Model Answer
0 min readIntroduction
International trade plays a crucial role in global economic integration, fostering efficiency and consumer welfare. While free trade generally leads to optimal resource allocation, governments often employ trade restrictions like import quotas to protect domestic industries. An import quota is a direct restriction on the quantity of a good that can be imported. This intervention distorts market signals, leading to changes in prices, production, and consumption patterns, and ultimately impacting consumer and producer surplus. This answer will analyze the effects of a 50-unit import quota on a good X, assuming a free trade initial condition and zero transportation costs, calculating the resulting changes in welfare.
Understanding the Initial Equilibrium
Let's assume that in the absence of any trade restrictions, the world price of good X is Pw. With zero transportation costs, both the importing and exporting countries face the same price. Let the initial quantity demanded be Qd and the initial quantity supplied be Qs. In a free trade scenario, the market clears at a price Pw and a quantity Qw (where Qw = Qd - Qs, representing the quantity imported).
Impact of the Import Quota
When an import quota of 50 units is imposed, the supply curve effectively shifts leftward by 50 units. This creates a new equilibrium where the quantity supplied is reduced. The price of good X will rise from Pw to Pq due to the reduced supply. The quantity consumed will decrease from Qw to Qc, and the quantity produced domestically will increase. Let's denote the new quantity consumed as Qc and the new quantity produced domestically as Qp. The quota will be fully utilized, meaning 50 units will be imported.
Calculating Consumer and Producer Surplus
To calculate the changes in consumer and producer surplus, we need to define the demand and supply curves. Let's assume a linear demand curve: P = a - bQd and a linear supply curve: P = c + dQs. (Where a, b, c, and d are constants).
Consumer Surplus (CS)
Consumer surplus is the area below the demand curve and above the price. The change in consumer surplus (ΔCS) is the loss in the area under the demand curve due to the higher price and lower quantity. ΔCS = - [(Pq - Pw) * (Qd(Pq) + Qd(Pw)) / 2]. This represents a reduction in consumer welfare.
Producer Surplus (PS)
Producer surplus is the area above the supply curve and below the price. The change in producer surplus (ΔPS) is the gain in the area above the supply curve due to the higher price and increased quantity produced domestically. ΔPS = [(Pq - Pw) * (Qp(Pq) + Qp(Pw)) / 2]. This represents an increase in producer welfare.
Calculating the Protection Cost (Deadweight Loss)
The protection cost, also known as the deadweight loss, represents the loss of overall welfare due to the quota. It is the sum of the loss in consumer surplus that is not offset by the gain in producer surplus. Protection Cost = |ΔCS| - ΔPS. Alternatively, it can be calculated as the area of the triangle formed by the quota restriction, representing the lost gains from trade.
Illustrative Example (with assumed values)
Let's assume the following:
- Demand Curve: P = 100 - Qd
- Supply Curve: P = 20 + Qs
- World Price (Pw): 30
Initially, Qd = 70, Qs = 10, and imports = 60.
With a quota of 50, imports are restricted to 50. The new supply curve becomes effectively Qs' = Qs - 50. Solving for the new equilibrium price (Pq):
100 - Qc = 20 + (Qs - 50) + 50 => 100 - Qc = 20 + Qs. Since Qs = 10, Pq = 40.
Qc = 60 and Qp = 20.
ΔCS = - [(40-30)*(60+70)/2] = -550
ΔPS = [(40-30)*(20+10)/2] = 150
Protection Cost = |-550| - 150 = 400
Therefore, in this example, the consumer surplus decreases by 550, the producer surplus increases by 150, and the protection cost is 400.
Conclusion
The imposition of an import quota, while benefiting domestic producers, leads to a net welfare loss for the importing country. The reduction in consumer surplus outweighs the increase in producer surplus, resulting in a protection cost representing the inefficient allocation of resources. This highlights the economic rationale for advocating free trade policies, despite potential short-term adjustments required for domestic industries. Further analysis could consider the distributional effects of the quota and the potential for alternative policy interventions like subsidies or retraining programs to mitigate the negative consequences.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.