Market supply

Consider the market for apple juice. In this market, the supply curve is given by QS = 100PJ
−20PA and the demand curve is given by QD = 1000−150PJ +100PT, where J denotes apple juice,
A denotes apples, and T denotes tea.
1) Assume that PA is fixed at 5 and PT = 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 PA = 11.25
Instructions:
a) Is it possible to reach a market equilibrium if the price of apple juice PJ remains
unchanged? Why? How much quantity of apple juice will finally be exchanged on
the market? (5 marks)
b) 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).