Consider an optimal saving problem under uncertainty in a two-period economy, t = 0 and t...

 

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Consider an optimal saving problem under uncertainty in a two-period economy, t = 0 and t = 1. Assume the consumer with initial wealth Yo has Bernoulli utility of the logarithmic form, and the consumer is trying to maximize expected utility of total consumptions at both periods: In(co) + BE[In(₁)], where ß is the time discount factor that measures how patient the consumer is. Suppose in this economy, there exists only one saving device, a stock, which provides return re in good state that occurs with probability and return TB in a bad state that occurs with probability 1 - T. Then what is the optimal amount of saving in stock for this consumer? How does the optimal saving depend on 7, and can we generalize this dependency property to any Bernoulli utility function? Consider an optimal saving problem under uncertainty in a two-period economy, t = 0 and t = 1. Assume the consumer with initial wealth Yo has Bernoulli utility of the logarithmic form, and the consumer is trying to maximize expected utility of total consumptions at both periods: In(co) + BE[In(₁)], where ß is the time discount factor that measures how patient the consumer is. Suppose in this economy, there exists only one saving device, a stock, which provides return re in good state that occurs with probability and return TB in a bad state that occurs with probability 1 - T. Then what is the optimal amount of saving in stock for this consumer? How does the optimal saving depend on 7, and can we generalize this dependency property to any Bernoulli utility function?

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In Yos 3 Ins1ra 17 Ins1TB The firstorder condition simplifies to 1 Yo 8 which l... View the full answer