Question

Assume a competitive market with the following demand and supply curve, D(p) =a-b*P and S(p)= c + d*. Assume the government imposes a tax of t on each unit sold. The equilibrium prices without (P) and with the tax (net price Pn and gross price Pg ) are

Answer 1

D(p) = a - b * p

S(p) = c + d * p

Tax is imposed of "t" on each unit sold.

Equilibrium occurs when demand = supply

a - b * p = c + d * p

p = [(a - c) / (d + b)]

At this price, quantity is = [(ad + bc) / (d + b)]

As tax is imposed in the market per unit sold, it will be shared among buyer as well as seller in the ratio of (demand curve touching price axis - equilibrium price) to (equilibrum price - supply curve touching price axis)

demand curve touching price axis - equilibrium price = (a / b) - [(a + c) / (d + b)] = [(ad + bc) / (bd + b2)]

equilibrum price - supply curve touching price axis =  [(a + c) / (d + b)] + (c / d) = [(ad + cb) / (bd + d2)]

Tax burden share = [(ad + bc) / (bd + b2)] / [(ad + cb) / (bd + d2)] = [(bd + d2) / (bd + b2)]

Consumer burden of tax = [(bd + d2) / (bd + d2 + bd + b2)] * t. Thus the price they pay is [(bd + d2) / (bd + d2 + bd + b2)] * t + [(a - c) / (d + b)]

Producer burden on tax = [(bd + b2) / (bd + d2 + bd + b2)] * t. Thus price producer receive is [(a - c) / (d + b)] - [(bd + b2) / (bd + d2 + bd + b2)] * t