analyze the maximum value function.
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2.1 Unconstrained Optimization
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2.2 Constrained Optimization
❖ 1. The same idea applies can be applied to the maximum-value function in constrained optimization.
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consume given income and prices.
❖ Note that the demand of a good depends on all prices. If we plot x1 (p, y) against pi, holding y and all prices other than pi constant, we get the demand curve of good i. A change in y or some pj , j≠ i, would be represented by a shift of the demand curve.
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5. Proof:
❖ (a) Multiplying both prices and income by the same factor leaves the budget set unchanged.