Question

Consider the market for apple juice. In this market, the supply curve is given by Q_S = 100P_J −20P_A and the demand curve is given by Q_D = 1000−150P_J +100P_T, where J denotes apple juice, A denotes apples, and T denotes tea.

1. Assume that P_A is fixed at 5 and P_T = 4. Calculate the equilibrium price and quantity in the apple juice market (5 marks);

Answer 1

QS = 100PJ - 20PA

QD = 1000 - 150PJ + 100PT

At the equilibrium level, QD = QS

Hence, 1000 - 150PJ + 100PT = 100PJ - 20PA

1000 - 150PJ + 100 x 4 = 100PJ - 20 x 5

1000 - 150PJ + 400 = 100PJ - 100

250PJ = 1500

PJ = 6

QS = 100PJ - 20PA

= 100 x 6 - 20 x 5

= 600 - 100

= 500

QD = 1000 - 150PJ + 100PT

= 1000 - 150 x 6 + 100 x 4

= 1000 - 900 + 400

= 500

Thus, equilibrium price = 6

Equilibrium quantity = 500

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