Answer to Question #312264 in Microeconomics for Robera

Question #312264

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 �

1
Expert's answer
2022-03-16T11:09:55-0400

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.


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