The market demand and supply functions for cotton are: Q_D = 10 - 0.04P and Q_S
ID: 1214123 • Letter: T
Question
The market demand and supply functions for cotton are: Q_D = 10 - 0.04P and Q_S = 38P - 20. a. To assist cotton farmers, suppose a subsidy of $0.10 a unit is implemented. Calculate the new price and quantity traded, the expense to the government and the new consumer and producer surplus. b. Did the increase in consumer and producer surplus exceed the increased government spending necessary to finance the subsidy? C. How much of the subsidy will consumers enjoy? Is this consistent with the relevant elasticities? Be sure to show your work and explain and graph your results.Explanation / Answer
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
b. Yes
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