Question

Assume that advertising shifts the demand curve for denim jeans to the right along the supply curve which pushes the denim jean price up by 125%. If the old equilibrium price of denim jeans is $8.76/pair and the old equilibrium quantity is 230 million pair, the elasticity of denim jean supply is 0.60 and the elasticity of demand is -0.766, what is the new equilibrium quantity demanded of denim jeans? What is the new equilibrium quantity supplied? (HINT: Be careful! Think about it.)

Answer 1

New price after 125% increase in price = $8.76 x 2.25 = $19.71

(i) Using mid-point method,

Elasticity of demand = (Change in quantity demanded / Average quantity demanded) / (Change in price / Average price)

Let new quantity demanded (In millions) = Qd.

- 0.766 = [(Qd - 230) / (Qd + 230)] / [$(19.71 - 8.76) / $(19.71 + 8.76)]

- 0.766 = [(Qd - 230) / (Qd + 230)] / (10.95 / 28.47)

- 0.766 = [(Qd - 230) / (Qd + 230)] / 0.3846

[(Qd - 230) / (Qd + 230)] = (-0.766) x 0.3846

[(Qd - 230) / (Qd + 230)] = - 0.2946

Qd - 230 = - 0.2946 x (Qd + 230)

Qd - 230 = - 0.2946 x Qd - 67.76

1.2946 x Qd = 162.24

Qd = 125.32

(ii) Using mid-point method,

Elasticity of supply = (Change in quantity supplied / Average quantity supplied) / (Change in price / Average price)

Let new quantity supplied (Million) = Qs

0.6 = [(Qs - 230) / (Qs + 230)] / [$(19.71 - 8.76) / $(19.71 + 8.76)]

0.6 = [(Qs - 230) / (Qs + 230)] / (10.95 / 28.47)

0.6 = [(Qs - 230) / (Qs + 230)] / 0.3846

[(Qs - 230) / (Qs + 230)] = 0.6 x 0.3846

[(Qs - 230) / (Qs + 230)] = 0.2308

Qs - 230 = 0.2308 x (Qs + 230)

Qs - 230 = 0.2308 x Qs + 53.07

0.7692 x Qs = 283.07

Qs = 368.01