Pur Autre Vie

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Sunday, February 22, 2015

Economics: Modeling Individuals

This is part of a series of posts on economics.  Unlike my typical posts, these posts are dynamic—I'm going to come back and edit them as my thoughts develop.  I am basically "thinking out loud."  I am trying to fit things together in a modular way, so that each piece stands on its own analytically.  But no promises.

We will model people as economic agents who engage in the following market activities:  working (selling labor in the labor market), consuming (buying goods and services), borrowing or saving (either buying or selling financial products), and investing (that is, spending money in anticipation of generating future wealth, but doing so outside the financial markets).  The difference between saving and investing can be illustrated with this example:  a saver might take $1,000 and put it in a bank account for future consumption, while an investor might take $1,000 and buy a solar panel so that he can enjoy cheaper electricity in the future.  Both are spending money to increase future consumption, but only one is doing so through the financial markets.  This is a non-standard use of the term "investing," and so I will try to be careful to make myself clear when using the term.

We are going to model people as though they are motivated to maximize their consumption over time.  However, we will be open to the possibility that people care more about present consumption than about future consumption, and more about near-future consumption than distant-future consumption.  We'll call this the consumption discount rate:  the rate at which future consumption is discounted in the individual's utility function.  We'll allow people to have different consumption discount rates.  We will also distinguish between the consumption discount rate and the effective discount rate, which may take into account other factors such as the market interest rate and the rate of inflation or deflation.  That will be a topic for another segment.  The consumption discount rate will vary between 0 and 1, with 0 indicating no preference for present spending, and 1 indicating no expected utility from future consumption.  You can determine the utility from a unit of consumption in the future by multiplying it by:


where d is the consumption discount rate and n is the number of time periods between now and when the consumption occurs.  (For current consumption, n = 0 and so consumption is not discounted at all.)

We will also allow for the possibility that people experience diminishing marginal utility from consumption at any given time.  This is reflected in a variable that on the high end approaches 1 and on the low end asymptotically approaches 0, as in the following equation:

U = Cm

where U represents utility, C represents consumption, and m represents the marginal utility variable.

So for instance, imagine that a person has $1,000 at time 0 and no expectation of working in the future.  This person might seek to transmit some of her spending power to the future (by saving or investing), even though future consumption is (other things being equal) less valuable than present consumption.  This is because (for instance) two instances of $500 consumption are collectively worth more utility than one instance of $1,000 consumption (although you would have to discount the second $500 round of consumption if she has a nonzero consumption discount rate).

In the example I've just given, the diminishing marginal utility of consumption is pushing in one direction (saving rather than consuming, so as to shift consumption to a time when its level is lower and its marginal value is therefore higher), while the consumption discount rate is pushing in the other (consuming rather than saving because present consumption is more valuable than future consumption).  It is also possible that both factors will push in the same direction:  for instance, an individual might borrow money and spend it today in the anticipation that she will be wealthier in the future.  In that case the person is increasing utility by shifting consumption toward the present and by shifting consumption toward a time when its level is low and therefore its marginal utility is high.

We will assume that work is unpleasant and people experience disutility from working (or utility from leisure time), so that people have to be paid wages to induce them to work.

Finally we will assume (or really just note) that people will seek the most advantageous means of shifting consumption/spending power from time period to time period.  So when they shift spending power to the future, they will look for financial products or investment opportunities that offer a high expected rate of return, and when they borrow they will look for a low rate of interest.  People who have diminishing marginal utility from consumption are risk-averse and they will also seek a certain degree of safety when saving or investing.  (In other words, someone who gets diminishing marginal utility from consumption is not indifferent between a certain $500 and a 1/2 probability of $1,000, because the first $500 of consumption is more valuable than the second $500.  Someone with no diminishing marginal utility from consumption is risk-neutral and would not generally have a preference between a certain $500 and a 1/2 probability of $1,000.)  So in other words people maximize their utility from borrowing, saving, or investing taking into account both the rate of return (or rate of interest) and the level of riskiness.


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