Question

2. Calculate price elasticity of demand, cross price elasticity of demand and income price elasticity of demand. Then indicate whether the alternative good is a complement or substitute. P =10, P_A=20, and I =100.

a) Q = 500 - 3P + 4P_A + I (I stands for income)

b) Q = 100 - 0.1P - 0.5P_A - 0.2I

Answer 1

Answer : a) Q = 500 - 3P + 4PA + I

=> Q = 500 - (3 * 10) + (4 * 20) + 100

=> Q = 500 - 30 + 80 + 100

=> Q = 650

Price elasticity of demand (Ep) = (Q / P) * (P / Q)

=> Ep = - 3 * (10 / 650)

=> Ep = - 0.05

Therefore, here the price elasticity of demand is - 0.05 .

Cross price elasticity of demand (Exy) = (Q / PA) * (PA / Q)

=> Exy = 4 * (20 / 650) = 4 * 0.03

=> Exy = 0.12

Therefore, the cross price elasticity of demand is 0.12 .

Here the two goods are substitute goods. Because in case substitute goods the cross price elasticity of demand is positive.

Income elasticity of demand (Ei) = (Q / I) * (I / Q)

=> Ei = 1 * (100 / 650)

=> Ei = 0.15

Therefore, the income elasticity of demand is 0.15 .

b) Q = 100 - 0.1P - 0.5PA - 0.2I

=> Q = 100 - (0.1 * 10) - (0.5 * 20) - (0.2 * 100)

=> Q = 100 - 1 - 10 - 20

=> Q = 69

Price elasticity of demand (Ep) = (Q / P) * (P / Q)

=> Ep = - 0.1 * (10 / 69)

=> Ep = - 0.01

Therefore, the price elasticity of demand is - 0.01 .

Cross price elasticity of demand (Exy) = (Q / PA) * (PA / Q)

=> Exy = - 0.5 * (20 / 69) = - 0.5 * 0.29

=> Exy = - 0.15

Therefore, the cross price elasticity of demand is - 0.15 .

Here the two goods are complementary goods. Because in case of complementary goods the cross price elasticity of demand is negative.

Income elasticity of demand (Ei) = (Q / I) * (I / Q)

=> Ei = - 0.2 * (100 / 69) = - 0.2 * 1.45

=> Ei = - 0.29

Therefore, the income elasticity of demand is - 0.29 .