$(26$ points$)$ Consider the three interconnected markets for goods $1,2,$ and $3$:

QS

$1=10+0\mathrm{.}5$P$1$

QD

$1=1500\mathrm{.}5$P$1+2$P$2$

QS

$2=5+2$P$2$

QD

$2=950\mathrm{.}5$P$2+0\mathrm{.}5$P$1$ P$3$

QS

$3=1\mathrm{.}5$P$3$

QD

$3=1200\mathrm{.}5$P$30\mathrm{.}5$P$2$

$($a$)(6$ points$)$ What is the equilibrium in the market? $($In other words, find Q$$

$1$

$,$ Q$$

$2$

$,$

Q$$

$3$

$,$ P

$$

$1$

$,$ P

$$

$2$

$,$ and P

$$

$3$

$.)$

$($b$)(2$ points$)$ How is good $2$ related to the other goods? Explain why.

$($c$)(6$ points$)$ Suppose the government imposes a $$4$ per unit tax on good $1($for

ease, imagine the tax is placed on the producers$).$ How does this impact the

equilibrium outcome? Does the outcome differ from the predictions of partial

equilibrium analysis?

$($d$)(6$ points$)$ Suppose the government imposes a $$4$ per unit tax on good $2($for

ease, imagine the tax is placed on the producers$).$ How does this impact the

equilibrium outcome? Does the outcome differ from the predictions of partial

equilibrium analysis?

$($e$)(6$ points$)$ Suppose the government imposes a $$4$ per unit tax on good $3($for

ease, imagine the tax is placed on the producers$).$ How does this impact the

equilibrium outcome? Does the outcome differ from the predictions of partial

equilibrium analysis?