Trade-Offs Involving Time and Risk in Economics
These are my notes and thoughts on trade-offs involving time and risk in economics.
Interest is the payment received for temporarily giving up the use of money. Economists have developed tools to calculate the present value of payments received at different points in the future. Economists have developed tools to calculate the value of risky payments.
Most decisions have costs and benefits that occur at different times. Other activities are also associated with up-front costs and delayed benefits. In general, almost all investments have risky returns.
The key variable that summarizes an intertemporal transformation of money is the interest payment. The amount of an original investment is referred to as principal. Interest is the payment received for temporarily giving up the use of one’s money.
The sum of the principal and interest is known as future value.
\[ (1 + r) * 100 \]
If you are collecting interest for multiple years, it is called compound interest. The compound interest equation looks like:
\[ (1 + r)^{T} * (Principal) \]
In this equation, r is the interest rate and T is the number of years that the investment lasts. To derive the compound interest equation, we assume that none of your interest payments are being withdrawn along the way. So, you earn interest on past interest payments.
Making a deposit effectively transfers spending from the present to the future. You deposit money now, and you withdraw it in the future.
The present value of a future payment is the amount of money that would need to be invested today to produce that future payment. Economists say that the present value is the discounted value of the future payment.
Discounting brings back money to the present and involves a reduction in magnitude, compounding takes money into the future and involves an increase in magnitude.
Economists say that this offer has a negative net present value. The net present value of an investment is the present value of the benefits minus the present value of the costs. A positive net present value represents
The present value concepts are useful tools, because many economic opportunities generate complex streams of future payments. We can now collapse all those future payments to a single number-the net present value of the project.
Net present value is one of the most important tools in economics and is universally used by businesses and governments to decide which projects to implement.
We just showed you how to discount future monetary payments to calculate a present value. We can also discount other future activities.
Suppose there is some future activity that will generate pleasure or some other form of well-being. Suppose that this benefit is not money. Economists refer to general well-being as utility. To make future utility comparable to current utility, we need to multiply the future utility by a factor less than 1. In general, this won’t be exactly the same factor that we used for monetary payments. However, both the factors that multiplicatively discount future monetary payments and the factors that multiplicatively discount future utility are less than 1.
Setting discount weights for activities is kind of arbitrary, but the process is to illustrate a point of how the process goes. The greater your discount weight-the more highly you weigh things that happen in the future-the more your current decisions are driven by the future consequences of those decisions.
Most economists do not have a view on what discount weights you should have. The discount weights reflect your tastes. If you sharply devalue things that occur in the future, you have low future discount weights. If you care about the future as much as the present, you have future discount weights that are close to 1.
To an economist, risk exists when outcomes are not known with certainty in advance. Risk can even exist if all possible outcomes are good outcomes. If something is risky, then it is said to have a component that is random.
A probability is the frequency with which something occurs. The probability that one of N particular numbers comes up is N/100.
When two outcomes are independent, knowing about one outcome does not help you predict the other outcome.
Now that you have had an introduction to probabilities, we can put these ideas to work. We are going to calculate an expected value, which is the sum of all possible outcomes or values, each weighted by its probability of occurring.
Empirical evidence reveals that many people actually are extremely averse to the chance of a small financial loss and are therefore willing to buy expensive insurance to reduce the risk of such losses. Loss aversion is the idea that people psychologically weight a loss much more heavily they they psychologically weight a gain.
Loss aversion is one important example of a risk preference. In general, economists distinguish three categories of risk preference; risk aversion, risk seeking, and risk neutrality.
When people are risk averse, they prefer the investment with the fixed return. When people are risk seeking, they prefer the investment with the risky return. When people are risk neutral, they don’t care about the level of risk and are therefore indifferent between the two investments. Thousands of empirical studies have shown that people are risk averse in most situations.
Most decisions have benefits and costs that occur at different times. To optimize, economic agents need to translate all benefits and costs into a single time period, so they can be compared.
Interest is the payment received for temporarily giving up the use of money. The present value of a future payment is the amount of money that would need to be invested today to produce that future payment. The net present value of a project is the present value of the benefit minus the present value of the costs.
Utility is a measure of satisfaction or well-being. Utils are individual units of utility. A discount weight multiplies delayed utils to translate them into current utils.
Risk means that some of the costs and benefits are not fixed in advance. A probability is the frequency with which something occurs. For example, a probability of 0.12 means that the event will happen 12 percent of the time on average. An expected value is a probability-weighted value.
Loss aversion is the property that people psychologically weight a loss much more heavily then they psychologically weight a gain. If two investments have the same expected return, but one investment has a fixed return and the other investment has a risky return, people with risk aversion prefer the investment with the fixed return.