Question

The price of a good rises from 4 dollras to 4.50 dollars and as a result, total revenue falls from 400 dollars to350 dollars Is the demand for the good elastic, inelastic, or unitelastic?

Short answer

Given the calculated elasticity of -1.78, the demand of the good is elastic.

Step-by-step solution

Determine Changes in Price and Quantity

Initially, price of the good was $4 and it rises to $4.50, so the increase in price is $0.50. Regarding quantity, because the good is expressed in terms of total revenue, we find the quantity by dividing total revenue by price. So initially the quantity (Q1) was 400/4= 100 units and finally it became 350/4.50 approximately 77.78 units, thus the decrease in quantity demanded is 22.22 units

Calculate Percentage Changes

Next calculate the percentage change in price and the percentage change in quantity using the formula for percentage change: (Final value - Initial value) / Initial value *100. The percentage change in price is (4.50 - 4) / 4 * 100 = 12.5%, while for quantity it's (77.78 - 100) / 100 * 100 = -22.22 %.

Evaluate Elasticity

Finally, to find out the nature of demand, divide the percentage change in quantity by the percentage change in price to get the price elasticity of demand which is -22.22 / 12.5 = -1.78. Since the result is more than one in absolute terms, the demand is elastic.

Key concepts

Price Elasticity

Price elasticity of demand is a measure that shows how the quantity demanded of a good or service reacts to a change in its price. If demand is elastic, it means that consumers are highly responsive to price changes. In contrast, if demand is inelastic, consumers are not as sensitive to price changes. The elasticity is calculated using the formula: \( \text{Price Elasticity of Demand} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}} \).
In a case where elasticity is greater than 1, demand is elastic. If it equals 1, it is unit elastic, and if it is less than 1, demand is inelastic. This understanding helps businesses set prices by predicting consumer reactions.

Percentage Change in Quantity

Percentage change in quantity refers to how drastically the amount of a good or service purchased alters when there is a price change. To find this, we use the formula: \( \frac{\text{Final Quantity} - \text{Initial Quantity}}{\text{Initial Quantity}} \times 100 \).
This gives a percentage value which can be negative or positive, depending on whether the demand decreased or increased. For the problem at hand, the quantity purchased fell from 100 to approximately 77.78 units owing to a price increase.

Percentage Change in Price

Understanding the percentage change in price is key to assessing demand elasticity. It is calculated by determining the difference between the final and initial prices, then dividing by the initial price. The formula is \( \frac{\text{Final Price} - \text{Initial Price}}{\text{Initial Price}} \times 100 \).
This calculation shows the rate of price changes as a percentage. In the exercise example, the price increased from \(4 to \)4.50, which is a 12.5% increase. Such changes help in understanding how changes in pricing impact the demand for goods.

Total Revenue

Total revenue is the total income a company generates from selling its goods or services. It is calculated by multiplying the price per unit by the number of units sold. In the context of elasticity, examining changes in total revenue helps determine whether demand is elastic or inelastic.
If total revenue decreases as prices increase, it often indicates that demand is elastic, as seen in the exercise. This happens because customers purchase significantly less at higher prices, impacting overall revenue. Observing these shifts is vital for businesses looking to make informed decisions about pricing and sales strategies.