A monopolist faces the following demand function for its product: Q = 45 - 5P The fixed costs of the monopolist are $12 and the variable costs are $5 per unit.
a) What are the profit-maximizing price and quantity? What will be the profits at these price and output levels?

Here Demand function is given by, Q = 45 -5P

ð  P =( 45-Q)/5........... (i)

No w Revenue is given by  ,

 R =  Q * P

ð  R =  Q * ( 45-Q)/5 )..... from  (I )

ð  R = 9Q-Q^2/5.... (II)

Here Marginal Revenue which is derivative of ( II), so,

MR =9-2Q/5 ..... (iii)

 Here marginal cost should be equal to Variable cost which is MC =5

At profit maximization,

MC = MR

ð  9-2Q/5 =5

ð  Q = 10

Hence, 10 is the profit maximizing quantity and the price is given from (i) which is 7. The profit is (7*10-12-5*7) =23

b) If the government imposes an annual tax on the firm of $10, what will be the profit-maximizing price, output, and profits? Who bears the burden of the tax? Why?