Two consumers a and b face the following utility maximization problems

Max U ^a = In x ^a + In y ^a

s.t, p _x x ^a + p _y (y ^a )y ^a = I ^a

Max U ^b = In x ^b + In y ^b

s.t, p _x x ^b + p _y y ^b = I ^b

where x and y are goods the price of which are p _x (x ^a ) and p _y and where I ^a , I ^b are the consumers incomes.

(a) Using the method of Lagrange derive equations characterizing the consumers optima.

(b) Show that the market fails to achieve consumption efficiency here.

Answer rating: 100% (QA)

a For consumer a L ln x ln y kI p x x py y dL dx 1 x k p x 0 1 dL dy 1y kpy y kpy 0 2 dL dk I p x x ... View the full answer