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Optimal Intertemporal Choice as Tangency Point
Discount Rate (Subjective Discount Rate)
Optimality Condition for Intertemporal Choice: MRS = MRT
To determine the optimal borrowing amount, an individual aims to reach their highest possible indifference curve while staying within their feasible frontier. This optimal point occurs where the indifference curve is tangent to the feasible frontier. At this point of tangency, the slope of the indifference curve (the Marginal Rate of Substitution, or MRS) is equal to the slope of the feasible frontier (the Marginal Rate of Transformation, or MRT). This fundamental condition is expressed by the formula:
\begin{align} \text{slope of the indifference curve (MRS) } = \text{ slope of the feasible frontier (MRT)} \end{align}
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Ch.9 Lenders and borrowers and differences in wealth - The Economy 2.0 Microeconomics @ CORE Econ
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Optimality Condition for Intertemporal Choice: MRS = MRT
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An individual's 'discount rate' reflects how much they value receiving something now compared to receiving it in the future. A high rate indicates a strong preference for the present, while a low rate indicates a willingness to wait for a future benefit. Match each behavior to the discount rate it most likely represents.
In the context of intertemporal choice, a person with a high subjective discount rate is necessarily making an irrational or poor financial decision.
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The economic term for the measure of an individual's impatience, which quantifies their preference for receiving a good or service now rather than later, is known as the ____.
An individual's personal valuation of receiving a benefit now versus in the future can be described by their subjective discount rate. A lower rate indicates more 'patience,' or a greater willingness to wait for a future reward. Which of the following individuals is demonstrating behavior consistent with the lowest subjective discount rate?
An individual with a subjective discount rate of zero would be indifferent between receiving a specific sum of money today and receiving the exact same sum of money one year from now, assuming no risk or changes in purchasing power.
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Figure: The Effect of a Higher Interest Rate on Julia's Optimal Choice
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An individual is deciding how to allocate their consumption between today and one year from now. At their current consumption plan, their personal willingness to trade future consumption for present consumption is 1.15 (meaning they are willing to give up 1.00 of present consumption). The market interest rate allows them to trade 1.08 of future consumption. To improve their overall well-being (utility), what action should this individual take?
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An individual makes choices about consumption in the present versus consumption in the future. Match each key concept related to this decision-making process with its correct description.
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Consider an individual deciding how to allocate consumption between the present and the future. If this person's subjective willingness to trade one unit of future consumption for one unit of present consumption is lower than the trade-off offered by the market interest rate, they have achieved their most preferred (optimal) balance of consumption over time.
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For an individual to achieve their optimal consumption plan over time, their subjective discount rate—the measure of their personal preference for present consumption over future consumption—must be equal to the market ________.
Arrange the following steps in the logical order that describes the process of finding an individual's optimal plan for consumption over two time periods (present and future).
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An individual is allocating their income between consumption now and consumption one year from now. At their current consumption level, they are personally willing to give up 1.00 of present consumption. The annual market interest rate is 7%. Which statement correctly analyzes this individual's situation?
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