Question

Per-unit Tax: The Isoland widget market has the following supply and demand functions: Supply: P = 20 + 2QS Demand: P = 160 − 2QD Suppose a per-unit tax of $40 is imposed on this market.

Draw a picture and calculate:

(a) Price consumers pay

(b) price producers receive

(c) Total tax revenue

(d) Consumer surplus

(e) Producer Surplus

(f) Consumer tax burden

(g) Producer tax burden

(h) Total welfare

(i) Deadweight loss

Answer 1

After tax the equilibrium has

160 - 2Q - 40 = 20 + 2Q

100 = 4Q

Q = 25 units

P(buyer) = 160 - 25*2 = $110

P(seller) = 20 + 2*25 = $70.

The figure is shown below

(a) Price consumers pay (after tax) = $110

(b) price producers receive (after tax) = $70

(c) Total tax revenue = tax*quantity sold = 40*25 = $1000

(d) Consumer surplus = 0.5*(160 - 110)*25 = $625

(e) Producer Surplus = 0.5*(70 - 20)*25 = $625

(f) Consumer tax burden = 0.5*(25 + 35)*(110 - 90) = $600

(g) Producer tax burden = 0.5*(25 + 35)*(90 - 70) = $600

(h) Total welfare = CS + PS = $1250

(i) Deadweight loss = 0.5*40*10 = $200.