Answer to Question #187987 in Microeconomics for Aaron

Question

An exclusive Yoghurt manufacturer sells 4,000 gallons per month at a price of 40 dollars each. when the price is reduced to 30 dollars sales increase to 6,000 gallons per month.

a. Calculate the price elasticity of demand for the Yoghurts over this price range.

b. Is demand elastic, unit elastic or inelastic?

c. Calculate the change in revenue due to the change in price.

Answer 1

$Soln,$

a.) price elasticity of demand of yoghurt.

$PED=\frac{\%\Delta Q}{\%\Delta P}$

$\%\Delta Q=\frac{6000-4000}{[6000+4000]\div2}=\frac{2000}{5000}$$\%gg$

$\%\Delta Q=\frac{2}{5}$

$\%\Delta P=\frac{\$30-\$40}{[\$30+\$40]\div2}=\frac {-10}{35}$

$\%\Delta P=\frac{-2}{7}$

$PED=\frac{2}{5}\div\frac{-2}{7}$

$=\frac{2}{5}\times\frac {7}{-2}=\frac{14}{-10}$

$PED={-1.4}$

b.) The above price elasticity of demand shows that demand of the product is inelastic because it is less than 1.

Moreover variables go in opposite directions but in same proportions.

c.) Change in revenue

$\Delta R=4000 P.M\times\$40=\$160000$

$\Delta R =6000P.M\times\$30=\$180000$

$\%\Delta R=\frac{180000-160000}{[180000+160000]\div2}$

$\%\Delta R=\frac{20000}{170000}=\frac{2}{17}$

$\%\Delta P=\frac{-2}{7}$ from above,

$=\frac{\%\Delta R}{\%\Delta P}=\frac{2}{17}\times\frac{7}{-2}=\frac{14}{-34}$

$\%\backslash DeltaQ=\backslash frac$

$=-0.4$

$\%$

$\%$

$\%\backslash Delta$

$\%\backslash Delta\; Q=\backslash frac\{2\}\{5\}$