Question

(3) Given the demand function for a consumer for some meat as follows: 9. = 5 +.02 Y-5 P. +.25 P2 Where q, is the amount of the meat demanded per week and p, its price a. Derive the demand curve for the meat for the consumer if the following conditions hold: Y = weekly income of the Consumer $100/week P2 = $12/kg is the price of fish. b. Draw the demand curve. c. What is the elasticity of the demand curve when the price is $20. d. Are the two goods fish and the meat complements or substitutes for the consumer? Give reasons for your answer.

Answer 1

Given, Q1= 5 + 0.02Y - 0.5P1 + 0.25P2

Y = $ 100/ week, P2 = $ 12 / kg

Q1= 5 + 0.02×100 - 0.5P1 + 0.25×12

Q1 = 5 + 2 - 0.5P1 + 3

Q1 = 10 - 0.5P1 (Demand function)

P1 = 20 - 2Q1 (Inverse demand function)

B. Refer the attached picture for the demand curve

P / $ 20 Demand Curve

C. When P1 = $ 20

Q1 = 10 - 0.5×20 = 0

Differentiating the demand function wrt P1, we get

dQ1/dP1 = -0.5

Elasticity of demand = (dQ1/dP1)×(P1/Q1) = -0.5 ×(20/0) = - Infinity

Since quantity demanded at that price is zero.

D. Q1= 5 + 0.02Y - 0.5P1 + 0.25P2

Differentiating the above equation wrt P2 we get

(dQ1/dP2) = + 0.25

Therefore the cross elasticity of demand for meat and fish will be positive. Hence, meat and fish are Substitute to each other.

Please contact if having any query will be obliged to you for your generous support. Your help mean alot to me please help. Thank you.