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Chapter 4: Problem 3

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

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

Step by step solution

01

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
02

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 %.
03

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.

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