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Chapter 2: Problem 2

Consider a competitive market for which the quantities demanded and supplied (per year) at various prices are given as follows: $$\begin{array}{|ccc|} \hline \begin{array}{c} \text { PRICE } \\ \text { (DOLLARS) } \end{array} & \begin{array}{c} \text { DEMAND } \\ \text { (MILLIONS) } \end{array} & \begin{array}{c} \text { SUPPLY } \\ \text { (MILIONS) } \end{array} \\ \hline 60 & 22 & 14 \\ \hline 80 & 20 & 16 \\ \hline 100 & 18 & 18 \\ \hline 120 & 16 & 20 \\ \hline \end{array}$$ 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 is 0.4, and at $100 is 0.55. b. The price elasticity of supply at $80 is -0.5, and at $100 is 0.5. c. The equilibrium price is $100 and the equilibrium quantity is 18 million units. d. If a price ceiling at $80 is introduced, there will be a shortage of 4 million.

Step by step solution

01

Calculate the price elasticity of demand at $80

To find the price elasticity of demand at $80, use the formula \(E_d = \frac{%ΔQ}{%ΔP}\). In this case, %ΔP is the percent change from $80 to $100, or \( \frac{100 - 80}{80} = 0.25 \). %ΔQ is the percent change in quantity demanded, or \( \frac{20 - 18}{20} = 0.10 \). Plugging these values in, \(E_d = \frac{0.10}{0.25} = 0.4 .\) So, the price elasticity of demand at $80 is 0.4.
02

Calculate the price elasticity of demand at $100

Repeating the process for the price of $100, %ΔP is the percent change from $100 to $120, or \( \frac{120 - 100}{100} = 0.20 \). %ΔQ is the percent change in quantity demanded, or \( \frac{18 - 16}{18} = 0.11 \). Plugging these in, \(E_d = \frac{0.11}{0.20}=0.55 .\) Therefore, the price elasticity of demand at $100 is 0.55.
03

Calculate the price elasticity of supply at $80 and $100

The calculation for supply elasticity is similar to demand. At $80, %ΔP is \( \frac{100 - 80}{80} = 0.25 \) and %ΔQ is \( \frac{16 - 18}{16} = -0.125 \). Thus, \(E_s = \frac{-0.125}{0.25} = -0.50 .\) At $100, %ΔP is \( \frac{120 - 100}{100} = 0.20 \) and %ΔQ is \( \frac{20 - 18}{20} = 0.10 \). Thus, \(E_s = \frac{0.10}{0.20} = 0.50 .\) The price elasticity of supply is -0.50 at $80 and 0.50 at $100.
04

Determine the equilibrium price and quantity

The equilibrium price and quantity is found where quantity demanded equals quantity supplied. From the table, it can be seen that this occurs at a price of $100, with a quantity of 18 million. Therefore, the equilibrium price is $100, and the equilibrium quantity is 18 million.
05

Analyze the impact of a price ceiling at $80

A price ceiling means that prices can't rise above a certain level. If a price ceiling is set at $80, the quantity demanded will exceed the quantity supplied. Checking the table, at $80, quantity demanded is 20 million, but quantity supplied is only 16 million. Therefore, there will be a shortage, and it will be 4 million units.

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Most popular questions from this chapter

A vegetable fiber is traded in a competitive world market, and the world price is \(\$ 9\) per pound. Unlimited quantities are available for import into the United States at this price. The U.S. domestic supply and demand for various price levels are shown as follows: $$\begin{array}{|c|c|c|} \hline \text { PRICE } & \begin{array}{c} \text { U.S. SUPPLY } \\ \text { (MILION LBS) } \end{array} & \begin{array}{c} \text { U.S. DEMAND } \\ \text { (MILIION LBS) } \end{array} \\ \hline 3 & 2 & 34 \\ \hline 6 & 4 & 28 \\ \hline 9 & 6 & 22 \\ \hline 12 & 8 & 16 \\ \hline 15 & 10 & 10 \\ \hline 18 & 12 & 4 \\ \hline \end{array}$$ a. What is the equation for demand? What is the equation for supply? b. At a price of \(\$ 9,\) what is the price elasticity of demand? What is it at a price of \(\$ 12 ?\) c. What is the price elasticity of supply at \(\$ 9 ?\) At \(\$ 12 ?\) d. In a free market, what will be the U.S. price and level of fiber imports?

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