Intertemporal Optimality Condition (ρ = r)
The specific optimality condition for intertemporal choice is derived from the general condition that the Marginal Rate of Substitution (MRS) must equal the Marginal Rate of Transformation (MRT). By substituting the expressions for the intertemporal MRS () and MRT (), we get the following:
$1 + \rho = 1 + r$
Subtracting 1 from both sides of the equation simplifies it to:
This result, which equates the subjective discount rate () with the market rate of interest (), represents the point of optimal consumption over time.
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