Equivalent variation

<h2 id="value-function-form">Value function form</h2>
Equivalently, in terms of the <a href="/facts/Indirect_utility_function/RebE3GnL">indirect utility function</a> (
 
 
 
 v
 (
 ⋅
 ,
 ⋅
 )
 
 
 {\displaystyle v(\cdot ,\cdot )}
 
),

 
 
 
 v
 (
 
 p
 
 0
 
 
 ,
 w
 +
 E
 V
 )
 =
 
 u
 
 1
 
 
 
 
 {\displaystyle v(p_{0},w+EV)=u_{1}}

This can be shown to be equivalent to the above by taking the expenditure function of both sides at 
 
 
 
 
 p
 
 0
 
 
 
 
 {\displaystyle p_{0}}

e
 (
 
 p
 
 0
 
 
 ,
 v
 (
 
 p
 
 0
 
 
 ,
 w
 +
 E
 V
 )
 )
 =
 e
 (
 
 p
 
 0
 
 
 ,
 
 u
 
 1
 
 
 )
 
 
 {\displaystyle e(p_{0},v(p_{0},w+EV))=e(p_{0},u_{1})}

w
 +
 E
 V
 =
 e
 (
 
 p
 
 0
 
 
 ,
 
 u
 
 1
 
 
 )
 
 
 {\displaystyle w+EV=e(p_{0},u_{1})}

E
 V
 =
 e
 (
 
 p
 
 0
 
 
 ,
 
 u
 
 1
 
 
 )
 −
 w
 
 
 {\displaystyle EV=e(p_{0},u_{1})-w}

One of the three identical equations above.
<a href="/facts/Compensating_variation/RgtjPKav">Compensating variation</a> (CV) is a closely related measure of welfare change.

<ul><li><a href="/facts/Microeconomic_Theory_(graduate_level_textbook)/Gce6b4Gs">Mas-Colell, A., Whinston, M and Green, J. (1995) Microeconomic Theory, Oxford University Press, New York</a>.</li>
<li>Greenwood, J. and K.A. Kopecky. "Measuring the Welfare Gain from Personal Computers," Economic Inquiry: 51, No. 1, pp. 336-347. 2013.</li></ul>

Equivalent variation open-in-new

Equivalent variation