Question

Consider a competitive market served by many domestic and foreign firms. The domestic demand for these firms’ product is Qd = 750 - 1.5P. The supply function of the domestic firms is QSD = 100 + 1P, while that of the foreign firms is QSF = 200.

a. Determine the equilibrium price and quantity under free trade.

Equilibrium price: $
Equilibrium quantity:  units

b. Determine the equilibrium price and quantity when foreign firms are constrained by a 100-unit quota.

Equilibrium price: $
Equilibrium quantity:  units

Answer 1

Solution:

a) Under free trade, total supply becomes Qs = QSD + QSF

Qs = 100 + 1P + 200

Qs = 300 + P

Equilibrium occurs where quantity demanded and quantity supplied equals. So,

Qd = Qs

750 - 1.5*P = 300 + P

(1.5 + 1)*P = 750 - 300

P = 450/2.5 = $180

And equilibrium quantity is 750 - 1.5*180 = 480 units

b) With constraint on foreign firms of 100 unit quota, now only 100 units can be imported from foreign, so total supply will be lower

Qs = QSD + QSF

Qs = 100 + 1P + 100 = 200 + P

Thus, equilibrium is now: Qd = Qs

750 - 1.5*P = 200 + P

(1 + 1.5)*P = 750 - 200

P = 550/2.5 = $220

And equilibrium quantity is Q = 750 - 1.5*220 = 420 units

Note that with the quota constraint, equilibrium price is higher. This is expected as when import quota is imposed, the country is trying to protect domestic sellers from foreign sellers, thereby reducing competition in the market as compared to free trade. This results in higher price for domestic consumers, and with higher price, quantity demanded (and so, quantity supplied as well) decreases.