Consider an individual with a utility function $($$ $,$ & $)=$$ $+$ & $.$ Their

income is Y $=$ $$100.$ The pre$-$tax market prices they face are p$1=$ $$5$ and p$2=$ $$1.$ Suppose a

unit tax of $$0\mathrm{.}25$ is introduced on good $1,$ that the statutory incidence of the tax is on firms,

that firms are perfectly competitive and that firms are perfectly elastic in their supply of both

goods.

a$.$ Derive the uncompensated demand functions for x $1$ and x $2.$

b$.$ What is the compensated own$-$price elasticity of demand for good $1?$

c$.$ Calculate consumer surplus before and after the tax is introduced.

d$.$ Calculate the revenue generated by the tax.

e$.$ Calculate the excess burden $($EB$)$ from this tax