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Chapter 2: Q3. (page 84)

Refer to Example 2.5 (page 59) on the market for wheat. In 1998, the total demand for U.S. wheat was Q = 3244 - 283P and the domestic supply was QS = 1944 + 207P. At the end of 1998, both Brazil and Indonesia opened their wheat markets to U.Sfarmers. Suppose that these new markets add 200 million bushels to U.S. wheat demand. What will be the free-market price of wheat and what quantity will be produced and sold by U.S. farmers?

Short Answer

Expert verified

The free market price will be $3.06, and the output produced and sold will be 2,578.02 units.

Step by step solution

01

Explanation 

If Brazil and Indonesia open their market up and add 200 million bushels to the U.S wheat market, the demand would change. The new demand would be:

Q = (3244 - 283P) + 200

Q = 3444 - 283P

The supply is, QS = 1944 + 207P

The free-market prices and quantity of wheat would be where the new demand of wheat equals supply.

Q = QS

3444 - 283P = 1944 + 207P

490P = 1500

P = 3.06

Substituting the price in the demand or supply equation will give the quantity:

Q = 3444 - 283P

Q = 3444 - 283(3.06)

Q = 3444 - 865.98

Q = 2578.02

Therefore, the free-market price and quantity would be:
$3.06 per bushel and 2,578.02 million bushels, respectively.

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Most popular questions from this chapter

Much of the demand for U.S. agricultural output has come from other countries. In 1998, the total demand for wheat was Q = 3244 - 283P. Of this, total domestic demand was QD = 1700 - 107P, and domestic supply was QS = 1944 + 207P. Suppose the export demand for wheat falls by 40 percent.

  1. U.S. farmers are concerned about this drop in export demand. What happens to the free-market price of wheat in the United States? Do farmers have much reason to worry?

  2. Now suppose the U.S. government wants to buy enough wheat to raise the price to $3.50 per bushel. With the drop in export demand, how much wheat would the government have to buy? How much would this cost the government?

Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows:

PRICE

(DOLLARS)

DEMAND

(MILLIONS)

SUPPLY

(MILLIONS)

602214
802016
1001818
1201620

a. Calculate the price elasticity of demand when the price is \(80 and when the price is \)100.

b. Calculate the price elasticity of supply when the price is \(80 and when the price is \)100.

c. What are the equilibrium price and quantity?

d. Suppose the government sets a price ceiling of $80. Will there be a shortage, and if so, how large will it be?

In Example 2.8 we examined the effect of a 20-percent decline in copper demand on the price of copper, using the linear supply and demand curves developed in Section 2.6. Suppose the long-run price elasticity of copper demand were -0.75 instead of -0.5.

  1. Assuming, as before, that the equilibrium price and quantity are P_ = $3 per pound and Q_ = 18 million metric tons per year, derive the linear demand curve consistent with the smaller elasticity.

  2. Using this demand curve, recalculate the effect of a 55-percent decline in copper demand on the price of copper.

Example 2.9 (page 76) analyzes the world oil market. Using the data given in that example:

a. Show that the short-run demand and competitive supply curves are indeed given by

D = 36.75 - 0.035P

SC= 21.85 + 0.023P

b. Show that the long-run demand and competitive supply curves are indeed given by

D = 45.5 - 0.210P

SC= 16.1 + 0.138P

c. In Example 2.9 we examined the impact on price of a disruption of oil from Saudi Arabia. Suppose that instead of a decline in supply, OPEC production increases by 2 billion barrels per year (bb/yr) because the Saudis open large new oil fields. Calculate the effect of this increase in production on the price of oil in both the short run and the long run.

In 2010, Americans smoked 315 billion cigarettes, or 15.75 billion packs of cigarettes. The average retail price (including taxes) was about \(5.00 per pack. Statistical studies have shown that the price elasticity of demand is -0.4, and the price elasticity of supply is 0.5.

  1. Using this information, derive linear demand and supply curves for the cigarette market.

  2. In 1998, Americans smoked 23.5 billion packs of cigarettes, and the retail price was about \)2.00 per pack. The decline in cigarette consumption from 1998 to 2010 was due in part to greater public awareness of the health hazards from smoking, but was also due in part to the increase in price. Suppose that the entire decline was due to the increase in price. What could you deduce from that about the price elasticity of demand?
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