ECO 3145 Lecture 5: Lecture 5.pdf
15 Jun 2014
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Document Summary
Necessary conditions for an optimum: the method of lagrange. Sufficient conditions for a global optimum: comparative statics. Envelope theorem: structure of the problem, structure of the problem. Vocabulary: who chooses the x"s: example: utility maximization x(f. C is a parameter : a constant value that is outside the control of the economic agent. Consumer seeks to maximize utility subject to a budget constraint x. 1i i denotes the price of good i and m is the. Necessary conditions for an optimum: the method of lagrange: substitution method in very simple problems, one can use the substitution method of simultaneous equations to turn a constrained optimisation into an unconstrained optimisation. Example: a discriminating monopolist, simon et blume, p. 649-50 i i = , and the cost function is represented as. By substituting the inverse demand function into the profit function, the constrained maximization problem is transformed into an unconstrained problem:
