Question

A monopolist has marginal costs MC = Q and home market demand P = 40 – Q (that is the MR = 40 – 2Q). The monopolist can also sell to a foreign market at a constant price P = 16. Find and graph the quantity produced, quantity sold in the home market, quantity sold in the foreign market, and price charged in the home market. Explain why the monopolist’s profits would fall if it were to produce the same quantity but sell more in the home market.

Answer 1

In the home market monopolist will produce at th

e point where MC = MR ( Marginal revenue)

P= 40-Q

Total revenue TR = PQ = Q*(40-Q) = 40Q - Q^{​​​​​​2}​​​​​

MR = TR/Q = 40- 2Q

MC = MR

Q = 40-2Q or 3Q= 40 or Q= 40/3

P= 40-40/3 = 80/3 = 26.667

In the above figure , the monopolist produces at E* in home market . P= 16 and MC curve intersects Q = 16 and hence I'm foreign market the monopolist sells 16 units of good at price per unit = 16.

In home market, marginal revenue that the monopolist earns depend on the demand curve. To sell every additional unit price in the domestic market falls guided by the demand curve. Monopolist produces at a point at which additional revenue which he gains by selling an additional unit of goods is equal to additional cost he incurs by producing an additional unit of good, this point is represented by E* in the graph. If he sell any unit more than 40/3 , marginal cost increases and marginal revenue decreases , and thus profit falls. Hence he won't sell more than 40/3 . This is the reason monopoly does not sell Q= 16 at P= 16 in home .

But in the foreign market marginal revenue is constant , it does not depends on quantity sold. No matter how many unit of its good the monopolist sells in the foreign market, he will gain marginal revenue 16. Therefore monopolist produces amount such that MC16 or Q16 . To gain maximum profit, monopolist produces Q = 16 .