The market demand and supply functions for cotton are: Q_D = 10 - 0.04P and Q_S
ID: 1214110 • 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 = 38P – 20
P = 10/19 + (1/38)Q + 0.10Q (since $0.10 subsidy per quantity is implemented)
Qd = 10 – 0.04P
P = 250 – 25Q
Therefore, 10/19 + (1/38)Q - 0.10Q = 250 – 25Q
947.2Q = 9,480
Q = 10
Putting Q = 10 in either Qs or Qd,
Q = 38P – 20
10 = 38P – 20
P = 0.80
Answer: The new price is $0.80 and quantity 10 units.
Expense to the government = 0.10Q = 0.10 × 10 = $1
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