Econ 281 Chapter4b - Corner Solutions Interior Optimums...

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1 Corner Solutions Interior Optimums occur when positive amounts of both goods are consumed to maximize utility Not everyone will maximize utility by consuming both goods: Not everyone buys a Porsche Not everyone values ballet shoes highly When utility is maximized and one good is not consumed, a Corner Solution exists
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2 Porsches Food IC 2 BL 0 B IC 1 A Point A consumes positive amounts of both  goods, but does not maximize utility Point B maximizes utility while consuming  only 1 good.
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3 Finding a corner solution 1) Solve for equilibrium as normal using the tangency condition: MU x /P x =MU y /P y 2) If either good is negative, zero of that good is consumed. (Unless negatives are valid) 3) Recalculate the basket that maximizes utility (using budget constraint).
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4 Two goods available: Siamese Cats and  Dachund Dogs I = $200 P c  = $100 P d  = $50 Utility is such that: MU c =d MU d =5+c
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5 Optimization Steps 1) P c c+P d d=I 100c+50d=200 2) MU c /MU d =P c /P d d/(5+c)=100/50 50d=500+100c d=10+2c
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