Econ 5201 Lecture 4

Econ 5201 Lecture 4 - Consumers Problem IV Income,...

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Consumer’s Problem IV Income, Substitution and Price Effects Consider the consumer’s problem: max U=U(x 1 , x 2 ) s.t. p 1 x 1 +p 2 x 2 =m We have seen that the optimal solution to the problem leads to the utility-maximizing bundle (x 1 *, x 2 *). Figure 1 x 2 C m/p 2 A x 2 ** R x 2 * P O x 1 * x 2 ** m/p B D x 1 Now suppose that p 1 and p 2 (Figure 1) remain unchanged but m is raised to m’. We know that the new budget line satisfying p 1 x 1 +p 2 x 2 =m’ represented by the line CD will be parallel to the old budget line AB. The point of tangency B of the new budget line with a higher indifference curve represents the new 1
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optimal bundle. Note that the new quantities are x 1 ** and x 2 **. The increase in quantity of x 1 (x 1 **-x 1 *) and x 2 (x 2 **-x 2 *) is known as the income effect . In general, when income increases, the new optimal point will be towards the northeast of the old point that is the income effect is positive for both goods. Goods with positive income effect are called normal goods. Return to the previous example of Ux x =+ 12 We saw that for m=m 0 and price (p 1 , p 2 ) x mp pp p 1 02 11 2 * () = + and x 2 01 21 2 * = + If m is increased to m 1 we solve the problem m a x x p 1 x 1 +p 2 x 2 =m 1 The new optimal bundle is x 1 2 ** = + and x 2 2 = + Thus the income effects are xx mm p 10 2 * −= 2 + and 2
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xx mm p pp p 22 10 21 2 ** * () −= 1 + respectively.
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This note was uploaded on 10/19/2010 for the course ECON 1202 taught by Professor Matel during the Fall '08 term at UConn.

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Econ 5201 Lecture 4 - Consumers Problem IV Income,...

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