NotesECN741-page7

# NotesECN741-page7 - following Result 1 If preferences are...

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ECN 741: Public Economics Fall 2008 1.2.1 Additive separable utility functions Suppose U is of the form U ( c 1 ,c 2 ,l ) = u 1 ( c 1 ) + u 2 ( c 2 ) - v ( l ) then H i = - U ii c i U i Our goal to relate H i to income elasticity of demand for good i . In order to do that, suppose there is a non-wage income m , such that p 1 c 1 + p 2 c 2 = l + m . Consider FOC of consumer (notice that I have ignored taxes for this part) U i ( c i ( p,m )) = p i φ ( p,m ) in which φ ( p,m ) is the lagrange multiplier on budget constrain. Let’s take derivative w.r.t m U ii ∂c i ∂m = p i ∂φ ∂m = U i φ ∂φ ∂m or U ii c i U i m c i ∂c i ∂m = m φ ∂φ ∂m . Let η i = m c i ∂c i ∂m . Then H i = - m φ ∂φ ∂m 1 η i Therefore, H i > H j if and only if η j > η i . Combine this with the above and we get the
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Unformatted text preview: following: Result 1 If preferences are additive separable, necessities should be taxed more than luxuries. Example : U ( c 1 ,c 2 ,l ) = log( c 1 ) + log( c 2-¯ c )-v ( l ) 1.2.2 Quasi-linear utility function Consider the utility function in the previous section and assume that v ( l ) = l . Then there is no income eﬀect and using income elasticities for guiding us about optimal taxes is not useful. However, we use price elasticities. Consider again the FOC of consumer U i ( c i ) = p i φ 7...
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## This note was uploaded on 12/10/2011 for the course MAT 121 taught by Professor Wong during the Fall '10 term at SUNY Stony Brook.

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