Market Equilibrium Analysis with Taxes: Supply and Demand Calculation

Published on May 24, 2026

Word-Problem

This problem involves calculating market equilibrium before and after a GST imposition, determining tax revenue, and analyzing deadweight loss using supply and demand functions.

Question

Answer

Based on the provided image, here is the step-by-step solution to the problem.

Given Data:

Demand function:
Supply function:
GST (tax per unit):

1. Market equilibrium before tax

Before tax, the price paid by consumers (

) is equal to the price received by producers (

). Let

.
At equilibrium,

Substitute

back into either equation to find the equilibrium quantity

Equilibrium before tax: , .

2. Equilibrium after tax

After a tax of

is imposed, the price consumers pay (

) is the price producers receive (

) plus the tax:

Substitute this into the demand equation:

Set

to find the new equilibrium:

Now, find the price consumers pay:

Find the new equilibrium quantity

Equilibrium after tax: , , .

3. Government tax revenue and deadweight loss

Government Tax Revenue:

Deadweight Loss (DWL):
The DWL is the area of the triangle between the demand and supply curves from the new quantity to the old quantity.

4. Why deadweight loss occurs after taxation

Deadweight loss occurs because the tax creates a “wedge” between the price consumers pay and the price producers receive. This increases the cost for buyers and decreases the revenue for sellers, which leads to a reduction in the quantity traded in the market (from

Because the quantity decreases, some mutually beneficial transactions (where the buyer’s valuation is higher than the seller’s cost) no longer take place. The loss of consumer and producer surplus from these lost transactions is not captured by the government as tax revenue, resulting in a net loss to total societal welfare.

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