Figure $5$

Refer to Figure $5.$

a$.$ If there is no government intervention, what is the equilibrium price and quantity of the good?

b$.$ Calculate the Consumer Surplus $($CS$),$ Producer Surplus $($PS$),$ and Total Surplus $($TS$)$ in this market, if there is no government intervention. Be sure to clearly label and state the value for each. For partial credit, provide your equations.

Suppose the government places a $$3$ tax per unit on this good, collected from the producer.

c$.$ How many units of this good will be bought and sold after the tax is imposed?

d$.$ Calculate the Consumer Surplus $($CS$),$ Producer Surplus $($PS$),$ Government Tax Revenues, and Total Surplus $($TS$)$ in this market, if the $$3$ tax is imposed. Be sure to clearly label and state the value for each. For partial credit, provide your equations.

e$.$ Is there any Deadweight Loss? If so calculate it and describe why it exists.