Question

Consider the market for apple juice. In this market, the supply curve is given by Q_S = 10P_J −5P_A and the demand curve is given by Q_D = 100−15P_J +10P_T, where J denotes apple juice, A denotes apples, and T denotes tea.

1. Assume that P_A is fixed at 1 and P_T = 5. Calculate the equilibrium price and quantity in the apple juice market ;
2. Suppose that a poor harvest season raises the price of apples to P_A = 2. Find the new equilibrium price and quantity of apple juice ;
3. Draw a graph to illustrate your answers .

Answer 1

Qs = 10PJ - 5PA

Qd = 100-15PJ + 10PT

a) PA = 1

PT = 5

Qs = 10PJ - 5

Qd = 100-15PJ + 10*5 = 150-15PJ

For equllibrium Qd = Qs

150-15PJ = 10PJ -5

155 = 25PJ

PJ = 155/25 = 6.2$

Equllibrium price of apple juice = 6.2$

Equllibrium quantity = 10PJ -5 = 10*6.2-5 = 57

b) PA = 2

PT = 5

Qs = 10PJ -5*2 = 10PJ -10

QD = 100-15PJ +10*5 = 150-15PJ

For equllibrium Qd = Qs

150-15PJ = 10PJ-10

160=25PJ

PJ = 6.4$

Equllibrium price of apple juice = 6.4$

Equllibrium quantity = 10PJ -10 = 10*6.4-10 = 54