Question

Consider the role of discount rates in problems involving long time horizons such as climate change. Suppose that a particular emissions abatement strategy would result in a \(\$ 500\) billion reduction in damages 50 years into the future. How would the maximum amount spent now to eliminate those damages change if the discount rate is 2 percent, rather than 10 percent?

Short answer

Answer: The present value of a \(\$ 500\) billion reduction in damages 50 years in the future is approximately \(\$ 183.95\) billion at a 2 percent discount rate and \(\$ 2.17\) billion at a 10 percent discount rate. This shows that the chosen discount rate greatly affects the present value of future damages. A lower discount rate places more importance on the future, while a higher discount rate decreases the urgency of addressing long-term problems like climate change.

Step-by-step solution

Convert discount rates to decimals

In this step, we convert the discount rates from percentages to decimals. For 2 percent: Discount rate = 2/100 = 0.02 For 10 percent: Discount rate = 10/100 = 0.10

Calculate present value for 2 percent discount rate

Now, we will use the present value formula to calculate the present value of the \(\$ 500\) billion reduction in damages 50 years in the future at a 2 percent discount rate. \( PV = \frac{500\text{ billion}}{(1+0.02)^{50}}\) \( PV \approx \$ 183.95\) billion

Calculate present value for 10 percent discount rate

Next, we will calculate the present value of the \(\$ 500\) billion reduction in damages 50 years in the future at a 10 percent discount rate. \( PV = \frac{500\text{ billion}}{(1+0.10)^{50}}\) \( PV \approx \$ 2.17\) billion

Compare present values at different discount rates

Finally, let's compare the present values calculated for the 2 percent and 10 percent discount rates. Present value with 2 percent discount rate: \(\$ 183.95\) billion Present value with 10 percent discount rate: \(\$ 2.17\) billion From the comparison, we can see that the amount spent now to eliminate future damages would vary greatly depending on the discount rate used. With a lower discount rate of 2 percent, the present value of the damages is significantly higher, which means more importance is placed on the future. On the other hand, with a higher discount rate of 10 percent, the present value of the damages is much smaller, thus decreasing the urgency of addressing the problem.

Key concepts

Present Value Calculation

Understanding the present value calculation is crucial in economic decision-making because it allows us to compare the value of money in the future to the value of money today. This is particularly helpful when assessing the costs and benefits of long-term projects, like those related to climate change mitigation strategies.

Let's dive into the steps provided in the textbook solution. To calculate the present value (PV), we must first convert the discount rate to a decimal. The formula for the present value is \( PV = \frac{FV}{(1+r)^t} \), where \( FV \) represents the future value, \( r \) is the discount rate, and \( t \) is the number of years in the future. For a \( USD 500 \) billion reduction in damages that would occur 50 years from now, the present value is significantly higher when calculated with a 2% discount rate, about \( USD 183.95 \) billion, compared to a 10% discount rate, which results in a present value of roughly \( USD 2.17 \) billion.

Why is this difference so critical? It reflects the importance that we place on the future. A lower discount rate indicates a stronger preference for future monetary values, implying a greater willingness to invest now for future benefits.

Climate Change Economics

Climate change economics engages with the monetary implications of climate-related actions and their long-term impact on economies. The textbook example demonstrates that the choice of discount rate can greatly affect the perceived value of emissions abatement strategies and efforts to reduce future damage.

When confronting the monumental task of managing climate change, governments and organizations must consider how much to invest in mitigation today to avoid potential damages later. If a society applies a low discount rate, this indicates it values the future highly and may be more inclined to pay a steeper upfront cost for mitigation measures, seeking to reduce future risk. Conversely, a high discount rate undervalues the future, potentially leading to underinvestment in mitigating climate harm and risking greater long-term costs and damage.

This exercise highlights the impact of discount rates on policy decisions. By comparing the calculated present values using different rates, we can see how discount rates shape our approach to addressing environmental issues. An informed choice on the discount rate can facilitate responsible economic strategies that weigh immediate costs against the long-term welfare of future generations.

Time Value of Money

The time value of money is a principle suggesting that a specific amount of money today is worth more than the same amount in the future due to its potential earning capacity. This concept underpins the discussion on the present value calculation in our textbook example concerning environmental economics.

The principle rests on the potential of money to grow through investment over time. In essence, having money now offers opportunities that won't be available should one opt to receive the same amount in the future. When we calculate that a \( USD 500 \) billion damage reduction in 50 years only equals a fraction of that sum in today's terms, using a 10% discount rate, this fundamentally reflects the opportunity cost of locking away resources that could otherwise be invested for growth.

Bringing this principle into the realm of climate change economics, when decision-makers use a higher discount rate, they essentially express a preference for current economic opportunities over long-term environmental sustainability. Deciding on the appropriate discount rate involves weighing the time value of money against the ethical and practical considerations of sustainable development and the well-being of future generations. The stark contrast between present values at 2% and 10% discount rates clearly demonstrates the sensitivity of long-term environmental investments to temporal and monetary perceptions.