Question

1. Subsidy. The market demand and supply functions for cotton are: Qd = 10 - .04P and Qs = 38P - 20

a.     Calculate the consumer and producer surplus.

To assist cotton farmers, suppose a subsidy of $0.10 a unit is implemented.

b.     Calculate the new level of consumer and producer surplus.

c.      Did the increase in consumer and producer surplus exceed the increased government spending necessary to finance the subsidy?

Answer 1

a)

Qs=Qd

38P-20=10-0.04P

38.04P=30

P=0.788

Q=38(0.788)-20=9.968

The government is offering a suppy side subsidy.The new supply equation will become Qs=38(P+0.10)-20

Qs=38P+3.8-20

Qs=38P-16.2

This will shift the supply curve vertically downwards .The distance between the new and the old supply curve will be the amount of subsidy which is 0.10

Qd=10-0.04P

Qs=Qd

38P-16.2=10-0.04P

38.04P=26.2

P=0.688

Qs=38(0.688)-16.2=9.97

Consumers are paying 0.688 per unit but producer would recieve 0.688+0.10= 0.788 per unit

The increase in consumer surplus is (0.788-0.688)*9.96 + (0.5)*(0.788-0.688)*(9.97-9.96)=0.996+0.0005=0.9965

The increase in producer surplus is NIL.

Government Expenditure=0.1*9.97=0.997

c. Yes