Question

In: Economics

Assume that bad weather shifts the supply curve for mangoes along the demand curve to the...

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.)

Solutions

Expert Solution

(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


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