The market demand function for corn is Qd = 15 2P and the market supply function
ID: 1193991 • Letter: T
Question
The market demand function for corn is Qd = 15 2P and the market supply function is Qs = 5P 6, both measured in billions of bushels per year. Suppose the government wants to raise the price to $4 per bushel. A supply-demand graph (like Figure 15.11) would help answer the questions below.
(a) What are the equilibrium price and quantity without any intervention? What would be the welfare consequences (i.e. what are the aggregate surplus, dead- weight loss, consumer surplus, producer surplus, and government revenue)?
(b) What are the equilibrium price and quantity if the government raises the price to $4 per bushel?
(c) Describe how the government can raise the price to $4 per bushel with a price floor. What would be the welfare consequences (i.e. what are the changes in aggregate surplus, deadweight loss, consumer surplus, producer surplus, and gov- ernment revenue)?
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(d) Describe how the government can raise the price to $4 per bushel with a price support program. What would be the welfare consequences (i.e. what are the changes in aggregate surplus, deadweight loss, consumer surplus, producer surplus, and government revenue)?
(e) Describe how the government can raise the price to $4 per bushel with a quota. What would be the welfare consequences (i.e. what are the changes in aggregate surplus, deadweight loss, consumer surplus, producer surplus, and government revenue)?
(f) Describe how the government can raise the price to $4 per bushel with a vol- untary production reduction program. What would be the welfare conse- quences (i.e. what are the changes in aggregate surplus, deadweight loss, consumer surplus, producer surplus, and government revenue)?
Explanation / Answer
a) According to the given equation Qd = 15 - 2P. Qs = 5P - 6.Thus at equilibrium Qd = Qs.Thus equating the 2 equations we get P = $3 while equilibrium quantity as 9 units.
Consumer surplus in this case will be (what consumers willing to pay - what they actually pay) = 1/2 * 9 * (15/2 - 3)=20.25
Producer surplus = 1/2 * 9 * (3 - 1.2 ) =8.1
Therefore AGGREGATE SURPLUS = consumer surplus + producer surplus = 20.25 + 8.1 = 28.35.
Dead weight loss here is 0 as well as government revenue is also 0.
b)However if price increases to $4 equilibrium price would be set at $4. Equilibrium quantity now however would be determined by the demand curve since producers are willing to supply 14 units at this price while consumers buy only 7 units.
c)Government can impose the price floor on the market by the granting minimum support prices for corn at $4.Thus guaranteeing the producers a price not less than $4.This can be maintained by government if it purchases the surplus quantity at $4 in the market at price $4.The welfare implications of the same would be
consumer surplus = 1/2 * 7 * (7.5 - 4) = 12.25
producer surplus = 1/2 * 14 *(4 - 1.2) = 1/2 * 14 * 2.8 =19.6.
government expenditure as it buys surplus quantity at $4 = 4 * (14 - 7) = 28.
However consumers would be charged for government expenditure via taxes thus new cosumer surplus = 12.25 - 28 = - 15.75 i.e loss in consumer surplus = (8 + 28 = 36)
Increase in producer surplus = 19.6 - 8.1 = 11.5.
Dead weight loss is the loss in total surplus = 36 - 11.5 =24.5.Consumers loose 36 dollars to compensate producers by 11.5 dollars.
d) same as part c)
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