Question

Suppose the Demand and supply curve for a particular product is as follows:

D(p)=60-15p

S(p)=15p+20

Suppose city council considers implementing a small lump sum tax of $T per unit traded (i.e. if the consumer pays p then the producer receives p-T).

Question: What is the tax incidence on consumers?

Hint 2: The derivative of demand and supply with respect to price is just the slope of the curves, in this case -15, and 15 respectively.

Answer 1

For demand function Q = a - bP and supply function Q = c + bP, when we have a tax T, then

price paid by buyers becomes (a - c + d*T)/(b + d)

price received by sellers becomes (a - c - b*T)/(b + d)

Here a = 60, b = 15, c = 20, d = 15

Hence price paid by buyers = (60 - 20 + 15T)/30 = 1.33 + 0.5T

And price received by sellers = (60 - 20 - 15T)/30 = 1.33 - 0.5T

Before tax, the market price is 1.33

This shows that consumers are paying 0.5 or 50% of tax and sellers are paying the remaining 50%. This is the tax incidence.

Thus tax incidence on consumers is 50%