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Preference and Utility (Utility maximization (optimal value: V(p,w)…
Preference and Utility
continuity assumption
preference preserves under limits: xn>=yn, we have x>=y
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Utility maximization
Basic assumptions:
preference: rational, continuous, local nonsatiation
u(.): continuous
budget sets: p>>0, w>0
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optimal solutions: x(p,w)
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optimal value: V(p,w)
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strictly increasing in w, nonincreasing in p
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Expenditure Minimization
Basic assumptions:
U(.) continuous, local nonsatiable;
p>>0, u>u(0)
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Expenditure function e(u,p)
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EMP and UMP
given w>0, h(p,V(p,w))=x(p,w), e(p,V(p,w))=w
given u>u(0), x(p,e(p,u))=h(p,u), V(p,e(p,u))=u
Basic assumption:
u(.) continuous, local nonsatiable;
perference strictly convex,
p>>0
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partial e(p,u)/partial p=h(p,u)
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Hicksian Demand: [p''-p']\cdot [h(p'',u)-h(p',u)]<=0