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Unformatted text preview: Income and substitution e f ect - Example These notes are on the example we covered on the week of February 13. Suppose a consumer’s utility is given by u ( x 1 , x 2 ) = x 1 x 2 . Suppose initially p 1 = 2 , p 2 = 1 and m = 10 . Consider a decrease in price of good 1 , and no change in the other price or in income. After the change, p 1 = 1 , p 2 = 1 and m = 10 . Let us f nd the total e f ect of this price change as well as its decomposition to an income e f ect and a substitution e f ect. Step 1- Find the old demand (with p 1 = 2) , the new demand (with p 1 = 1) and the total e f ect of this price change. To shorten the calculation we f nd the demand as a function of p 1 and then substitute p 1 = 2 or p 1 = 1 . We must solve: max x 1 ,x 2 x 1 x 2 s.t. x 1 ≥ , x 2 ≥ p 1 x 1 + x 2 = 10 Since this is a Cobb-Douglas utility there must be an interior solution (else u ( x 1 , x 2 ) = 0) . At the interior solution the indi f erence curve is tangent to the budget line....
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This note was uploaded on 02/23/2008 for the course ECON 3130 taught by Professor Masson during the Spring '06 term at Cornell University (Engineering School).
- Spring '06