Consumer_Theory_2_S08

Consumer_Theory_2_S08 - Utility Maximization and Choice...

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Utility Maximization and Choice Chapter 4 Define budget sets and budget constraint Set of available alternatives Characterize optimal choice: Graphical characterization Utility maximization subject to budget constraint Mathematical Solution Technique: Lagrange method To determine optimal choices
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Budget Sets (1) Budget Set: Contains all consumption bundles that are within a consumer’s budget. Budget depends on consumer’s income and on prices. M is consumer’s income or budget p n is price of good n . Budget Set is determined by consumer’s income and prices: All x=(x 1 ,x 2 ,…,x n ) s.t. Determination of optimal choice: Maximize Utility subject to budget constraint. n n n x p M
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Budget Sets (2) Graphical Representation Budget set is triangle below the budget constraint: Rewrite to make line relation explicit: y p x p M y x + = x y y x p p = slope y p M = intercept x p M = intercept Budget Set x p p p M y y x y =
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Budget Sets (3) Effect of income increase: Budget constraint shifts up, slope remains the same. x y
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Budget Sets (4) Effect of Price change: Budget constraint rotates around intercept x y x y Decrease of p x Decrease of p y
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Utility Maximization (1) Optimal Choice: Maximize utility subject to the budget constraint: Consumer’s choice variables: x, y Monotonicity implies: Constraint is always binding, consumer spends entire budget ( ) y p x p M y x U y x + subject to , max
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