In the market of apples, the demand and supply functions are respectively P = Q 2 D 10QD + 150, P = Q 2 S + 14QS + 22

1. Derive the equilibrium price and quantity for apples. Suppose now that the government decides to impose a tax of $t per apple (paid by apple farmers to the government).

2. Write down the equilibrium quantity as functions of t.

3. If it is known that the equilibrium quantity is 3, work out the value of t.

4. If, instead of imposing a tax, the government provides a subside of $42 per apple (paid to apple farmers by the government), find the new equilibrium price and quantity