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. If you plan to raise your price by 10 percent, the quantity demanded will likely decrease by approximately 15 percent to around 1530 units. b. If you raise your price by 10 percent, your revenue will likely decrease.

Step-by-step solution

Calculate the Price Elasticity of Demand

You can calculate the price elasticity of demand using the formula \[ \text{Elasticity} = \frac{\% \text{ change in Quantity}}{\% \text{ change in Price}} \]. The percentage change in Quantity is \((1800 - 1200) / 1200 = 0.5\) or 50%. The percentage change in Price is \((30 - 45) / 45 = -0.33\), or -33.3%. So the price elasticity of demand is \(0.5 / -0.33 = -1.5\).

Predict the Quantity Demanded

If you raise the price by 10 percent, the quantity demanded would decrease by \(1.5 \times 10\% = 15\%\), so the newly estimated demand would be \(1800 \times (1 - 0.15) = 1530\) units.

Determine the Effect on Revenue

Also, since the price elasticity of demand is -1.5 (in absolute values bigger than 1), this indicates that it's elastic. An elastic demand means that the percentage change in quantity demanded is greater than the percentage change in price. So if you increase the price by 10 percent, your revenue is likely to decrease.