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Figure: Julia's Borrowing Decision with Optimal and Suboptimal Choices
This diagram illustrates Julia's intertemporal consumption choices, plotting 'consumption now' against 'consumption later' in dollars. Her feasible frontier, at a 10% interest rate, is a straight line connecting the points (0, 100) and (91, 0), and it passes through the consumption bundles E (58, 36) and F. The diagram features four convex indifference curves. The optimal choice is at point E, where an indifference curve is tangent to the feasible frontier, satisfying the condition that the Marginal Rate of Substitution (MRS) equals the Marginal Rate of Transformation (MRT). Point F, which has lower present consumption and higher future consumption than E, represents a suboptimal choice, as it lies on an intersecting, lower indifference curve. Another even lower indifference curve also intersects the frontier, while a fourth, higher indifference curve is unattainable as it lies entirely above the frontier.
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Incomplete Derivation of the Optimality Condition
Figure: Julia's Borrowing Decision with Optimal and Suboptimal Choices
Optimality Condition for Intertemporal Choice: MRS = MRT
Diagram of Julia's Optimal Choice at a 10% Interest Rate
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The Rationale for Tangency in Consumption Choice