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Constrained Optimization in Economics: Maximizing Utility and Output

Learn about how economic actors optimize their resources with examples, methods, and a consumer preference scenario. Solve optimization problems with substitution and Lagrange multiplier methods.

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Constrained Optimization in Economics: Maximizing Utility and Output

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  1. Topic 9 Constrained Optimization Jacques 5.5 and 5.6

  2. The behaviour of economic actors is often constrained by the economic resources they have at their disposal • Examples: • –Individuals maximising utility will be subject to a budget constraint • –Firms maximising output will be subject to a cost constraint • The function we want to maximise is called the objective function • The restriction is called the constraint

  3. Method 1: By Substitution

  4. Method 2: By The Lagrange Multiplier

  5. Example 1 • Question • A consumers preferences can be represented by the Utility Function, U(x,y)=x.y. How much will the utility maximising consumer demand of goods x and y if they have an income of €100, the price of good x is €5 and the price of good y is €1?

  6. Solution • Solution: (x*,y*) = (10,50) and U = 500

  7. Lagrangean Method:

  8. Lagrangean Method:

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