Question

The market demand and supply is described by the following equations QD = 250 - 2P QS 3P 1) Find the market equilibrium. 2) What is the CS, PS, and W in this market? 3) Assume that the government introduces a equilibrium? price ceiling of p = 15. What is the new 4) Find the change in CS, PS, and W. Is there Dead Weight Loss? if so, of how much? 5) What does this tell you about the welfare situation of the agents in the market as a result of the introduction of the tax?

Answer 1

Qd = 250 -2P

Qs = 3P

1)

Equilibrium condition:

Qd = Qs

250 -2P = 3P

250 = 5P

P = 250 /5

= 50

Q = 3(50)

= 150

2)

Qd = 250 -2P

Inverse:

P = 120 - 0.5Q

Qs = 3P

Inverse:

P = (1/3)Q

CS:

= 0.5Base(Height)

=0.5(120 -50)(150)

= 5250

PS :

= 0.5 (150)(50)

= 3750

W = C+S

= 9000

3)

Qd = 250 -2P

Qs = 3P

Price ceiling:

Qd = 250 - 2(15)

= 250 - 30

= 220

Qs = 3(15)

= 45

Excess Demand = 220 - 45

= 175

Price = 15

Q = 175

4)

PS = 0.5*15*45

=337.5

CS = 0.5(120 -97.5)(45) +(97.5-15)*45

= 4218.75

W = 4556.25

Loss of W = 9000 - 4556.25

= 4443.75