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 situations （c）, determine the following items (i-viii)

(c) A market with subsidy S=9.

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)

Subsidy shifts supply curve rightward by $9 and new supply function is

Q = - 8 + 4(P + 9) = - 8 + 4P + 26 = 18 + 4P

Equating with demand,

76 - 8P = 18 + 4P

12P = 58

P = 4.83 (price paid by buyers)

Price received by sellers = 4.83 + 9 = 13.83

Q = 76 - (8 x 4.83) = 76 - 38.64 = 37.36

(ii)

In pre-subsidy equilibrium,

76 - 8P = - 8 + 4P

12P = 84

P = 7 (price paid by buyers)

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

(iii)

Price received by sellers after subsidy = 13.83

(iv)

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

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

= (1/2) x (9.5 - 4.83) x 37.36

= 18.68 x 4.67

= 87.24

(v)

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

Producer surplus = area between price received by sellers and supply curve

= (1/2) x (13.83 - 2) x 37.36

= 18.68 x 11.83

= 220.98

(vi)

Government receipt = - Subsidy cost = - 9 x 37.36 = - 336.24

(vii)

Net benefit = CS + PS - Subsidy cost

= 87.24 + 220.98 - 336.24

= - 28.02

(viii)

Deadweight loss = (1/2) x Unit subsidy x Change in quantity

= (1/2) x 9 x (37.36 - 20)

= 4.5 x 17.36

= 78.12