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Chapter 6: Problem 3

The accompanying table gives part of the supply schedule for personal computers in the United States. $$ \begin{array}{c|c} \text { Price of computer } & \text { Quantity of computers supplied } \\\ \$ 1,100 & 12,000 \\\ 900 & 8,000 \end{array} $$ a. Calculate the price elasticity of supply when the price increases from $\$ 900\( to \)\$ 1,100$ using the midpoint method. Is it elastic, inelastic or unit-elastic? b. Suppose firms produce 1,000 more computers at any given price due to improved technology. As price increases from \(\$ 900\) to \(\$ 1,100\), is the price elasticity of supply now greater than, less than, or the same as it was in part a? c. Suppose a longer time period under consideration means that the quantity supplied at any given price is \(20 \%\) higher than the figures given in the table. As price increases from \(\$ 900\) to \(\$ 1,100,\) is the price elasticity of supply now greater than, less than, or the same as it was in part a?

Short Answer

Expert verified
In this exercise, we first calculated the price elasticity of supply using the midpoint method and found it to be 2, which is elastic. With improved technology, the price elasticity of supply decreased to approximately 1.82, making it less elastic than before the improvement. However, when considering a longer time period, the price elasticity of supply remained the same at 2, indicating no change in elasticity.

Step by step solution

01

Calculate the price elasticity of supply using the midpoint method

To calculate the price elasticity of supply, we can use the formula: $$ E_\text{s} = \frac{\% \Delta Q_\text{s}}{\% \Delta P} $$ where \(E_\text{s}\) is the price elasticity of supply, \(\% \Delta Q_\text{s}\) is the percentage change in quantity supplied, and \(\% \Delta P\) is the percentage change in price. To calculate \(\% \Delta Q_\text{s}\) and \(\% \Delta P\), we can use the midpoint method: $$ \% \Delta Q_\text{s} = \frac{\text{new quantity supplied} - \text{old quantity supplied}}{\text{average of the quantities}} \times 100\% $$ $$ \% \Delta P = \frac{\text{new price} - \text{old price}}{\text{average of the prices}} \times 100\% $$ Now we can plug in our values: $$ \% \Delta Q_\text{s} = \frac{12,000 - 8,000}{10,000} \times 100\% = 40\% $$ $$ \% \Delta P = \frac{1,100 - 900}{1,000} \times 100\% = 20\% $$ Finally, we can calculate \(E_\text{s}\): $$ E_\text{s} = \frac{40\%}{20\%} = 2 $$
02

Determine if the price elasticity of supply is elastic, inelastic or unit-elastic

Since our calculated \(E_\text{s}\) is greater than 1, the supply is elastic.
03

Analyze the change in price elasticity of supply with improved technology

The technology improvement causes the production of 1,000 more computers at any given price. This means that the new supply schedule will have 9,000 and 13,000 computers at the respective prices. We will calculate the new price elasticity of supply using the midpoint method: $$ \% \Delta Q_\text{s} = \frac{13,000 - 9,000}{11,000} \times 100\% \approx 36.36\% $$ $$ E_\text{s} = \frac{36.36\%}{20\%} \approx 1.82 $$ The new \(E_\text{s}\) is less than the original. So the price elasticity of supply is now less than it was in part a.
04

Analyze the change in price elasticity of supply with a longer time period

The longer time period causes the quantity supplied at any given price to be 20% higher. Thus, the new supply schedule will have 9,600 and 14,400 computers at the respective prices. We will calculate the new price elasticity of supply using the midpoint method: $$ \% \Delta Q_\text{s} = \frac{14,400 - 9,600}{12,000} \times 100\% = 40\% $$ $$ E_\text{s} = \frac{40\%}{20\%} = 2 $$ With the longer time period, the price elasticity of supply remains the same as it was in part a.

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Most popular questions from this chapter

The U.S. government is considering reducing the amount of carbon dioxide that firms are allowed to produce by issuing a limited number of tradable allowances for carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) emissions. In an April 25 , 2007, report, the U.S. Congressional Budget Office (CBO) argues that "most of the cost of meeting a cap on \(\mathrm{CO}_{2}\) emissions would be borne by consumers, who would face persistently higher prices for products such as electricity and gasoline \(\ldots\) poorer households would bear a larger burden relative to their income than wealthier households would." What assumption about one of the elasticities you learned about in this chapter has to be true for poorer households to be disproportionately affected?

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