A monopolist has an inverse demand curve given by py12y and

A monopolist has an inverse demand curve given by p(y)=12-y and marginal cost is 2y. What will be its profit-maximizing level of output? Suppose the government decides to put a tax on this monopolist so that for each unit it sells it has to pay the government $2. What will be the output under this form of taxation?

Solution

For a monopolist, profit maximizing output will be attained at a point where Marginal revenue=Marginal Cost ,ie, MR=MC

P=12-y

It implies P.y=12y-(y)^2

Thereforr MR= d(P.y)/dy=12-2y

MC=2y

It implies 12-2y=2y

12=4y

Y=3

Therefore profit maximizing output in the case above is 3

Now ,if government starts charging tax of $3 per output,his MC will increase to 2y+2

Profit max. Output in new case- MR=MC

12-2y=2y+2

10=4y

Y=2.5

This will be profit maximizing output in new case