Question

Assuming that the equation f(Q, P1, P2, Y) = 10P1Q1 + 5Q1 - 2P2 - 4Y -18 =0

defines an implicit demand function Q1 = Q1(P1, P2, Y), find own price elasticity , cross elasticity and income elasticity at a point (P1, P2, Y) = (2, 1, 20)

Answer 1

$f(Q_1P_1P_2,Y)= 10P_1Q_1+5Q_1-2P_2-4Y-18$

Where; (P1, P2, Y) = (2, 1, 20)

$Q_1= \frac{2P_2+4Y+18}{10P_1+5}$ =4

$Own Price Elasticity=\frac{\Delta Q}{\Delta P}\times \frac{p}{Q}$

$=\frac{\Delta Q}{\Delta P_1}=10\times \frac{P}{Q}$

$10\times \frac{2}{4}=$5

$Own Price Elasticity=\frac{\Delta Q}{\Delta P_2}\times \frac{p_2}{Q}$

Cross elasticity= $\frac{1}{4}\times -2= \frac{-2}{4}= -0.5$

$Income Elasticity =\frac{\Delta Q}{\Delta I}\times \frac{I}{Q}$

$=\frac{-4}{4}\times 20=-20$