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 dead weight loss will this generate?
Start by drawing supply and demand curves and solve for an equilibrium price and quantity. Now draw in the quota. Dead weight loss will be the triangle area which is:
a) to the right of the quota
b) under demand, and
c) above supply
you may need to use some basic algebra/geometry to numerically solve.
To calculate the deadweight loss generated by the import quota, we first need to understand the concept of deadweight loss.
Deadweight loss refers to the economic inefficiency that occurs when the quantity of a good or service produced and consumed is not at the equilibrium level. In this case, the quota reduces the quantity traded to below the equilibrium level, leading to deadweight loss.
Here's how we can calculate the deadweight loss generated by the import quota:
Step 1: Determine the equilibrium quantity and price without the import quota.
To find the equilibrium quantity and price, set the domestic demand equal to the domestic supply: Q = 100 - P = P.
Solving this equation for P, we get: P = 50.
Substitute this equilibrium price into either the demand or supply equation to find the equilibrium quantity: Q = P = 50.
Step 2: Find the quantity imported without the quota.
Since the world price for coffee is $20 per unit, and the domestic equilibrium price is $50, the quantity imported before the quota is the difference between the domestic equilibrium quantity and the domestic supply at the equilibrium price:
Quantity Imported = Equilibrium Quantity - Domestic Supply = 50 - 50 = 0 units.
Step 3: Find the new quantity traded after the import quota.
The import quota limits imports to 10 units, so the new quantity traded will be 10 units.
Step 4: Calculate the deadweight loss.
Deadweight loss is calculated as the area of the triangle formed between the supply curve, demand curve, and the new quantity traded.
We can break down the deadweight loss into two triangles, one above the domestic supply curve and one below the domestic demand curve.
Triangle 1: Calculate the area of the triangle formed above the domestic supply curve.
The base of this triangle is the difference between the equilibrium quantity and the new quantity traded (50 - 10 = 40 units).
The height of this triangle is the difference between the domestic price and the world price ($50 - $20 = $30).
The area of Triangle 1 is (1/2) * base * height = (1/2) * 40 * 30 = 600.
Triangle 2: Calculate the area of the triangle formed below the domestic demand curve.
The base of this triangle is the difference between the equilibrium quantity and the new quantity traded (50 - 10 = 40 units).
The height of this triangle is the difference between the domestic price and the world price ($50 - $20 = $30).
The area of Triangle 2 is also 600.
The total deadweight loss is the sum of Triangle 1 and Triangle 2:
Total Deadweight Loss = Triangle 1 + Triangle 2 = 600 + 600 = 1200.
Therefore, the import quota generates a deadweight loss of 1200.