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?