Question

suppose the a domestic monopolist has cost c= 50+.25q^2 .home demand is p = 100-.5q

what is the monopolist level of outprice and profoits in xlosed economy
suppose open for world a trade and world prive is 40   and domestic firm faces world market   how much the country import and export
fi d the consumer and producer surplus. with free trade
comapre trade profit worh monopolist output which is higher explain

Answer 1

Monopolists cost is given by

c=50+0.25q^2

Marginal cost=MC=dc/dq=0.5q

p=100-0.5q

TR=p*q=(100-0.5q)*q=100q-0.5q^2

MR=dTR/dq=100-q

Set MR=MC for profit maximization,

100-q=0.5q

q=200/3=66.67

p=100-0.5*200/3=200/3=66.67

In absence of world trade

Price=200/3=66.67

Quantity=200/3=66.67

Total cost,c=50+0.25q^2=50+0.25*(200/3)^2=1161.11

TR=(200/3)*(200/3)=4444.44

Profit=TR-c=4444.44-1161.11=3283.33

Let us find producer and consumer surplus

Producer surplus is the area under supply curve and above equilibrium price

PS=1/2*((200/3)-0)*((200/3)-0)=2222.22

Consumer surplus is the area under supply curve and above equilibrium price

CS=1/2*((200/3)-0)*(100-(200/3))=1111.11

Now let us assume world trade begins

Let us see how much, monopolist can produce at a world price of 40 (or say how much it produces at which MC=40)

Set MC=40

0.5q=40

q=80

We know that producer had to supply at world's price level. Above which there world be no demand.

So, producer would produce 80 units (as calculated above).

Demand at p=40 is

p=100-0.5q

40=100-0.5q

0.5q=60

q=120

There is a demand of 120 units at this level. So, 80 units will be supplied by monopolist and remaining 40 units (i.e. 120-80) will be imported.   

Let us calculate profit in this situation

TR=p*q=40*80=3200

Total cost,c=50+0.25q^2=50+0.25*(80)^2=1650

Profit=TR-c=3200-1650=1550

Total profit has reduced as a result of world trade.