Linear probability model: Difference between revisions

Latest revision as of 21:01, 12 December 2013

Equivalent variation (EV) is a measure of how much more money a consumer would pay before a price increase to avert the price increase. Because the meaning of "equivalent" may be unclear, it is also called extortionary variation. John Hicks (1939) is attributed with introducing the concept of compensating and equivalent variation.

It is a useful tool when the present prices are the best place to make a comparison.

The value of the equivalent variation is given in terms of the expenditure function ( $e (\cdot, \cdot)$ ) as

$E V = e (p_{0}, u_{1}) - e (p_{0}, u_{0})$

$= e (p_{0}, u_{1}) - w$

$= e (p_{0}, u_{1}) - e (p_{1}, u_{1})$

where $w$ is the wealth level, $p_{0}$ and $p_{1}$ are the old and new prices respectively, and $u_{0}$ and $u_{1}$ are the old and new utility levels respectively.

Value function form

Equivalently, in terms of the value function ( $v (\cdot, \cdot)$ ),

$v (p_{0}, w + E V) = u_{1}$

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

$e (p_{0}, v (p_{0}, w + E V) = e (p_{0}, u_{1})$

$w + E V = e (p_{0}, u_{1})$

$E V = e (p_{0}, u_{1}) - w$

One of the three identical equations above.

References

Mas-Colell, A., Whinston, M and Green, J. (1995) Microeconomic Theory, Oxford University Press, New York.

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+'''Equivalent variation''' (EV) is a [[Measurement|measure]] of how much more money a consumer would pay ''before'' a price increase to avert the price increase.  Because the meaning of "equivalent" may be unclear, it is also called ''extortionary variation''. [[John Hicks]] (1939) is attributed with introducing the concept of [[compensating variation|compensating]] and equivalent variation.
+It is a useful tool when the present prices are the best place to make a comparison.
+The value of the equivalent variation is given in terms of the [[expenditure function]] (<math>e(\cdot,\cdot)</math>) as
+<math>EV = e(p_0, u_1) - e(p_0, u_0) </math>
+<math>   = e(p_0, u_1) - w </math>
+<math>   = e(p_0, u_1) - e(p_1, u_1) </math>
+where <math>w</math> is the wealth level, <math>p_0</math> and <math>p_1</math> are the old and new prices respectively, and <math>u_0</math> and <math>u_1</math> are the old and new utility levels respectively.
+==Value function form==
+Equivalently, in terms of the [[value function]] (<math>v(\cdot,\cdot)</math>),
+<math> v(p_0,w+EV) = u_1 </math>
+This can be shown to be equivalent to the above by taking the expenditure function of both sides at <math>p_0</math>
+<math> e(p_0,v(p_0,w+EV) = e(p_0,u_1) </math>
+<math> w+EV = e(p_0,u_1) </math>
+<math> EV = e(p_0,u_1) -w </math>
+One of the three identical equations above.
+== See also ==
+[[Compensating variation]] (CV) is a closely related measure of welfare change.
+== References ==
+* Mas-Colell, A., Whinston, M and Green, J. (1995) ''Microeconomic Theory'', Oxford University Press, New York.
+[[Category:Welfare economics]]
+{{econ-stub}}

Linear probability model: Difference between revisions

Latest revision as of 21:01, 12 December 2013

Value function form

See also

References

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