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Economics - Microeconomics - Profit Function

Profit Function
  Given any production set Y, we have seen how to calculate the profit function, π(p), which gives us the maximum profit attainable at prices p. The profit function possesses several important properties that follow directly from its definition. These properties are very useful for analyzing profit-maximizing behavior.

The Profit function is, by definition, the maximum profits the firm can make as a function of the vector of prices of the net outputs:

π( p) = py such that y is in Y.

Cost Minimization

  • Calculus analysis of cost minimization:
    Let us consider the problem of finding a cost-minimizing way to produce a given level of output:

    Such that f(x) = y

    We analyze this constrained minimization problem using the method of Lagrange multipliers. Begin by writing the Lagrangian

    £(λ,x) = wx – λ(f(x) – y)

  • Bordered Hessian matrix: This is called Bordered Hessian matrix.

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