Question

Suppose the domestic demand for coffee is given by the equation Q = 100 - P, domestic supply by the equation Q = P. The world price for coffee is $20 per unit. The government decides to impose an import quota limiting imports to 10 units. How much deadweight loss will this generate?

Please explain clearly using graphs.

Answer 1

With free trade and price of 20,

Domestic demand (Qd) = 100 - 20 = 80

Domestic supply (Qs) = 20

Import quota = Domestic demand - Domestic supply

(100 - P) - P = 10

100 - 2P = 10

2P = 90

P = 45

Qd = 100 - 45 = 55

Qs = 45

Deadweight loss = (1/2) x Change in price x (Change in Qd + Change in Qs) = (1/2) x (45 - 20) x (80 - 55 + 45 - 20)

= (1/2) x 25 x 50

= 625

In following graph, AB & CD are domestic demand & supply curves of the good. Pre-trade equilibrium is at point E with price P1 & quantity Q1. With free trade, world price is P* (= 20) for which domestic consumption is Q2 (= 80) and domestic production is Q3 (= 20), so imports equal (Q2 - Q3).

When an import quota (= 10) is imposed such that maximum allowed imports equal (Q4 - Q5 = 10), it will increase the domestic price to Pt (= 45) with domestic consumption being Q4 (= 55) and domestic production being Q5 (= 45). The import quota leads to a decrease in domestic demand (Q4 < Q2), increase in domestic consumption (Q5 > Q3) and decrease in imports [(Q4 - Q5) < (Q2 - Q3)]. Deadweight loss is sum of areas of triangles GJK and FHL.