Answer to Question #44840 in Finance for Mohseen Khan

Question

Consider a small country in which the demand and supply curves of a
particular commodity are respectively given as:
Qd=120-20P (1)
Qs=20P (2)

where Qd is the quantity demanded, Qs the quantity supplied, and P the price.

(a) compute the equilibrium price and quantity under conditions of autarky and
the elasticity of demand (Ed ) and supply (Es ) at the point of equilibrium.

(b) Suppose now that the country decides to engage in trade for this particular
commodity and the international price Pw=1. Compute Qd , Qs, imports (M),
Ed , Es , and the changes in consumers’ surplus, producers’ surplus and in total
welfare. Discuss your answer.

(c) Lets assume that the country imposes a tariff t =1 per unit. Compute Qd , Qs ,
M, Ed , Es , and the changes in consumers’ surplus, producers’ surplus, total
welfare and in tariff revenue (TR) and compare the results with free trade case.

Answer 1

Qd = 120 - 20P, P = 6 - Q/20
Qs = 20P, P = Q/20
(a) The equilibrium price and quantity under conditions of autarky will be in the point, where Qd = Qs
120 - 20P = 20P
40P = 120
Pe = $3
Qe = 20*3 = 60 units.
The elasticity of demand (Ed) = Pd' = 1/20 and supply Es = Ps' = 1/20 too at the point of equilibrium.
(b) If now the international price is Pw = $1. Qd = 120 - 20*1 = 100 units, Qs = 20*1 = 20 units, imports (M) = 120 - 20 = 100, Ed = 1/20, Es = 1/20, the consumers’ surplus will increase, producers’ surplus will decrease and total welfare will increase.
(c) If the country imposes a tariff t =$1 per unit. Qd = 120 - 20*2 = 80 units, Qs = 20*2 = 40 units, M = 80 - 40 = 40 units, Ed = 1/20, Es = 1/20, consumers’ surplus will decrease, producers’ surplus will increase, total welfare will decrease, tariff revenue (TR) will increase.