Question

15. In the following two panels, the demand for good X shifts due to a change in income (Panel A) and a change in the price of a related good Y (Panel B). Holding the price of good X constant at $50, calculate the following elasticities: Price of good X (dollars) Price of good X (dollars) D'(M = $65,000) D(M = $60,000) DIPy = $20) D'(Py = $24) 1 0 0 50 56 Quantity of Panel A 4450 Quantity of X Panel B a. Panel A shows how the demand for X shifts when income increases from $60,000 to $65,000. Use the information in Panel A to calculate the income elasticity of demand for X. Is good X normal or inferior? b. Panel B shows how the demand for X shifts when the price of related good Y increases from $20 to $24. Use the information in Panel B to calculate the cross-price elasticity. Are goods and Y substitutes or complements? I n demand for good X is estimated to be

Answer 1

a) Here, Y1 = 60,000     Q1 = 50

               Y2 = 65,000     Q2 = 56

Income elasticity of demand = (Q2 - Q1) / (Y2 - Y1) * (Y1 + Y2) / (Q1 + Q2)

                                               = (56 - 50) / (65,000 - 60,000) * (60,000 + 65,000) / (50 + 56)

                                               = (6 / 5,000) * (125,000 / 106)

                                               = 750,000 / 530,000

                                               = 1.41

Since income elasticity of demand is positive, good X is a normal good.

b) Here,P_Y1 = 24     Q_X1 = 44

               P_Y2 = 20     Q_X2 = 50

Cross-price elasticity = (Q_X2 - Q_X1) / (P_Y2 - P_Y1) * (P_Y1 + P_Y2) / (Q_X1 + Q_X2)

                                               = (50 - 44) / (20 - 24) * (24 + 20) / (50 + 44)

                                               = (6 / -4) * (44 / 94)

                                               = 264 / -376

                                               = -0.70

Since cross-price elasticity is negative, the good X and good Y are complements.