10, and the inverse demand function is given by P = 100 - Q, where Q is the total quantity demanded, find the equilibrium quantity produced by each firm.
Question 2
Consider a firm operating in a perfectly competitive market with a production function Q = 2L^0.5K^0.5. If the price of the good is $10 and the wage rate is $5 per unit of labor, what is the optimal level of labor to hire?
Question 3
A company has a fixed \cost of ₦100,000 and a variable \cost of ₦50 per unit. If the selling price is ₦75 per unit, what is the break-even point?
Question 4
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%?
Question 5
A consumer's utility function is given by ( u(x,y) = xy ). If the consumer's income is ₦1,000 and the prices of x and y are ₦5 and ₦10 respectively, what is the consumer's optimal bundle?
Question 6
A consumer's utility function is given by ( u(x,y) = xy ). If the consumer's income is ₦1,000 and the prices of x and y are ₦5 and ₦10 respectively, what is the consumer's optimal bundle?
Question 7
A firm's production function is given by Q = 100L^0.5K^0.5, where Q is output, L is labor, and K is capital. If the firm's labor and capital are fixed at 100 units each, calculate the marginal product of labor (MPL) and marginal product of capital (MPK).
Question 8
A firm is producing a product with a production function F(x) = 2x^2 + 3x. If the firm's \cost function is C(x) = 10x + 20, what is the marginal \cost when the output is 5 units?
Question 9
A country's balance of payments is given by the equation BOP = X - M, where BOP is the balance of payments, X is the exports, and M is the imports. If the country's exports are ₦100 billion and the imports are ₦120 billion, what is the balance of payments?
Question 10
A firm's \cost function is given by C = 100 + 2L + 3K, where C is \cost, L is labor, and K is capital. If the firm's labor and capital are fixed at 100 units each, calculate the marginal \cost (MC) and average \cost (AC).
Question 11
A firm is producing a good with a production function \( Q = 2L^2 + 3K \). If the price of labor is ₦50 per hour and the price of capital is ₦100 per unit, what is the optimal level of labor and capital?
Question 12
A government is considering a tax on a particular good to raise revenue. If the tax rate is 10% and the demand for the good is given by Q = 100 - 2P, what is the optimal tax revenue?
Question 13
The government of Nigeria plans to increase the production of rice by 20% through the use of irrigation. If the current production is 2 million metric tons, what will be the new production level?
Question 14
A consumer is faced with the following utility function: U = 2x + 3y. If the prices of the two goods are $5 and $10 respectively, and the consumer has a budget of $50, what is the optimal bundle of goods?
Question 15
A firm's revenue function is given by R = 100Q - 2Q^2, where R is revenue and Q is quantity sold. If the firm sells 20 units, calculate the firm's marginal revenue (MR) and average revenue (AR).
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