ECON401 Lecture 7: integrability examples
13 Feb 2017
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Mwg argue that under quite general conditions, the answer is yes. As mwg explain, the rst step is to use duality and the envelope theorem to integrate backwards from the demand equations to the expenditure function. The next step is to use the expenditure function to nd the equation of a typical indiference curve. In a two-good demand system suppose x1 (p1, p2, w) = aw p1. Find the equation for a typical indi erence curve u0 = u (x1, x2). Use the envelope theorem and duality to write. Fix x2 = x0: we want the x . Draw a picture to persuade yourself that x . 1 + p0 f (p1) = 0 implies. Thus, at the optimal value of p1, x . So we started with a cobb-douglas demand system and we have worked backwards to obtain the equation for a cobb-douglas indi erence curve.
