Calculate the income elasticities for the following demand functions.
a) x(p,m) = m/2p*
b) x(p,m) = 10/p*
Demand is given by "x =\\frac{ m}{(2p)}"
Price elasticity is given by
"Ep=\\frac{ \\frac{dx}{x}}{ \\frac{dp}{p}} =\\frac{ dx}{dp} \\times \\frac{p}{x}"
"\\frac{dx}{dp} = \\frac{-m}{2} \\times \\frac{ 1}{p\\\\^2}"
Plugging in,
"Ep=\\frac{ -m}{2} \\times \\frac{ 1}{p^2} \\times \\frac{2p^2}{m} = -1"
Income elasticity is given by
"Em =\\frac{\\frac{dx}{x}}{ \\frac{dm}{m}} = \\frac{dx}{dm} \\times \\frac{m}{x}"
"\\frac{dx}{dm} =\\frac{ 1}{2p}"
Plugging in,
"Em= \\frac{1}{(2p)} \\times 2p = 1"
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