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Chapter 4: Problem 12

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

Expert verified
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

01

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 \(0.5 / -0.33 = -1.5\).
02

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.
03

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.

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Most popular questions from this chapter

An individual sets aside a certain amount of his income per month to spend on his two hobbies, collecting wine and collecting books. Given the information below, illustrate both the price-consumption curve associated with changes in the price of wine and the demand curve for wine. $$\begin{array}{|ccccc|} \hline \begin{array}{c} \text { PRICE } \\ \text { WINE } \end{array} & \begin{array}{c} \text { PRICE } \\ \text { B00K } \end{array} & \begin{array}{c} \text { QUANTITY } \\ \text { WINE } \end{array} & \begin{array}{c} \text { QUANTITY } \\ \text { BOOK } \end{array} & \text { BUDGET } \\ \hline \$ 10 & \$ 10 & 7 & 8 & \$ 150 \\ \hline \$ 12 & \$ 10 & 5 & 9 & \$ 150 \\ \hline \$ 15 & \$ 10 & 4 & 9 & \$ 150 \\ \hline \$ 20 & \$ 10 & 2 & 11 & \$ 150 \\ \hline \end{array}$$

Vera has decided to upgrade the operating system on her new \(P C .\) She hears that the new Linux operating system is technologically superior to Windows and substantially lower in price. However, when she asks her friends, it turns out they all use PCs with Windows. They agree that Linux is more appealing but add that they see relatively few copies of Linux on sale at local stores. Vera chooses Windows, Can you explain her decision?

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Suppose the income elasticity of demand for food is 0.5 and the price elasticity of demand is \(-1.0 .\) Suppose also that Felicia spends \(\$ 10,000\) a year on food, the price of food is \(\$ 2,\) and that her income is \(\$ 25,000\) a. If a sales tax on food caused the price of food to increase to \(\$ 2.50,\) what would happen to her consumption of food? (Hint: Because a large price change is involved, you should assume that the price elasticity measures an arc elasticity, rather than a point elasticity.) b. Suppose that Felicia gets a tax rebate of \(\$ 2500\) to ease the effect of the sales tax. What would her consumption of food be now? c. Ts she better or worse off when given a rebate equal to the sales tax payments? Draw a graph and explain.
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