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MATH
[1251]

Methods from Economic applications

All methods from Economic applications.

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Formulate a production problem

To maximise production under a budget:

  1. identify the production function Q=f(E,L)Q=f(E,L);
  2. write the feasible set qE+pL≤B,E,L≥0;qE+pL\le B, \qquad E,L\ge0;
  3. if increasing either input increases output, replace the inequality by the binding budget equation qE+pL=BqE+pL=B;
  4. apply the constrained-extrema method and interpret the resulting inputs.

If output increases with either input, an allocation leaving budget unused cannot be optimal, because some additional productive input could be purchased. Without this monotonicity assumption (or if inputs are indivisible), keep the inequality and compare interior, axis and slack candidates instead.

  1. [1]:Production function
  2. [2]:Budget constraint
  3. [3]:Optimal Cobb-Douglas allocation

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Formulate a production problem