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?

Short Answer

Expert verified

a. The price elasticity of demand at $80 will be -0.4 and at $100 will be -0.556.

b. The price elasticity of supply at $80 will be 0.5 and at $100 will be 0.555.

c. The equilibrium price will be $100, and the quantity will be 18 million.

d. This price ceiling will create a shortage of supply by 4 million.

Step by step solution

01

Explanation for part (a)

The price elasticity when the price = $80 would be;

Ed=QP×PQQ=20-22P=80-60=-220×8020=-0.4

When price = $100

Ed=QP×PQQ=18-20P=100-80=-220×10018=-0.556

Thus, price elasticity at prices $80 and $100 will be -0.4 and -0.556, respectively.

02

Explanation for part (b)

The price elasticity of supply when price =$80 would be;

Es=QP×PQQ=16-14P=80-60=220×8016=0.5

When price = $100

Es=QP×PQQ=18-16P=100-80=220×8018=0.555

Thus, the price elasticity of supply at prices $80 and $100 would be 0.5 and 0.555, respectively.

03

Explanation for part (c)

The equilibrium price and quantity are where demand equals the supply. In the table above, we see that both demand and supply are equal at $100. Therefore, equilibrium prices are $100, and the equilibrium quantity is 18 million.

04

Explanation for part (d)

If the government sets price celling at $80, then the quantity demanded would be 20 million, and the quantity supply would be 16 million (given in the table above). Thus, this will create a shortage of supply of 4 million in the market.

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Most popular questions from this chapter

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?

What is the effect of a price ceiling on the quantity demanded of the product? What is the effect of a price ceiling

on the quantity supplied? Why exactly does a price ceiling cause a shortage?

Does a price ceiling change the equilibrium price?

The rent control agency of New York City has found that aggregate demand is QD = 160 - 8P. Quantity is measured in tens of thousands of apartments. Price, the average monthly rental rate, is measured in hundreds of dollars. The agency also noted that the increase in Q at lower P results from more three-person families coming into the city from Long Island and demanding apartments. The city’s board of realtors acknowledges that this is a good demand estimate and has shown that supply is QS = 70 + 7P.

  1. If both the agency and the board are right about demand and supply, what is the free-market price? What is the change in city population if the agency sets a maximum average monthly rent of \(300 and all those who cannot find an apartment leave the city?

  2. Suppose the agency bows to the wishes of the board and sets a rental of \)900 per month on all apartments to allow landlords a “fair” rate of return. If 50 percent of any long-run increases in apartment offerings comes from new construction, how many apartments are constructed?

Refer to Example 2.10 (page 81), which analyzes the effects of price controls on natural gas.

  1. Using the data in the example, show that the following supply and demand curves describe the market for natural gas in 2005–2007:

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Demand: Q = 0.02 - 1.8PG+ 0.69PO

Also, verify that if the price of oil is \(50, these curves imply a free-market price of \)6.40 for natural gas.

  1. Suppose the regulated price of gas was \(4.50 per thousand cubic feet instead of \)3.00. How much excess demand would there have been?

  2. Suppose that the market for natural gas remained unregulated. If the price of oil had increased from \(50 to \)100, what would have happened to the free market price of natural gas?

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