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Answer the following:
(Many of the questions are easier if you sketch a supply and demand diagram).
1. Assume the U.S. corn market is perfectly competitive and the yearly market demand (marginal benefit) for corn is approximated by:
where P is the price per bushel, and Q is the total yearly quantity demanded (in billions of bushels). The supply (marginal cost) of corn is given by:
Given the information above, answer the following questions:
a) Show (by solving) that the free market competitive equilibrium price is $7 and quantity of corn exchanged is 20 (billion) bushels per year.
Set supply = demand (MB=MC) and solve:
11 – 0.2Q = 1 + 0.3Q
10 = 0.5Q
QE = 20 billion bushels
PE = (11 – 0.2*20) = $7 per bushel
b) Calculate the consumer surplus (CS) and producer surplus (PS) in the corn market at the free market equilibrium. Show that total net benefits are $100 billion per year.
CS = ½ * 20 * 4 = $40 billion per year
PS = ½ * 20 * 6 = $60 billion per year
Total net benefits = CS + PS = $100 billion
2. Agricultural income support programs can take many forms. Using the same market supply and demand curves as in question 1, consider the impact of the following programs on the corn market:
a) Guaranteed corn price: the U.S. government promises that producers will receive $8 per bushel of corn. However, the government allows the market price of corn to adjust so that all corn that is produced under this guarantee is sold to consumers. The government then pays farmers (using tax dollars) the difference between this “market-clearing price” and the guaranteed price of $8 for each bushel produced.
What quantity of corn will farmers produce and sell under this program? Show that the market-clearing price must fall to $6.33 per bushel. Show that the DWL from the program is nearly $3 billion, and the cost to taxpayers is a little under $40 billion, per year.
Farmers will produce the quantity along the supply curve where P = $8. This is:
8 = 1 + 0.3Q
Q = 23.33 billion bushels
To sell this quantity, market price must fall to the point on the demand curve where Q = 23.33 billion. This is:
P = 11 – 0.2(23.33)
P = $6.33 per bushel
The DWL is the triangle area between the supply and demand curves from Q = 20 (the efficient quantity) to Q = 23.33 (the program quantity). This is:
DWL = ½ * 3.33 * 1.67 [where 3.33 is (23.33 – 20) and 1.67 is ($8 - $6.33)]
DWL = $2.78 billion per year
The cost to taxpayers is the difference between the guaranteed price and the actual market price ($8 - $6.33 = $1.67) times the TOTAL market quantity of 23.33 billion. This cost is:
Taxpayer cost = $1.67 * 23.33 = $38.96 billion per year
b) Price floor: the U.S. government sets the market price of corn such that it can be no less than $8 per bushel. Because farmers will produce more corn than is demanded at this price, the government also uses tax dollars to purchase any surplus corn produced.
Calculate the quantity of corn produced by farmers, purchased by consumers, and purchased by the government under this program. Show that the cost of this program to taxpayers is considerably higher than in part (a). By the way, what does the government do with the corn it purchases?
Farmers produce the quantity corresponding to P = $8 on the supply curve. This is: Qproduced = 23.33 billion (calculated as in part (a))
