Question

tb mc qu. 06-66 (algo) alfs hamburgers sells... alfs hamburgers sells 200 hamburgers per day when the price is $8. large increases in ground beef prices force alfs to raise the price to $10, and the firm only manages to sell 140 hamburgers per day. using the midpoint formula, the price - elasticity - of - demand coefficient multiple choice 0.63 and elastic. 1.59 and elastic. 1.59 and inelastic. 0.63 and inelastic.

Explanation:

Step1: Identify values for mid - point formula

Let $Q_1 = 200$, $Q_2=140$, $P_1 = 8$, $P_2 = 10$.

Step2: Calculate the percentage change in quantity demanded

The formula for percentage change in quantity demanded using mid - point method is $\%\Delta Q=\frac{Q_2 - Q_1}{\frac{Q_2+Q_1}{2}}\times100$.
$\%\Delta Q=\frac{140 - 200}{\frac{140 + 200}{2}}\times100=\frac{- 60}{170}\times100\approx - 35.29\%$.

Step3: Calculate the percentage change in price

The formula for percentage change in price using mid - point method is $\%\Delta P=\frac{P_2 - P_1}{\frac{P_2+P_1}{2}}\times100$.
$\%\Delta P=\frac{10 - 8}{\frac{10 + 8}{2}}\times100=\frac{2}{9}\times100\approx22.22\%$.

Step4: Calculate price - elasticity of demand

The price - elasticity of demand ($E_d$) is given by $E_d=\frac{\%\Delta Q}{\%\Delta P}$.
$E_d=\frac{-35.29\%}{22.22\%}\approx - 1.59$. We take the absolute value, $|E_d|\approx1.59$. Since $|E_d|> 1$, demand is elastic.

Answer:

1.59 and elastic.