Question

Market demand is given as Qd = 200 – P. Market supply is given as Qs = 4P.

a. Calculate equilibrium price and quantity

a. If an excise tax of $4 per unit is imposed on sellers, calculate the price consumers pay Pc and the price sellers receive Ps.

c. Also, calculate the dead weight loss and consumer surplus after the tax.

Answer 1

Answer:  Market demand is Qd = 200 – P

Market supply is Q_s = 4P

a). Equilibrium price and quantity :

At equilibrium  Qd = Q_s

Hence 200 - P = 4P

=> P = $40

Substituting the value of P into Supply equation:

Q_s = 4 * P

=> Q_d = Q_s = 160

Q = 160

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b). An excise tax of $4 per unit is imposed on sellers;

The demand and Supply functions can be rewritten as (Since in equilibrium quantities will be same, hence we are taking it as Q) :

Q = 200 – P

=> P = 200 -Q

similarly

Q = 4P

=> P = Q/4

With $4 tax on Sellers, the supply equation after tax is

P = Q/4 + 4

Hence, the new equilibrium quantity after tax can be found from equating new supply equation with demand function

Q/4 + 4 = 200 - Q

=> 1.25 Q = 196

Q_t = 156.8

Price (P_s) sellers receive is from pre-tax supply equation - Q_t = 4 P

=> P_s = 156.8 / 4

=> P_s = $39.2

Price (P_c) consumers pay is obtained from demand equation

Q_t = 200 – P_c

=> P_c = 200 -156.8

=> P_c = $43.2

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c). The dead weight loss and consumer surplus after the tax

Deadweight loss is calculated from ½ x $4 x (160 – 156.8) = $6.4

Dead weight loss = $6.4

Consumer Surplus after tax = P_c - P =43.2 - 40

=> $3.2

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