Question

You run a small business and would like to predict what will happen to the quantity demanded for your product if you raise your price. While you do not know the exact demand curve for your product, you do know that in the first year you charged \(45 and sold 1200 units and that in the second year you charged \)30 and sold 1800 units.

a. If you plan to raise your price by 10 percent, what would be a reasonable estimate of what will happen to quantity demanded in percentage terms?

b. If you raise your price by 10 percent, will revenue increase or decrease?

Short answer

a. A 10-percent rise in price would bring a 10-percent fall in demand.

b. The revenue will remain constant.

Step-by-step solution

Explanation of part (a)

The price elasticity needs to be known to determine the change in demand due to a price change. The arc method is used to find the price elasticity.

$$\begin{gathered} Ep=\frac{\left|△Q\right|}{\left|△P\right|}\times \frac{AverageP}{AverageQ} \\ \left|△Q\right|=\left|1800-1200\right|=600 \\ \left|△P\right|=\left|30-45\right|=15 \\ AverageQ=\frac{1800+1200}{2}=1500 \\ AverageP=\frac{30+45}{2}=37.5 \\ Therefore; \\ Ep=\frac{600}{15}\times \frac{37.5}{1500}=1 \end{gathered}$$

The price elasticity is unitary elastic equal to 1, which means the percentage change in demand will be the same as a percentage change in price. Hence, a 10% decrease in demand will occur with a 10% increase in price.

Explanation of part (b)

When the demand is unitary elastic, the revenue remains constant;this is because if the producer raises the price to increase the revenue, the demand will decrease in the same proportion since elasticity is equal to 1. Therefore, fewer units will be sold at a high price, and the total revenue will remain constant.