Question

In a hypothetical country, for an arbitrary good, the demand curve for that good is “Q= 200 - 4 P”. For the supply side, the fixed cost is 100 and the average cost is "0.5Q +20 + 100/Q".

(a) If there is free trade, and the world price p^w = 42. Under perfect competition, what is the consumer surplus and producer surplus? (3 points)

(b) If there is free trade, and the world price p^w = 42. Under monopoly, what is the consumer surplus and producer surplus? (3 points)

(c) In a hypothetical home country, for arbitrary firms and hypothetical goods, the fixed cost is $25, the constant marginal cost is $12, the demand curve for that good is “Q= 200 - 4 P”, the total sales of the whole industry is 1600 units.

In a hypothetical foreign country, the arbitrary firms face the same costs. The only difference here is the total sales, which is 900 units.

Based on PP curve [Notes: P = c + 1/(b x n)] and CC curve, what is the equilibrium number of the firms inside the industry for that home and foreign country? What is the equilibrium number of firms in the whole world if there is free trade? What is the trade pattern for this model? (4 points)

Answer 1

As per the Equilibrium conditions, that is MR=MC, the Equilibrium price and quantity in the domestic country without free trade= $45 and 20 units respectively

See the graph------

a) If there is free trade ( Pw=$42) under Perfect Competition------

After free trade, we gind that domestic supply is restricted to 18 units and demand is 32 units

* Consumer surplus= 1/2×32×(50-42)=$128

* Producers surplus=1/2×18×(42-20)=$198

b) Under free trade(pw=$42), under monopoly-----

* Consumers surplus will decrease

* Producers surplus- will increase

C) Equilibrium number of Quantity in the world under free trade----

In foreign country=188units

In home country=12 units

Explanation-----

Home country Equilibrium---

200-4p=12

P=$47

Putting this value in demand equation----

Qd= 200-4(47)=12 units

Total world Supply = 200

Home Supply= 12

Foreign supply=200-12=188 units