Economics 1010a1 Lecture Notes - Ultimatum Game, Exponential Discounting, Dynamic Inconsistency
8 Mar 2014
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In the standard model: wtp should be independent of whether you already have it. Equation to solve for when/how much work to do on a given day. Solve for u(xt, xt+1, xt+2)= -xt^2 = 1/2xt+1^2 - 1/4xt+2^2 (this is called exponential discounting) Given constraint xt + xt+1 + xt+2 = 12. Express original equation in terms of two variables. Partially differentiate with respect to the remaining variables. Mon= 12/7 ; tues 24/7 ; wed 48/7. Nothing has changed, so your plans will be time consistent (ie. what you thought you were going to do in the future is exactly what you are going to do when you get to the future) U(xm,xt,xw)= -xm^2 - 1/2xt^2 - 1/3xw^2 (this co-efficient is changed; so optimal decision is different) s. t. How you discount the behaviour determines whether you"ll be time consistent or not.
