ECON 100A Lecture 10: ECON 100A 10-14-2016
Document Summary
Max f (x1, x2) s. t. g (x1, x2) = c. At (x1*,x2*): (dx2/dx1 | g (x1,x2) = c) = (dx2/dx1 | f (x1,x2) = k, g1(x1*,x2*) / g2(x1*,x2*) = f1(x1*,x2*) / f2(x1*,x2*) This means that there exist some scalar such that f1(x1*,x2*) = g1(x1*,x2*) f2(x1*,x2*) = g2(x1*,x2*) To summarize max f(x1,x2) s. t. g(x1,x2) = c. The solution (x1*, x2*) satisfies f1 (x1*, x2*) = g1 (x1*, x2*) and f2 (x1*, x2*) = g2 (x1*, x2*) and g (x1*, x2*) = c. For the case of several valuables: max (x1, ,xn) f (x1, , xn) s. t. g (x1, , xn) = c. Lagrangian function (x1, , xn, ) = f (x1, , xn) + (c g (x1, , xn)) / x1 = f1 (x1, , xn) + g1 (x1, , xn)) = 0. / xx = f2 (x1, , xn) + g2 (x1, , xn)) = 0.
