Demand for product A is given by:

Q_D = 500 - 50 P + 10 Y

Where P = Price of A and Y = average income

And the supply of A is given by:

Q_S = 50 P - 200P_B

Where P_B = Price of B

If Y = 10 and P_B = 2, what is the equilibrium price and quantity of A and how do I solve for the equilibrium price of A as a function of income. 

If Y = 10, what is the equilibrium price of A?

Given that Y = 10 and P_B = 2, how do I calculate the price elasticity of demand and the price elasticity of supply.

Suppose the government places a $1/ton specific tax on A.

1. How do I calculate the new equilibrium price and quantity for the A market.
2. How much of the tax would get passed on to the consumer?
3. How can I verify using the calculus approach for solving for the burden of the tax. I really struggle with the calculus parts.