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# Elasticity and Inelasticity

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Problem 1

Suppose that the U.S. Department of Agriculture (USDA) administers the price floor for cheese, set at \$0.17 per pound of cheese. (In real life, the actual price floor was officially set at \$16.10 per hundredweight of cheese. One hundredweight is 100 pounds.) At that price, according to data from the USDA, the quantity of cheese produced in 2009 by U.S. producers was 212.5 billion pounds, and the quantity demanded was 211 billion pounds. To support the price of cheese at the price floor, the USDA had to buy up 1.5 billion pounds of cheese. The accompanying diagram shows supply and demand curves illustrating the market for cheese.

a. In the absence of a price floor, the maximum price that a few of the consumers are willing to pay is \$0.20 for a pound of cheese whereas the market equilibrium price is \$0.13 per pound. The graph also shows that the minimum price at which a few of the producers are willing to sell is \$0.06 per pound. In the absence of a price floor, how much consumer surplus is created?

b. How much producer surplus?

c. What is the total surplus?

d. The maximum price that a few of the consumers are willing to pay is \$0.20 per pound of cheese, and the price floor is set at \$0.17 per pound. With the price floor at \$0.17 per pound of cheese, consumers buy 211 billion pounds of cheese. How much consumer surplus is created now?

e. The minimum price at which a few of the producers are willing to sell a pound of cheese is \$0.06, and the price floor is set at \$0.17 per pound. With the price floor at \$0.17 per pound of cheese, producers sell 212.5 billion pounds of cheese (some to consumers and some to the USDA). How much producer surplus is created now?

f. The surplus cheese USDA buys is the difference between the quantity of cheese producers sell (212.5 billions of pounds of cheese) and the quantity of cheese consumers are willing to buy at the price floor (211 billions of pounds of cheese). How much money does the USDA spend on buying up surplus cheese?

g. Taxes must be collected to pay for the purchases of surplus cheese by the USDA. As a result, total surplus (producer plus consumer) is reduced by the amount the USDA spent on buying surplus cheese. Using your answers for parts bâ€”d, what is the total surplus when there is a price floor?

h. How does this compare to the total surplus without a price floor from part a?

Problem 2

The accompanying table shows the price and yearly quantity sold of ice cream cones on Sidfield Island.

Price of Ice Cream Cones Quantity of Ice Cream Cones Demanded
\$1 3000
\$2 2400
\$3 1600
\$4 800

a. Using the midpoint method, calculate the price elasticity of demand when the price of an ice cream cone rises from \$1 to \$2.

b. What does this estimate imply about the price elasticity of demand for ice cream cones?

c. Using the midpoint method (show your work), calculate the price elasticity of demand when the price of an ice cream cone rises from \$3 to \$4.

d. What does this estimate imply about the price elasticity of demand for ice cream cones?

e. Notice that the estimates from (a) and (b) above are different. Why do price elasticity of demand estimates change along the demand curve?

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#### Solution Preview

Problem 1

a. Consumer surplus is the difference between the total amount the consumers are willing to pay and the actual amount they pay for a product.
Consumer surplus can be calculated using the formula referring to the graph as:
[Base * Height]/2
Base = 211.5 billion
Height = .20 - .13 â‡’ .07
Consumer surplus = [211.5 * .07]/2
â‡’ \$7.4025 billion

b. Producer surplus is the difference between what producers are willing to supply and the actual price they receive.
Producer surplus can be calculated using the formula referring to the graph as:
[Base * Height]/2
Base = 211.5 billion
Height = .13 - .06 â‡’ .07
Producer surplus = [211.5 * .07]/2
â‡’ \$7.4025 billion

c. Total surplus = Producer surplus + Consumer surplus
â‡’ \$7.4025 billion + \$7.4025 billion
â‡’ \$14.805 ...

#### Solution Summary

The solution discusses the answers to problems regarding elasticity and inelasticity.

\$2.49