An Econ Math problem

Suppose you have the following demand and supply schedules: Qd = 90 - 5P + 2Y and Qs= 10 + 6P where Qd and Qs are quantity demanded and supplied, respectively, P is the price of the good, and Y is the average income in the area (in 10,000).

a) Suppose Y = 3.5. Find the equilibrium quantity and price.

b) Find the amount of consumer surplus and producer surplus.

c) Suppose the consumers must pay a 5 cents per unit tax. Explain what happens to the demand curve.

d) Find the new equilibrium price and quantity after the tax.

e) How much tax revenue will be collected? What happens to consumer and producer surpluses?

f) Now the government decides to eliminate the unit tax on this good, and instead imposes a 0.1 income tax. How will this change the equilibrium price and quantity?

g) How does the income tax affect consumer and producer surplus compared to the unit tax?

h) Find the income elasticity of demand when there is no tax. Then find the income elasticity of demand when there is per unit tax. Finally, find the income elasticity of demand when there is an income tax. Do they differ? Why or why not?