ECON 2X03 Lecture : Tutorial Workbook Solutions.pdf
8 Jul 2013
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Material prepared by h holmes and robert d"aurelio, ma. Production function in general is y = f(z1, z2) Fixed-proportions production is y = min ( z1/ amt of z1 needed, z2/ amt of z2 needed ) Cobb-douglas variable-proportions production function is y = az1 uz2 v. Long run cost minimization problem is min w1z1 + w2z2. If z2 is fixed at z2 , the total product fn is tp (z1 ) = f(z1 , z2 ) Mp(z1) = slope of tp( z1 ) = f(z1 , z2 ) [since tp is a fn only of z1, it"s not a partial derivative per se] z1 , z2 st y = f(z1, z2) Diminishing mp sets in where mp is maximized, where d mp/d z1 = 0. Ap( z1 ) = tp( z1 ) z1. For one variable input, the cost minimization problem is: min w1z1 z1 st y = tp (z1) Smc (y) = vc"(y) = d vc(y) dy.
