Question

Market Regulation

Using the supply and demand functions

qD = 12 - 3p

qS = -3 + 2p

suppose a price ceiling of p = 2 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 = 4? How would our results change?

Please help, I cant figure out the right formulas to use for each!

Answer 1

a) At price ceeiling p=2, the quantity demanded is:

qD = 12 - 3p

qD = 12 - 3*2

qD = 6

The quantity supplied is:

qS = -3 +2p

qS = -3 +2*2

qS= 1

Hence, the market demand is 6 and the market supply is 1 at price ceiling p=2

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b) The excess demand at price ceiling p=2 is difference between the market demand and market supply. Hence, the excess demand is:

Excess demand = Market demand - market supply

Excess demand = 6 - 1

Excess demand = 5

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c) Without price ceiling of p=2, the equilibrium is given by:

qD =qS

12-3p = -3 + 2p

5p =15

p = 3

q = 3

The price intercept as followed from market demand is: qD = 0

This implies, 12-3p=0

Hence, p=4

The Consumer surplus is: (1/2)*(3-0)*(4-3) = 1.5

The price intercept as followed from market supply is: qS = 0

This implies, -3 + 2p =0

Hence, p=1.5

The Producer surplus is: (1/2)(3-0)*(3-1.5)=2.25

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d)

At price ceiling p=2, the market supply is 1

At price ceiling p = 2, the producer surplus is given by: (1/2)*(1-0)*(2-1.5) = 0.25

At q=1, the willingness to pay by the consumer is given by qD=12-3p

This implies, p = (11/3) or 3.67

The consumer surplus is given by: (1/2)*(4-3.67)*(1-0) + (1-0)*(3.67-2) = 1.835

The dead-weight loss is: (1/2)*(3.67-2)*(3-1) = 1.67

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e) When price ceiling is p=4

Market demand is qD = 12-3p = 12-3*4 = 0

Market supply is: qS = -3 +2p = -3 + 2*4 = 5

Consumer surplus = 0

Since, no quantity is sold, producer surplus is 0

The dead-weight loss is sum of consumer surplus & producer surplus in absence of price ceiling.

Hence, dead-weight loss = 1.5 + 2.25 = 3.75