Question

Consider the following demand equation for good a. Good a demands is a function of income (Y) and prices of good b and c. QDa(p,Y,pb,pc) = 12 − 3pa + 5Y −3pb +4pc. Pa = 2 Y=500 Pb = 3 Pc = 5 a. Calculate elasticity of demand. Does it respect law of demand? is it elastic or inelastic? Why? b. Calculate elasticity of income. Is it inferior or nomal good? Why? c. Calculate cross-price elasticities with good b. Is good b a complement or substitute? Why? d. Calculate cross-price elasticities with good c. Is good c a complement or substitute? Why?

Answer 1

a) QDa = 12 − 3pa + 5Y −3pb +4pc

Substituting the values

QDa = 12 − 3(2) + 5(500) − 3(3) + 4(5) = 12 - 6 + 2500 - 9 + 20 = 2517

Price elasticity of demand = (∆QDa / ∆Pa) * (Pa / QDa) [Where, (∆QDa / ∆Pa) is the price coefficient of good a in the demand function]

PED = -3 * (2 / 2517) = - 0.002

The absolute value of PED is 0.002. Since PED is less than 1, demand is inelastic

b) Income elasticity of demand = (∆QDa / ∆Y) * (Y / QDa)

                                                  = 5 * (500 / 2517)

                                                  = 0.99

Since IED is positive, it is a normal good

c) cross-price elasticity with good b = (∆QDa / ∆Pb) * (Pb / QDa)

                                                           = -3 * (3 / 2517)

                                                            = -0.003

Since cross-price elasticity with good b is negative, good b is a complement.

d) cross-price elasticity with good c = (∆QDa / ∆Pc) * (Pc / QDa)

                                                           = 4 * (5 / 2517)

                                                            = 0.007

Since cross-price elasticity with good c is positive, good c is a substitute.