Answer to Question #258582 in Microeconomics for Sonu

Question

Suppose that the demand curve for wheat is Q=100-10p and that the supply curve is Q=10p.what are the effects of a subsidy (negative tax) of s=1 per unit on the equilibrium government subsidy cost,consumer surplus,producer surplus, ,welfare, and dead weight loss?

Answer 1

Solution:

Derive equilibrium before subsidy:

At equilibrium: Qd = Qs

100 – 10P = 10P

100 = 10P + 10P

100 = 20P

P = 5

Equilibrium price = 5

Substitute in the demand function to derive equilibrium quantity:

Q = 100 – 10P

Q = 100 – 10(5) = 100 – 50 = 50

Q = 50

Equilibrium quantity = 50

Consumer surplus = ½ x 50 x (10 – 5) = 125

Producer surplus = ½ x 50 x (50 – 0) = 125

 

Derive new equilibrium after subsidy:

First calculate the new Qs function:

Qs = 10P

Qs = 10 (P + 1)

Qs = 10P + 1

Set: Qd = Qs

100 – 10P = 10P + 1

100 – 1 = 10P + 10P

99 = 20P

P = 4.95

New equilibrium price = 4.95

Substitute in either the demand or supply function to derive the equilibrium quantity:

Qs = 10P + 1

Qs = 10(4.95) + 1

Q = 49.5 + 1 = 50.5

New equilibrium quantity = 50.5

The effects of the subsidy are as follows:

Consumer surplus gain = ½ $\times$ (5 – 4.95) $\times$ (50.5 – 50) + 50 $\times$ (5 – 4.95) = 0.025 + 2.5 = 2.525

Producer surplus gain = ½ $\times$ (5.95 – 5) $\times$ (50.5 – 50) + 50 $\times$ (5.95 – 5) = 0.2375 + 47.5 = 47.7375

Government subsidy cost = 50.5 $\times$ 1 = 50.5

Welfare = Total Benefit – Total Cost

Total benefit = CS + PS = 2.525 + 47.7375 = 50.265

Total Cost = 50.5

Welfare = 50.265 – 50.5 = -0.2375

Deadweight Loss = -0.2375