Answer to Question #163028 in Microeconomics for Amna

Question

The demand curves for good X of three consumers (A, B and C) are given by the equations:

Q Ad = 100 – 0.2x

Q Bd = 300 – 0.5Px and

Q Cd = 500 - 0.8P

The market supply curve for X is: MCx =50+8.5Q. Determine the market equilibrium if X were a private

good. Will the market equilibrium be the same/different if X were instead a public good? Why? In case X

is a public good, determine the tax share of each individual using the benefit principle of taxation. Draw

graphs to illustrate your answer.

b) Using the information on demand and costs given in part (a), explain what might happen if individual B

volunteers to provide this good for all. Draw graphs and explain.

Q.2 Using the information in Q.1, suppose that:

(i) Individual C states that his marginal benefit is 250.

(ii) Individual A states that his marginal benefit is 100.

Calculate their Clarke tax liability. Also show each case using an appropriate diagram.

Answer 1

a) Total market demand is:

Qd = QAd + QBd + QCd = 900 - 1.5Px or Px = 2/3Q - 600.

If X is a private good, then in equilibrium Qd = Qs, so:

600 - 2/3Q = 50 + 8.5Q,

Q = 60 units,

P = 560.

If X were instead a public good, then the market equilibrium will change.

The tax share of the third individual will be the highest, as he consume the highest quantity among customers.

b) if individual B volunteers to provide this good for all, then the equilibrium price will decrease.

Q.2

(i) If individual C states that his marginal benefit is 250, then his tax liability will be higher.

(ii) If individual A states that his marginal benefit is 100, then his tax liability will be lower.