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Consider an economy in which a decision maker faces the following economic problem. In each period the economy has an exogenous endowment y_t. This is

Consider an economy in which a decision maker faces the following economic problem. In each period the economy has an exogenous endowment y_t. This is deterministic but can potentially vary over time. The decision maker has the following preferences: \sum_{t=0}^\infty \beta^t \ln(c_t) where \beta < 1 is the discount factor and c_t is consumption. The endowment may be consumed or stored for the future. Let k_t denotes the stored endowment at the beginning of period t and notice that it evolves as: k_{t+1} = (k_t + y_t - c_t)(1-\delta). Notice that the amount stored cannot be negative, so k_{t+1} \ge 0 in each period and state. Assume k_0 = 0. Assume that the endowment is constant over time, so y_t = y. Describe in word the nature of the trade-off faced by the decision maker

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