![]() Write down the budget constraint that the individual faces. ![]() The savings carried over from the first to the second period earn an asset income at the going interest rate r, and we assume that the individual starts the first period without any assets. 5 The individual’s choice is how much of her income to save in the first period of life to consume more in the second period of life. 4 Its inverse, 1 / θ, is the elasticity of intertemporal substitution measuring an individual’s willingness to depart from consumption smoothing to earn higher interest income. The parameter θ measures the risk aversion of the individual (i.e., the concavity of the utility function). ![]() The discount factor is determined by the discount rate, denoted by ρ > 0 via the relationship β = 1 / ( 1 + ρ ). In this formulation, β ∈ ( 0, 1 ) is the discount factor measuring how much weight an individual attaches to future consumption (i.e., it measures impatience).
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