Question

Given the Demand function Q1 = 100-P1+0.75P2-0.25P3+0.005Y Calculate the price, income and

cross-price elasticity of demand and interpret the result respectively at P1=8, P2=15, P3=30 and

also Y=8,000 �

Answer 1

Given that

$Qd=100-P_1+0.75P_2-0.25P_3+0.005Y$

$\frac{\delta{Q}}{\delta{P_1}}=-1$

$Q=100-8+0.75(15)-0.25(30)+0.005(8000)$

P

$Q=135.75$

$\epsilon =\frac{\delta{Q}}{\delta{P_1}}\frac{P_1}{Q}$

$\epsilon=-1(\frac{8}{135.75})$

$\epsilon_{P_1}=- 0.06$

A 1% increase in price will bring about a 6% change in the quantity of P₁

$\epsilon_{P_2}=\frac{\delta{Q}}{\delta{P_2}}\frac{P_2}{Q}$

$\epsilon_{P_2}=0.75(\frac{15}{135.75})$

$\epsilon_{P_2}=0.08$

P₂ is a substitute good.

$\epsilon_{P_3}=\frac{\delta{Q}}{\delta{P_3}}\frac{P_3}{Q}$

$\epsilon_{P_3}=-0.25(\frac{30}{135.75})$

$\epsilon_{P_3}=-0.06$

P₃ is a complementary good

$\epsilon_{Y}=\frac{\delta{Q}}{\delta{Y}}\frac{Y}{Q}$

$\epsilon_{Y}=0.005(\frac{8000}{135.75})$

$\epsilon_{Y}=0.29$

Since $\epsilon_{Y}<1$ , the good is income inelastic.