Question

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

The price elasticity of supply is 2, which is elastic. With improved technology or a longer time period, the price elasticity of supply remains unchanged at 2.

Step-by-step solution

Understand the Midpoint Method

The midpoint method for elasticity is used to calculate the percentage change in quantity supplied and the percentage change in price in a way that is independent of the direction of change. The formula for the Price Elasticity of Supply (PES) using the midpoint method is: PES = (Q2 - Q1) / [(Q2 + Q1)/2] / (P2 - P1) / [(P2 + P1)/2], where Q1 and Q2 are the initial and final quantities, and P1 and P2 are the initial and final prices.

Calculate the Price Elasticity of Supply

Plug the numbers into the PES formula: Q1 = 8,000, Q2 = 12,000, P1 = \(900, P2 = \)1,100. PES = (12,000 - 8,000) / [(12,000 + 8,000)/2] / (1,100 - 900) / [(1,100 + 900)/2] which simplifies to PES = (4,000) / (10,000) / (200) / (1,000). Thus, PES = (0.4) / (0.2) which equals 2.

Determine Elasticity Type

Since the calculated PES is 2, which is greater than 1, the supply is elastic. Elastic supply means that the percentage change in quantity supplied responds more than proportionately to the percentage change in price.

Analyze the Impact of Improved Technology

With an increase of 1,000 computers supplied at every price level due to improved technology, the new quantity supplied at each price is 1,000 units higher. However, this does not change the percentage change between Q1 and Q2 or between P1 and P2 when calculating elasticity. Therefore, the price elasticity of supply remains the same as in part a.

Examine the Effect of a Longer Time Period

If the quantity supplied at any given price is 20% higher, we simply multiply the original quantities by 1.2. However, as with improved technology, this does not affect the percentage changes used in the elasticity calculation. Therefore, the price elasticity of supply remains the same as in part a.

Key concepts

Midpoint Method

The midpoint method is a widely recognized approach for calculating elasticity, which measures the responsiveness of one variable to changes in another. In the realm of economics, elasticity is used to gauge how the quantity of a good supplied, or demanded, changes in response to price fluctuations.

When applying the midpoint method to calculate elasticity, you consider the average between the initial and final quantities, as well as the average between the initial and final prices. This is done to obtain a consistent measurement that doesn’t depend on the path from the initial to the final state.

Here's a simplified breakdown – if you're evaluating the change from point A to point B, the midpoint method takes the middle point between A and B as the base for percentage changes. For elasticity of supply, the formula is given by:
\[\begin{equation}\text{Price Elasticity of Supply (PES)} = \frac{\text{Change in Quantity Supplied}}{\text{Average Quantity Supplied}} \div \frac{\text{Change in Price}}{\text{Average Price}}\end{equation}\]This method is useful because it provides a more balanced elasticity calculation that is not skewed by the starting or ending values, making it a more reliable tool in economic analysis. Moreover, it helps in making comparisons between different goods or time periods more meaningful.

Elasticity of Supply

The elasticity of supply refers to the degree to which the quantity of supplied goods responds to a change in price. In simpler terms, it indicates how much the supply of a product will increase or decrease when its price rises or falls.

The price elasticity of supply (PES) offers insights into the supply flexibility of a product. If a product has an elastic supply, its quantity supplied will change significantly when the price changes. Conversely, when the supply is inelastic, the quantity supplied changes very little with price movements. In mathematical terms, supply is considered elastic when the PES is greater than 1, inelastic when PES is less than 1, and unit-elastic when PES is exactly 1.

Understanding the elasticity of supply is crucial for businesses and policymakers. It affects decisions on pricing, production, and inventory management. For example, in the exercise provided, the increase in price from \(900 to \)1,100 led to a substantial increase in the quantity of computers supplied, indicating a supply that is sensitive to price changes and therefore elastic, with a PES calculated at 2.

Microeconomic Concepts

Microeconomic concepts are essentially the building blocks for understanding the economic behavior of individuals and firms, and how they interact within a market to make decisions about resource allocation and pricing. These concepts encompass supply and demand, elasticity, opportunity costs, market structures, and many other principles that explain the functioning of economic agents.

Central to microeconomics is the concept of supply and demand which predicts how the market price for a good or service is determined and how goods and services are allocated among people. Elasticity measures the responsiveness of demand or supply to changes in prices or income. In the context of the exercise, understanding the elasticity of supply helps in predicting how technological improvements or extended time periods will affect the market.

Improved technology, as discussed in part b of the exercise, can shift the supply curve outward, indicating a technological advancement that makes production more efficient. However, this does not necessarily affect the elasticity unless it changes the proportionate relationship between the price and quantity. The example also touches on the importance of time when considering supply, suggesting that in a longer time frame, firms are typically more responsive to price changes because they have more time to adjust their production levels.