Question

If the inverse demand curve is

P=200−Q

and the marginal cost is constant at $20​,

how does charging the monopoly a specific tax of τ=​$14 per unit affect the monopoly optimum and the welfare of​ consumers, the​ monopoly, and society​ (where society's welfare includes the tax​ revenue)? What is the incidence of the tax on​ consumers?

As a result of the​ tax, the profit-maximizing quantity decreases by ____ units and the​ profit-maximizing price increases by ​$_____   ​(Enter numeric responses using real numbers rounded to two decimal​ places.)

Consumer surplus decreases by ​$______

The​ monopoly's surplus (producer surplus) decreases by $ ­­­­_____

Finally, society's welfare decreases by $____

The consumer incidence of the tax is ___%

Answer 1

Answer:

Given, the inverse demand curve is P=200−Q and the marginal cost is constant at $20​.

Thus, MR=200-2Q and MC=20

In equilibrium, MR=MC=>200-2Q=20=>Q=90 and P=110

But when a specific tax of τ=​$14 per unit charges marginal cost of the the monopoly increases by the same amount of tax. Thus after tax imposition the new MC of the firm will be, MC_tax=20+14=34

Thus after tax imposition,

In equilibrium, MR=MC_tax=>200-2Q=34=>Q=83 and P=117

Hence, as a result of the​ tax, the profit-maximizing quantity decreases by 7 units and the​ profit-maximizing price increases by ​$7.

Consumer surplus decreases by ​=0.5*(200-110)*90-0.5*(200-117)*83=4050-3444.5=$605.5

The​ monopoly's surplus (producer surplus) decreases by = 0.5*(110-20)*90-0.5*(117-20)*83=4050-4025.5=$24.4

Finally, society's welfare decreases by =$605.5+$24.4=$629.9

The consumer incidence of the tax is = tax*Q=14*83=$1162