The demand for good X is estimated to be Q_x^d = 10,000 − 4P_X + 5P_Y + 2M + A_X, where P_X is the price of X,P_Y is the price of good Y,M is income,and A_X is the amount of advertising on X.Suppose the present price of good X is $50,P_Y = $100,M = $25,000,and A_X = 1,000 units.Based on this information,the income elasticity of good X is: A) 0.008. B) 0.082. C) 0.82. D) 8.2.

Question

Quizplus · Accepted Answer

The income elasticity of demand (E) is calculated as the percentage change in quantity demanded divided by the percentage change in income. Given the demand function Qd = 10,000 - 4Px + 5Py + 2M + Ax, where M is income, the coefficient of M (2) represents the change in quantity demanded for a unit change in income. To find the income elasticity, we use the formula E = (dQ/dM) * (M/Q). Substituting the given values: M = $25,000, and assuming Q is the quantity demanded when M = $25,000, Px = $50, Py = $100, and Ax = 1,000 units, we calculate Q = 10,000 - 4(50) + 5(100) + 2(25,000) + 1,000 = 10,000 - 200 + 500 + 50,000 + 1,000 = 61,300. Therefore, E = (2) * (25,000 / 61,300) ≈ 0.82, indicating that good X is a normal good with a relatively elastic income elasticity.

The Demand for Good X Is Estimated to Be Qxd

The Demand for Good X Is Estimated to Be Q_x^d