Question

The ABC Pencil Co. was considering a price increase and wished to determine the elasticity of demand. An economist and a market researcher, Key and Worce, were hired to study demand. In a controlled experiment, it was determined that at \(8 \mathrm{c}, 100\) pencils were sold yielding an elasticity of 2.25. However, key and worce were industrial spies, employed by the EF Pencil Co. And sent to \(\mathrm{ABC}\) to cause as much trouble as possible. So key and worce decided to change the base for their elasticity figure, measuring price in terms of dollars instead of pennies ( i.e., \(\$ .08\) for \(8 \mathrm{c}\) and \(\$ .10\) for \(10 c\) ). How will this sabotage affect the results?

Short answer

In conclusion, Key and Worce's attempt to sabotage the results by changing the unit of measurement for price from cents to dollars will not affect the elasticity of demand, as it is a unitless measure. The elasticity of demand remains the same at 2.25, irrespective of the price being expressed in cents or dollars.

Step-by-step solution

Understanding the Concept of Elasticity of Demand

The elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in price, and thus, it is a unitless measurement. It measures how responsive the quantity demanded of a good is to a change in its price. Given the form of calculation, its value should not depend on the units of price or quantity.

Calculating the Elasticity of Demand Using Cents

Given in the problem, when the price is 8 cents per pencil, 100 pencils were sold and the elasticity was 2.25.

Calculating the Elasticity of Demand Using Dollars

8 cents is equivalent to $0.08 and this does not change the number of pencils sold, that is 100. Now, upon recalculating the elasticity, theoretically, it should yield exactly the same number. So, the elasticity of demand should still be 2.25.

Noting the Effect of the Sabotage

Changing the unit of measurement for price from cents to dollars does not affect the elasticity of demand since it is a unitless measurement. Therefore, Key and Worce's sabotage in changing the base for their elasticity figure will not affect the result given the theoretical principles of economics. Hence, the sabotage orchestrated by Key and Worce has no impact on the calculated elasticity of demand. This is because elasticity of demand is a dimensionless measure and does impact by a change in the unit of measure for price or quantity.

Key concepts

Price Elasticity

Price elasticity of demand is a critical concept in economics, defining how the quantity demanded of a commodity responds to changes in its price. A product with high price elasticity will see significant changes in demand when its price fluctuates, whereas a product with low price elasticity will see minor demand changes in response to price adjustments.

For example, commodities like gasoline typically have lower elasticity because consumers will continue to buy it despite price changes, up to a point. Conversely, luxury goods often have higher elasticity because consumers can forgo these purchases or seek alternatives if prices rise. Understanding price elasticity helps businesses make informed pricing decisions and anticipate how changes might affect demand.

Demand Analysis

Demand analysis is the examination of consumer desire to purchase goods and services at various prices. It involves exploring factors like consumer preferences, income levels, and market trends. By studying demand, businesses can predict sales and plan their production, marketing, and pricing strategies accordingly.

Demand analysis is integral to maximizing profits and maintaining competitiveness. It can also reveal insights into consumer behavior, such as sensitivity to price changes, which is particularly relevant when considering price elasticity of demand.

Unitless Measurement

In the field of economics, many measurements are unitless, which means they are not expressed in terms of any particular physical unit like pounds, dollars, or liters. Price elasticity of demand is an example of such a unitless measurement. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Being unitless allows elasticity to be a comparative measure across different products, prices, and markets regardless of the underlying units. This feature also protects the calculation from manipulation through unit changes, as highlighted in the textbook exercise.

Percentage Change in Quantity Demanded

The percentage change in quantity demanded is a measurement that reveals how much the quantity demanded of a commodity changes in response to a one percent change in price. Economists calculate it by taking the difference in quantity demanded at two different price points, dividing by the original quantity, and then multiplying by 100 to express it as a percentage.

This calculation is a cornerstone of determining the price elasticity of demand and is critical for businesses when considering price changes. By analyzing such percentages, companies can predict how a potential price alteration might affect their sales volume.

Economic Experimentation

Economic experimentation involves conducting controlled trials to observe economic behaviors and validate theories. In controlled market experiments, like the one described in the textbook problem, researchers can manipulate certain variables, such as price, and measure the outcome on demand.

Such experimentation can provide valuable data on consumer behavior and market dynamics. However, it is essential to maintain the integrity of the data, as tampering, like the change in unit of measurement attempted by the spies in the exercise, could mislead the experiment's outcomes—if not for the unitless nature of elasticity measurements.