Question

Suppose the demand function for a firm’s product is given by 𝐿𝑛 𝑄𝑥 𝑑 = 7 − 1.5𝐿𝑛𝑃𝑥 + 2𝐿𝑛𝑃𝑦 − 0.5𝐿𝑛𝑀 + 𝐿𝑛𝐴 Where Px = $15, Py = $6, M = $40,000, and A =$350. a. Determine the own price elasticity of demand, and state whether demand is elastic, inelastic, or unitary elastic. (3mks) b. Determine the cross-price elasticity of demand between good X and good Y, and state whether these two goods are substitutes or complements. (3mks) c. Determine the income elasticity of demand, and state whether good X is a normal or inferior good. (3mks) d. Determine the own advertising elasticity of demand. (3mks

Answer 1

$lnQ_xd=7-1.5lnP_x+2lnP_y-0.5lnM+lnA$

$P_x=$ $$15$ , $P_y=$ $$6$ , $M=40000, A=$ $$350$

$lnQ=7-1.5ln(15)+2ln(6)-0.5ln(40000)+ln(350)$

$lnQ=7-4.0624+3.5835-5.2983+5.8579$

$lnQ=7.0811$

$Q=e^{7.0811}=1189.276$

a)$E_p=\frac{dQ}{dP}\times \frac{P}{Q}=-1.5\times\frac{350}{1189.276}=-0.441, inelastic$$demand$

b)$E_cpx=$ $\frac{dQ}{dP_X}\times \frac{P_X}{Q}, P_X=$$$15$

$=-1.5\times\frac{15}{1189.276}=-0.0189$

$E_cpx=\frac{dQ}{dP_Y}\times \frac{P_Y}{Q},P_Y=$ $$6$

$=2\times\frac{6}{1189.276}=0.01$

X and Y are substitutes.

c)$E_I=\frac{dQ}{dI}\times \frac{I}{X}=0.5\times \frac{40000}{15}=-1.333$

X is an inferior good.

d) $AED=\frac{dQ}{dA}\times \frac{A}{Q}=1\times\frac{350}{1189.276}=0.29$