Answer to Question #250424 in Macroeconomics for Aman

Question #250424
commodities, X and Y. The income of Mr.Alemu is $200, and price of X is 5 and the price of Y is 15. The demand function for the comnmodity is given as:

Qx=100-0.75)y +0.251px1/3 + 2p3/2

where Qx is quantity demand of commodity X. 7Px is the price of commodity X, p, is
1
Expert's answer
2021-10-12T12:26:48-0400

Price elasticity of demand "= \\frac{dQ_x}{dP} \\times \\frac{P }{ Q}"


"Q_x=100 - 0.75y +0.251 px^{\\frac{1}{3}} + 2py^{\\frac{3}{2}}"


"Qx=100 - 0.75\\times200 +0.251 px^{\\frac{1}{3}} + 2 \\times 15^{\\frac{3}{2}}"


"Qx=100 - 150 + 0.251 px^{\\frac{1}{3}} + 2 \\times 58.09475"


"Qx = - 50 + 0.251 px^{\\frac{1}{3}} + 116.1895"


"Qx = - 50 + 0.251 px^{\\frac{1}{3}} + 116.1895"


"Qx = 66.1895 + 0.251 px^{\\frac{1}{3}}"


"Qx = 66.1895 + 0.251 \\times 5^{\\frac{1}{3}}"


"Qx = 66.1895 + 0.251 \\times 1.709976"


"Qx = 66.1895 + 0.4292"


"Qx = 66.6187"


"Price\\space elasticity\\space of\\space demand = \\frac{dQx}{dP} \\times \\frac{P }{ Q}"


Differentiating equation 1, with respect to P, we get "\\frac{dQx}{dP}"


"\\frac{dQx}{dP} = \\frac{1}{3} \\times \\frac{0.251 }{px^{\\frac{2}{3}}}"


"\\frac{dQx}{dP} = \\frac{0.0836 }{ px^{\\frac{2}{3}}}"


"Price \\space elasticity\\space of\\space demand = \\frac{dQx}{dP }\\times\\frac{ P }{ Q}"


"Price \\space elasticity\\space of\\space demand = [\\frac{0.0836}{ px^{\\frac{2}{3}}}]\\times* [\\frac{5 }{ 66.6187}]"


"Price\\space elasticity\\space of \\space demand = [\\frac{0.0836 }{ 5^{\\frac{2}{3}}}]* [\\frac{5 }{ 66.6187}]"


"Price \\space elasticity\\space of\\space demand = [\\frac{0.0836 }{ 2.924018}] * [\\frac{5}{66.6187}]"


"Price\\space elasticity\\space of\\space demand = 0.0285 \\times 0.0750"


Price elasticity of demand = 0.0021


Price elasticity of demand is very near to 0, thus we can conclude that the price elasticity of demand is inelastic in nature.


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