Question

Consider the following supply and demand functions qD = 16 - 4p qS = -2 + 5p

Market Regulation Using the supply and demand functions from problem 1, suppose a price ceiling of p = 1 were implemented.

a) How much is supplied to the market and how much is demanded?

b) What is the excess demand?

c) Calculate the consumer surplus, producer surplus, and welfare level without the price ceiling.

d) Calculate the consumer surplus, producer surplus, welfare level, and dead weight loss with this price ceiling.

e) What if the price ceiling were p = 5? How would our results change?

Answer 1

We are given the supply and demand functions as

qD = 16 - 4p qS = -2 + 5p

Now suppose a price ceiling of p = 1 were implemented.

a) How much is supplied to the market and how much is demanded?

qD (P = 1) = 16 - 4*1 = 12 units

qS (P = 1) = -2 + 5*1 = 3 units

b) What is the excess demand?

Excess demand ED = qD - qS = 12 - 3 = 9 units

c) Calculate the consumer surplus, producer surplus, and welfare level without the price ceiling.

Without price ceiling, market equilibrium price and quantity are

qS = qD

-2 + 5p = 16 - 4p

9p = 18

p = 2.

q = 16 - 4*2 = 8 units.

CS = 0.5*(Max price - current price)*current qty = 0.5*(4 - 2)*8 = $8

PS = 0.5*(current price - minimum price)*current qty = 0.5*(2 - 0.4)*8 = $6.4

d) Calculate the consumer surplus, producer surplus, welfare level, and dead weight loss with this price ceiling.

CS = 0.5*(4 - 3.25)*3 + (3.25 - 1)*3 = 7.875

PS = 0.5*(1 - 0.4)*3 = 0.9

DWL = 0.5*(3.25 - 1)*(8 - 3) = 5.625