POST UTME OSUSTECH 2019 Economics | Objective
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Question 1
A firm has a production function Q = 2L + 3K, where Q is the output, L is the labor, and K is the capital. If the firm wants to produce 20 units of output, and the wage rate is $10 per hour, and the rental rate of capital is $5 per hour, find the optimal quantities of labor and capital.
Question 2
A firm's demand function is given by Q = 100 - 2P. If the firm's marginal revenue function is MR = 200 - 2Q, what is the price elasticity of demand?
Question 3
A government wants to reduce the budget deficit by increa\sing taxes. If the tax rate is increased from 20% to 25%, and the tax base remains cons\tant, what is the percentage change in tax revenue?
Question 4
A consumer has a utility function U(x, y) = 2x + 3y, where x and y are the quantities of two goods. If the prices of the goods are $2 and $3, respectively, and the consumer has a budget of $10, find the optimal quantities of the goods.
Question 5
A government imposes a tax on a firm's output. The firm's supply curve shifts to the left. What is the effect of this tax on the firm's profit-maximizing output and price?
Question 6
A monopolist faces a demand curve given by P = 100 - 2Q. The firm's marginal \cost (MC) is given by MC = 10 + 2Q. What is the monopolist's profit-maximizing quantity and price?
Question 7
A firm's \cost function is given by C(q) = 2q^2 + 10q + 100. If the firm's revenue function is R(q) = 20q, what is the profit-maximizing quantity of output?
Question 8
A country is experiencing a recession, and the government is considering implementing a fiscal policy to stimulate the economy. Analyze the potential effects of a tax cut on the economy, including the impact on aggregate demand and the potential for inflation.
Question 9
A firm is considering the introduction of a new product. The product has a fixed \cost of ₦100,000 and a variable \cost of ₦50 per unit. The selling price of the product is ₦75 per unit. If the firm expects to sell 10,000 units of the product, what is the minimum price it should charge to break even?
Question 10
A firm's production function is given by Q = 2L^\( 1/2 \)K^\( 1/2 \), where Q is output, L is labor and K is capital. If the firm's current labor and capital inputs are L = 16 and K = 9, respectively, what is the marginal product of labor (MPL) when the firm is producing 12 units of output?
Question 11
A government imposes a tax on a firm's output. The firm's supply curve shifts to the left. What is the effect of this tax on the firm's profit-maximizing output and price?
Question 12
A firm is producing a good u\sing two inputs, labor and capital. The production function is given by Q = 2L^0.5K^0.5, where Q is the quantity of output, L is the amount of labor, and K is the amount of capital. If the firm is currently producing 100 units of output u\sing 4 units of labor and 9 units of capital, what is the marginal product of labor?
Question 13
A consumer's utility function is given by U = 2X + 3Y. If the consumer has a budget of ₦100 and the prices of X and Y are ₦20 and ₦30 respectively, what is the consumer's optimal bundle?
Question 14
A consumer has the following utility function: \( U = 2x + 3y \). The prices of x and y are \( P_x = 2 \) and \( P_y = 3 \), respectively. Find the consumer's budget constraint.
Question 15
Consider a consumer with a utility function U(x,y) = 2x + 3y - x^2 - y^2. If the consumer's budget constraint is 2x + 3y = 12, find the optimal values of x and y u\sing Lagrange multipliers.
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