Answer to Question #175848 in Microeconomics for michele ford

Question

5.1. Suppose that the price of whiskey increases from R100 to R150 a bottle and as a result the quantity demanded decreases from 1 100 bottles to 800 bottles.
5.1.1. Use the ARC (midpoint) formula to calculate the price elasticity of demand for whiskey. (3)
5.1.2. Based on the calculated elasticity value in 5.1.1, indicate whether the demand in the market for whiskey is elastic or inelastic. (1)
5.1.3. Based on your answer in 5.1.2, illustrate the elasticity of demand in the market for whiskey. Clearly indicate the correct percentage changes in price and quantity on the elasticity graph. (4)
5.1.4. Explain how producers could increase total revenue given the calculated elasticity coefficient.

Answer 1

5.1.1) The price elasticity of demand for whiskey can be calculated as follows:

$$E_d=\dfrac{\%\Delta Q}{\%\Delta P}=\dfrac{\dfrac{Q_2-Q_1}{0.5(Q_2+Q_1)}}{\dfrac{P_2-P_1}{0.5(P_2+P_1)}},$$

$​ ​ ​$

$$E_d=\dfrac{\dfrac{800-1100}{0.5(800+1100)}}{\dfrac{R150-R100}{0.5(R150+R100)}}=-0.79.$$

5.1.2) As we can see, the price elasticity of demand is $E_d=0.79$ (we don't bother to sign minus). Because, $E_d<1$, the market for whiskey is inelastic.

5.1.3) As we can see, when the price changed by 40% the quantity demanded falls by 31%.

5.1.4) Since the price elasticity of demand is inelastic, producers could increase the price in order to increase the total revenue.