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

If new quantity demanded be Q1, then

- 0.15 = [(Q1 - 1,455,300) / (Q1 + 1,455,300)] / [$(2.53 - 1.15) / $(2.53 + 1.15)]

- 0.15 = [(Q1 - 1,455,300) / (Q1 + 1,455,300)] / (1.38 / 3.68)

- 0.15 = [(Q1 - 1,455,300) / (Q1 + 1,455,300)] / 0.375

[(Q1 - 1,455,300) / (Q1 + 1,455,300)] = 0.375 x (- 0.15)

[(Q1 - 1,455,300) / (Q1 + 1,455,300)] = - 0.0563

Q1 - 1,455,300 = - 0.0563 x (Q1 + 1,455,300)

Q1 - 1,455,300 = - 0.0563Q1 - 81,860

1.0563Q1 = 1,373,439

Q1 = 1,300,236

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

If new quantity supplied be Q2, then

0.85 = [(Q2 - 1,455,300) / (Q2 + 1,455,300)] / [$(2.53 - 1.15) / $(2.53 + 1.15)]

0.85 = [(Q2 - 1,455,300) / (Q2 + 1,455,300)] / (1.38 / 3.68)

0.85 = [(Q2 - 1,455,300) / (Q2 + 1,455,300)] / 0.375

[(Q2 - 1,455,300) / (Q2 + 1,455,300)] = 0.375 x 0.85

[(Q2 - 1,455,300) / (Q2 + 1,455,300)] = 0.3188

Q2 - 1,455,300 = 0.3188 x (Q2 + 1,455,300)

Q2 - 1,455,300 = 0.3188Q2 + 463,877

0.6812Q2 = 1,919,177

Q2 = 2,817,347

NOTE: Mid-point method is used for both elasticity calculations.