Question

A monopoly firm sells its product to two countries: A and B. Demand in the two countries are QA = 100 – 2p and QB = 80 – p. Firm’s cost function is C = 100 + 10Q. Find the firm’s total profit and the prices it charges in the two countries.

Answer 1

Sol :

In Monopoly Firm' demand curve is equal to Average Revenue and Marginal revenue is equal to Price of the product.

Qa = Price (AR)

100 - 2p = P

100 = 3p

$33.33 = Price 1 , Qa = 33

Qb = 80 - P

P + P = 80

2P = 80

P2 = $40 , Qb = 20

Cost = 100 + 10Q
       A = 100 + 10(33)

           = 100 + 330 = $430

       B = 100 + 10(20) = $300

(i) (a) Total Profiit of firm A = Total Revenue - Total Cost                        ..........................(1)

Total Revenue1 = Price x Quantity                              Total Cost = $430

                          = 33.33 x 33

                           =$1100

Putting values in (1)

    TP1 = 1100 - 430 = $670

(b)

Total Profiit of firm B = Total Revenue - Total Cost                        ..........................(1)

Total Revenue1 = Price x Quantity                              Total Cost = $300

                          = 40 x 20

                           =$800

Putting values in (1)

    TP2 = 800 - 300 = $500

(c) Total Profit = A + B

                      = 670 + 500 = $1170

(ii) Price for country A = $33.33

     Price for country B = $40

(Calculation of price is given above)