A player who expects to consume a stream of payments (x1, x2,.., XT) over periods i=1,2,...,...

 

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A player who expects to consume a stream of payments (x1, x2,.., XT) over periods i=1,2,..., T and who evaluates per-period payments using the utility function u(x), will evaluate his discounted sum of future utilities in period t=1 as V(x1, x2,.., XT) = 8t-1 u(xt) Intermediate Microeconomics, Games and Behaviour 5 ECB2VMIE 2023-2024 Where 8 E (0,1) is the player's discount factor, which he uses to discount future utility. a) Consider a player with u(x+) = ln(x+) who needs to allocate a fixed budget K across three periods (i.e. T = 3) and with discount factor 8 = 1. Write down the player's optimization problem. Solve the player's optimization problem with respect to the optimal per-period consumption x1, x2, x3 assuming that he will not waste any of his budget. A player who expects to consume a stream of payments (x1, x2,.., XT) over periods i=1,2,..., T and who evaluates per-period payments using the utility function u(x), will evaluate his discounted sum of future utilities in period t=1 as V(x1, x2,.., XT) = 8t-1 u(xt) Intermediate Microeconomics, Games and Behaviour 5 ECB2VMIE 2023-2024 Where 8 E (0,1) is the player's discount factor, which he uses to discount future utility. a) Consider a player with u(x+) = ln(x+) who needs to allocate a fixed budget K across three periods (i.e. T = 3) and with discount factor 8 = 1. Write down the player's optimization problem. Solve the player's optimization problem with respect to the optimal per-period consumption x1, x2, x3 assuming that he will not waste any of his budget.

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Answer The players optimization problem can be formulated as fol... View the full answer