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(Solved): 1. Consider a cake-eating problem of a consumer that derives utility from having cake and eating it ...




1. Consider a cake-eating problem of a consumer that derives utility from having cake and eating it too:
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\max _{\left\{c_{
1. Consider a cake-eating problem of a consumer that derives utility from having cake and eating it too: subject to , with given. Assume that . (i) Formulate the cake-eating problem recursively by writing down a Bellman equation. (ii) Solve for the value function and policy functions explicitly assuming the following utility functional form: , with .


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(i) The Bellman equation for the cake-eating prob
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