Question

Currently, the price of good Z is $20 and the quantity demanded is 16,000 units. In past studies, the price elasticity of demand for Z was found to be -1.25. If the company wants to increase production to 20,000 units, what price of Z will have to be set?

Answer 1

By the definition of the price elasticity of demand, we get:

$$E_d=\dfrac{\%\Delta Q}{\%\Delta P}=\dfrac{\dfrac{Q_2-Q_1}{Q_1}}{\%\Delta P},$$ $$\%\Delta P=\dfrac{\dfrac{Q_2-Q_1}{Q_1}}{E_d},$$ $$\%\Delta P=\dfrac{\dfrac{20000-16000}{16000}}{-1.25}=-0.2\times100\%=-20\%.$$

So, the price of good Z decreases by 20%:

$P=\$20\cdot0.2=\$4.$ Therefore, the new price of good Z will be:

$$P_{new}=\$20-\$4=\$16.$$