Question

Consider a perfectly competitive market where the market demand curve is given by Q = 76−8P and the market supply curve is given by Q=−8+4P. In the situations (d), determine the following items (i-viii)

(d) A market with price ceiling C = 5.

i) The quantity sold in the market.

ii) The price that consumers pay (before all taxes/subsidies).

iii) The price that producers receive (after all taxes/subsidies).

iv) The range of possible consumer surplus values.

v) The range of possible producer surplus values.

vi) The government receipts.

vii) The net benefit.

viii) The range of deadweight loss.

Answer 1

(i)

When P = 5,

Qd = 76 - 8 x 5 = 76 - 40 = 26

Qs = - 8 + 4 x 5 = - 8 + 20 = 12

Market quantity sold = min(Qd, Qs) = min(12, 26) = 12

(ii)

Price consumers pay = 5

(iii)

Price producers receive = 5

(iv)

From demand function, when Q = 0, P = 76/8 = 9.5

When Q = 12, from demand function: 12 = 76 - 8P, or P = (76 - 12)/8 = 64/8 = 8 (demand price)

Consumer surplus (CS) = area between demand curve and price

= (1/2) x [(9.5 - 5) + (8 - 5)] x 12

= 6 x (4.5 + 3)

= 6 x 7.5

= 45

(v)

From supply function, when Q = 0, P = 8/4 = 2

Producer surplus = area between price and supply curve

= (1/2) x (5 - 2) x 12

= 6 x 3

= 18

(vi)

Government receipt = 0

(vii)

Net benefit = CS + PS

= 45 + 18

= 63

(viii)

In free market equilibrium, Qd = Qs

76 - 8P = - 8 + 4P

12P = 84

P = 7

Q = - 8 + 4 x 7 = - 8 + 28 = 20

Deadweight loss = (1/2) x (demand price - ceiling price) x Change in quantity

= (1/2) x (8 - 5) x (20 - 12)

= (1/2) x 3 x 8

= 12