Suppose that a perfectly competitive market is described by the following supply and demand equations: QD = 300 – P and QS = 2P. Suppose that government subsidizes this good: for each unit sold government pays $15 to the seller.
(a) What is the government expenditure on this subsidy?
(b) What is the deadweight loss as a result of this subsidy?
Thanks for your help.
To find the government expenditure on this subsidy, we need to calculate the number of units sold that qualify for the subsidy and multiply it by the subsidy amount.
(a) Government expenditure on this subsidy:
Step 1: Set the demand equation (QD) equal to the supply equation (QS) to find the equilibrium price:
300 - P = 2P
Step 2: Solve for the equilibrium price:
300 = 3P
P = 100
Step 3: Substitute the equilibrium price into either the demand or supply equation to find the equilibrium quantity:
QD = 300 - P = 300 - 100 = 200
QS = 2P = 2(100) = 200
The equilibrium quantity is 200.
Step 4: Determine the number of units sold that qualify for the subsidy. Since the government pays $15 per unit sold, we need to find the quantity demanded (QD) at a price equal to or greater than the subsidy amount ($15).
QD = 300 - P
300 - 15 = 285
The quantity demanded at a price of $15 or higher is 285.
Step 5: Calculate the government expenditure by multiplying the subsidy amount ($15) by the quantity sold that qualifies for the subsidy (285):
Government expenditure = $15 x 285 = $4,275
Therefore, the government expenditure on this subsidy is $4,275.
(b) To find the deadweight loss resulting from the subsidy, we need to compare the quantity produced and consumed with the quantity that would have been produced and consumed in the absence of the subsidy.
Step 1: Calculate the quantity produced and consumed with the subsidy:
QS = 2P
2(100) = 200
The quantity produced and consumed with the subsidy is 200.
Step 2: Calculate the quantity that would have been produced and consumed without the subsidy:
QD = 300 - P
300 - 100 = 200
The quantity that would have been produced and consumed without the subsidy is also 200.
Step 3: Find the difference between the two quantities:
Deadweight loss = Quantity without subsidy - Quantity with subsidy
Deadweight loss = 200 - 200 = 0
Therefore, the deadweight loss as a result of this subsidy is zero.