Question

The demand equation for widgets is given by : Qd = a –bP + cG and the supply equation is given by Qs = α + βP - ρN; where P price of widget, G is price of substitutes for widget, and N is price of inputs. Find equilibrium price and quantity.

6. Suppose there is a tax $T levied on each widget sold so that consumers pay Pc = Pp +T where Pp is price producers receive in #5 above. Find equilibrium Pc and Pp .

Answer 1

In equilibrium, Qd = Qs

a - bP + cG = α + βP - ρN

P x (β + b) = a + cG + ρN - α

P = (a + cG + ρN - α) / (β + b)

Q = a - b x [(a + cG + ρN - α) / (β + b)] + cG = a - [(ab + bcG + bρN - bα) / (β + b)] + cG

After the tax, Pc = Pp + T

Qd = a - bPc + cG = a - b x (Pp + T) + cG = a - bPp - bT + cG

Qs = α + βPp - ρN

Equating after-tax Qd and Qs,

a - bPp - bT + cG = α + βPp - ρN

Pp x (β + b) = a - bT + cG + ρN - α

Pp = (a - bT + cG + ρN - α) / (β + b)

Pc = [(a - bT + cG + ρN - α) / (β + b)] + T = [(a - bT + cG + ρN - α + Tβ + bT) / (β + b)]