Question

Consider the following supply and demand functions

q_D = 12 - 3p
q_S = -3 + 2p

Using the supply and demand functions, suppose a price ceiling of p = 2 were implemented.

1. How much is supplied to the market and how much is demanded?
2. What is the excess demand?
3. Calculate the consumer surplus, producer surplus, and welfare level without the priceceiling.
4. Calculate the consumer surplus, producer surplus, welfare level, and dead weight loss withthis price ceiling.
5. What if the price ceiling were p =4? How would our results change?

Answer 1

a. Q supplied = 1 and Q demanded = 6
b. The excess demand = 5
c. CS= 0.5*3*1 = 1.5, PS = 0.5*3*(3-1.5)= 2.25, welfare level = CS+PS = 1.5+0.75=3.75
d. CS= 0.5*(4-3.67)*1+(3.67-2*1) = 1.835, PS = 0.5*(2-1.5)*1 = 0.25, welfare level =
CS+PS = 1.835+0.25=2.085, DWL =0.5*(3.67-2)*2 = 1.67
e. Q supplied = 5 and Q demanded = 0
The excess demand = 0
CS= 0.5*3*1 = 1.5, PS = 0.5*3*(3-1.5)= 2.25, welfare level = CS+PS = 1.5+0.75=3.75

CS= 0, PS = 0.5*3*(4-1.5)= 3.75, welfare level = CS+PS = 0+3.75=3.75
DWL =0