Question

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Assignment Questions

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);
2. Suppose that a poor harvest season raises the price of apples to P_A = 11.25

1. Is it possible to reach a market equilibrium if the price of apple juice P_J remains unchanged? Why? How much quantity of apple juice will finally be exchanged on the market? (5 marks)
2. Find the market price necessary to restore equilibrium. Deduce the equilibrium quantity of apple juice (5 marks);

3. Draw a graph to illustrate your answers (5 marks).

Answer 1

Qs = 100Pj - 20Pa

Qd = 1000-150Pj+100Pt

Pa = 5, Pt = 4

Qs = 100Pj - 20*5 => Qs = 100Pj-100

Qd = 1000-150Pj+100*4 => Qd = 1400-150Pj

In equilibrium, Qs = Qd

100Pj - 100 = 1400 - 150Pj

250Pj = 1500

Pj = 6

Qs = 600-100 = 500

b) If Pa = 11.25 and Price oj juice dos not change then Pj = 6. Substituting this in equation of Qs and Qd, we get

Qs = 100*6-20*11.25 = 600-225 = 375

Qd = 1000-150*6+400 = 1400-900 = 500

Clearly demand is more than supply. Therefore the market is not in equilibrium. Only 375 will be supplied. There will be excess demand.

c) To ensure equilibrium,

Qs = 100Pj - 20*11.25 => Qs = 100Pj - 225

Qd = 1400-150Pj

Qs =Qd

100Pj - 225 = 1400-150Pj

Pj = 6.5

Q = 425