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Formula for the Discount Rate (ρ)
An individual's discount rate, symbolized by the Greek letter rho (ρ), is calculated based on the slope of their indifference curve for present and future consumption. The formula is: ρ = (slope of the indifference curve) - 1. Note that the absolute value of the slope is used in this calculation.
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Ch.9 Lenders and borrowers and differences in wealth - The Economy 2.0 Microeconomics @ CORE Econ
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Formula for the Discount Rate (ρ)
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Example of Calculating Present Value
Optimality Condition for Intertemporal Choice: MRS = MRT
Two individuals, Sam and Maria, are each offered a choice between receiving $500 today or a guaranteed payment of $550 in one year. Sam chooses to receive the $500 today, while Maria chooses to wait for the $550 in one year. Based solely on this information, what can be inferred about their individual valuations of present versus future consumption?
A person's 'subjective discount rate' reflects how much they value having something now compared to having it in the future. A high discount rate indicates a strong preference for present benefits over future ones. Which of the following individuals is demonstrating behavior consistent with a high discount rate?
Financial Decision-Making and Personal Valuation
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.
Explaining Divergent Choices
Evaluating Personal Financial Philosophies
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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An individual's indifference curve, which illustrates their trade-offs between consumption today and consumption in the future, has a slope of -1.05 at their current consumption level. Based on this information, what is this individual's discount rate (ρ)?
An individual who is perfectly patient, valuing an extra unit of consumption in the future exactly the same as an extra unit of consumption today, would have an indifference curve with a slope of -1 at their current point of consumption.
Calculating Indifference Curve Slope from Discount Rate
Calculating a Personal Discount Rate
An individual's trade-off between consumption today and consumption in the future can be visualized with a curve. The slope of this curve at a given point indicates the individual's impatience. The personal discount rate (ρ) is calculated from this slope. Match each given slope to the correct discount rate (ρ) that would be calculated from it.
An individual's personal discount rate (ρ) is calculated by taking the absolute value of the slope of their indifference curve for present and future consumption and subtracting ____.
Comparing Patience Levels Using Indifference Curves
An economist is studying the saving habits of two individuals, Sam and Maria. The slope of Sam's indifference curve, which represents his trade-offs between consumption today and consumption in the future, is -1.15. The slope of Maria's indifference curve for the same trade-off is -1.04. Based on this information, which of the following statements is correct?
An economist wants to determine an individual's personal discount rate (ρ) by examining their preferences for consumption now versus in the future. The economist has identified the slope of the individual's indifference curve at their current consumption bundle. Arrange the following steps in the correct order to calculate the discount rate.
An economist observes that at their current consumption level, an individual is willing to trade 1.08 units of future consumption for exactly 1 unit of present consumption, remaining equally satisfied. The economist concludes, "This individual has a low preference for immediate gratification and is likely a patient long-term planner." Based on the formula for the personal discount rate (ρ), evaluate the economist's conclusion.
Calculating Indifference Curve Slope from Discount Rate
Calculating a Personal Discount Rate