Answer to Question #81488 in Microeconomics for PIFOU Bianconeri

Question #81488
An agent with an endless lifespan owns exactly one unit of a good which she consumes during her life. The good is perfectly storable and the agent does not acquire any further holdings. Her consumption in period t is given by xt. The lifetime-utility function is given by:

u(x_0,x_1,x_2,…)=∑_(t=0)^∞▒〖β^t ln⁡(x_t ),〗 where by 0 <β< 1.

Calculate the agent’s optimal consumption for each period.
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