Question

Assume that bad weather shifts the supply curve for mangoes along the demand curve to the left which increases the mango price to $2.53/mango. If the original equilibrium price of mangoes is $1.15/lb and the original equilibrium quantity is 1,455,300 mangoes, the elasticity of mango supply is 0.85 and the elasticity of demand is -0.15, what is the new equilibrium quantity demanded of mangoes? What is the new equilibrium quantity supplied? (HINT AGAIN: Be careful! Think about it.)

Answer 1

(i) Using mid-point method,

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

Let new quantity demanded = Qd.

- 0.15 = [(Qd - 1,455,300) / (Qd + 1,455,300)] / [$(2.53 - 1.15) / $(2.53 + 1.15)]

- 0.15 = [(Qd - 1,455,300) / (Qd + 1,455,300)] / (1.38 / 3.68)

- 0.15 = [(Qd - 1,455,300) / (Qd + 1,455,300)] / 0.375

[(Qd - 1,455,300) / (Qd + 1,455,300)] = (-0.15) x 0.375

[(Qd - 1,455,300) / (Qd + 1,455,300)] = - 0.0563

Qd - 1,455,300 = - 0.0563 x (Qd + 1,455,300)

Qd - 1,455,300 = - 0.0563 x Qd - 81,860

1.0563 x Qd = 1,373,439

Qd = 1,300,236

(ii) Using mid-point method,

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

Let new quantity supplied = Qs

0.85 = [(Qs - 1,455,300) / (Qs + 1,455,300)] / [$(2.53 - 1.15) / $(2.53 + 1.15)]

0.85 = [(Qs - 1,455,300) / (Qs + 1,455,300)] / (1.38 / 3.68)

0.85 = [(Qs - 1,455,300) / (Qs + 1,455,300)] / 0.375

[(Qs - 1,455,300) / (Qs + 1,455,300)] = 0.85 x 0.375

[(Qs - 1,455,300) / (Qs + 1,455,300)] = 0.3188

Qs - 1,455,300 = 0.3188 x (Qs + 1,455,300)

Qx - 1,455,300 = 0.3188 x Qs + 463,877

0.6812 x Qs = 1,919,177

Qs = 2,817,347