Question

suppose that your demand schedule for pizza is as follows

price: $8,$10,$12,$14,$16

quantity demanded( income $16.000): 40,32,24,16,8

quantity demanded( income $20.000): 50,45,30,20,12

a. use the midpoint method to calculate your price elasticity of demand as the price of pizza increases from $8 to $10 if (i) your income is $16,000 and (ii) your income is $20,000.

b. calculate your income elasticity of demand as your income increases from $16,000 to $20,000 if (i) the price is $12 and (ii) the price is $16

Answer 1

The midpoint formula

$Price\space elasticity\space of\space demand=\frac{\frac{(Q_2-Q_1)}{[(Q_2+Q_1)/2]}}{\frac{(P_2-P_1)}{[(P_2+P_1)/2}}$

i

$Price\space elasticity\space of\space demand=\frac{\frac{(32-40)}{[(32+40)/2]}}{\frac{(10-8)}{[(10+8)/2}}$

$=\frac{-8}{36}\times\frac{9}{2}=-1$

ii

$Price\space elasticity\space of\space demand=\frac{\frac{(45-50)}{[(45+50)/2]}}{\frac{(10-8)}{[(10+8)/2}}$

$=\frac{-5}{47.5}\times\frac{9}{2}=-047368211$

b

$\frac{\Delta I}{\Delta P}\times\frac{P}{I}$

$=\frac{20,000-16,000}{16-12}\times\frac{12}{16000}$

$=\frac{4000}{4}\times\frac{12}{16000}$

$=\frac{3}{4}=0.75$