7. Interest rates and saving with exponential period utility. A country's representative individual has the exponential period

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7. Interest rates and saving with exponential period utility. A country's representative individual has the exponential period utility function

$$ u(C) = -\gamma \exp(-C/\gamma) $$

(\( \gamma > 0 \)) and maximizes \( U_1 = u(C_1) + \beta u(C_2) \) subject to

$$ C_1 + R C_2 = Y_1 + R Y_2 = W_1 $$

[where \( R = 1/(1 + r) \)].

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