Econ501aL5 - Computing an Example (see Binger and Hoffman,...

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Computing an Example (see Binger and Ho f man, p. 147- 149): u ( x, y )= xy + x + y The consumer’s utility maximization problem is max xy + x + y (1) subject to : p x x + p y y = M To solve (1), we set up the Lagrangean expression, L = xy + x + y + λ [ M p x x p y y ] . The f rst-order conditions are given by x : y +1 λp x =0 (2) y : x +1 λp y =0 (3) λ : M p x x p y y =0 . (4)
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We can solve (2) and (3) to eliminate λ , yielding the equation for the income-consumption curve: y = p x p y ( x +1) 1 . (5) Equation (5) is the condition, MRS = p x /p y . By plugging (5) into the budget equation (4), we can solve for the generalized demand function for x. Then plug x into (5) to get y : x = M + p y p x 2 p x and y = M + p x p y 2 p y . (6) Equation (6) gives us the ordinary demand function, the Engel curve, or the cross-price demand function, depend- ing on which variables we plug in numbers for.
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x = M + p y p x 2 p x 1. For f
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Econ501aL5 - Computing an Example (see Binger and Hoffman,...

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