Answer
a)
i) Elasticity is -1
ii) Elasticity is -.4736
b)
i) Elasticity is 1.222
ii) Elasticity is 1.1
Work Step by Step
a)
i)
$Elasticity = \frac{(Q_{2}-Q_{1})/[(Q_{2}+Q_{1})/2}{(P_{2}-P_{1})/[(P_{2}+P_{1})/2}$
$Elasticity = \frac{(32-40)/[(32+40)/2}{(10-8)/[(10+8)/2}$
$Elasticity = \frac{(-8)/[72/2]}{2/[(18)/2]}$
$Elasticity = \frac{(-8)/(36)}{2/(9)}$
$Elasticity = \frac{-2/9}{2/9}$
$Elasticity = -1$
ii)
$Elasticity = \frac{(45-50)/[(45+50)/2}{(10-8)/[(10+8)/2}$
$Elasticity = \frac{-5/47.5}{2/9}$
$Elasticity = \frac{-.10526}{.2222}$
$Elasticity = -.4736$
b)
i)
income elasticity = percent change in quantity demanded/percent change in income
$Elasticity = \frac{(Q_{2}-Q_{1})/[(Q_{2}+Q_{1})/2}{(I_{2}-I_{1})/[(I_{2}+I_{1})/2}$
$Elasticity = \frac{(30-24)/[(30+24)/2]}{(12000-10000)/[(12000+10000)/2}$
$Elasticity = \frac{(6/27)}{(12000-10000)/[(12000+10000)/2}$
$Elasticity = \frac{(6/27)}{2000/11000}$
$Elasticity = \frac{6/27}{2/11}$
$Elasticity =.22222/.1818181$
$Elasticity = 1.222$
ii)
income elasticity = percent change in quantity demanded/percent change in income
$Elasticity = \frac{(Q_{2}-Q_{1})/[(Q_{2}+Q_{1})/2}{(I_{2}-I_{1})/[(I_{2}+I_{1})/2}$
$Elasticity = \frac{(12-8)/[(12+8)/2]}{(12000-10000)/[(12000+10000)/2}$
$Elasticity = \frac{(4/20)}{(12000-10000)/[(12000+10000)/2}$
$Elasticity = \frac{(1/5)}{2000/11000}$
$Elasticity = \frac{1/5}{2/11}$
$Elasticity =.2/.1818181$
$Elasticity = 1.1$
