5 ms·

Consumption smoothing is a perfectly valid use of debt. Suppose I have utility = log(consumption), but my income is volatile. If I have 1 income in year 1 but

Consumption smoothing is a perfectly valid use of debt. Suppose I have utility = log(consumption), but my income is volatile. If I have 1 income in year 1 but 10 income in year 2, and use no credit, my utility is log(1)+log(10) = 2.3. If I use credit, I can have utility log(5.5 / (1+r)), with r the interest rate. At 10% interest, that's 3.2. At 20% interest that's 3.0. At 50% interest that's 2.6. So even at 50% interest I'm increasing my utility by 10% due to the use of credit.

navait 11y ago
While that's a valid point, the parent was speaking in generalities across most people - given that most people have consistent incomes from wages, do they really need consumption smoothing?
carlob 11y ago
Correct, but a bit misleading. You're taking a person that has income that increases tenfold over a year. For most people the rate of increase of income is smaller than credit card interest rates, and you can really justify high interest rates when you assume that you're going to make a lot of money next year, but then again Steinbeck said that most Americans think of themselves as temporarily embarrassed millionaires :)
- yummyfajitas 11y ago
  Probably "year" is the wrong time period, but lots of people have very volatile income. A consultant can easily have 10x variance in income from month to month. A musician or actor might have 0 gigs one month and 5 gigs the next. Shortening the time period just lowers the financing costs.
  - carlob 11y ago
    True, but still how many broke musicians and actors should be considering this month's zero income a fluctuation and get into credit card debt and how many should just be more conservative with their spending?
    - yummyfajitas 11y ago
      If you look at my example, the person with peak income of $10 spent a bit under $5.5/month. Both time periods were "fluctuations" from his average income of $5.5.
      - carlob 11y ago
        Yeah but the first one was 1 the second was 10, not the other way around. After one month at 1 how do you know you're going to average out at 5.5?
cperciva 11y ago
If I use credit, I can have utility log(5.5 / (1+r)), with r the interest rate. At 10% interest, that's 3.2. At 20% interest that's 3.0. At 50% interest that's 2.6. Correct idea, incorrect math. The optimum is found with (11+r)/(2 + 2r) consumption in year 1 and (11+r)/2 consumption in year 2, for a total utility of 2 log(11+r) - 2 log(2) - log(1+r); at (10%, 20%, 50%) interest rates this yields (3.33, 3.26, 3.09) total utility.
- yummyfajitas 11y ago
  Good catch, I wildly oversimplified. That's what I get for doing arithmetic before coffee. Key idea is that since utility is concave, smoothing it out is a win. Now just trade off the gains from smoothing against the losses from financing, and you are golden.
  - infinite8s 11y ago
    Why is utility modeled concavely?
    - nordsieck 11y ago
      https://tgmstat.wordpress.com/2014/01/22/declining-marginal-utility-and-the-logarithmic-utility-function/ https://tgmstat.wordpress.com/2014/01/22/declining-marginal-...
    - TJSomething 11y ago
      Due to the Law of diminishing marginal utility.
    - yummyfajitas 11y ago
      My utility from eating (in one time period) $800 worth of food is less than 2 x utility of eating $400 worth of food. Doubling my consumption doesn't double my happiness. Concavity is a way of formalizing this intuition; it means, roughly speaking, that f(2x) <= 2f(x). Econ uses log(x) as a simple model, but the same idea would apply to any convex function albeit with different arithmetic.
_yosefk 11y ago
I suspect that the average person - actually, make it 99.5% of the people - is better off with advice along the lines of "if you can possibly help it, don't get into debt to buy anything that can't be used to make enough money to offset the interest, and be very careful even " then "get into debt as long as the utility offsets the interest." I think so because I doubt that most people (regardless of how good they are at math) can trust their current selves to compare utility from consumption to disutility from having to pay back (meaning that their future self will often disagree strongly with their current self.) This is not to say that someone else should be trusted with decisions about savings and loans other than the saver/borrower (forcing someone to put money into a pension fund on the grounds that they're irrational and then not really paying the pension back is a bit too common for my taste), just that "by default, don't get into debt" is good advice. More generally, IMO quite often clever utilitarian maximization works worse than simple rules designed to keep you out of trouble first, and seek "utility" later. (I guess I don't quite believe in people being utility-seeking machines, not to mention ones having stable preferences, nor do I believe that a person is truly better off having achieved more utility per unit of time.) I realize it's not a satisfactory argument, of course, if one does believe in utility maximization as a good way to think about these things, and I really wish I could back this up so it's more than a hunch...
imgabe 11y ago
In the scenario where you can predict with certainty that your income will increase by tenfold in one year, sure, that's rational. That is not a realistic situation for most people.

navait 11y ago

While that's a valid point, the parent was speaking in generalities across most people - given that most people have consistent incomes from wages, do they really need consumption smoothing?

carlob 11y ago

Correct, but a bit misleading. You're taking a person that has income that increases tenfold over a year. For most people the rate of increase of income is smaller than credit card interest rates, and you can really justify high interest rates when you assume that you're going to make a lot of money next year, but then again Steinbeck said that most Americans think of themselves as temporarily embarrassed millionaires :)

yummyfajitas 11y ago
Probably "year" is the wrong time period, but lots of people have very volatile income. A consultant can easily have 10x variance in income from month to month. A musician or actor might have 0 gigs one month and 5 gigs the next. Shortening the time period just lowers the financing costs.
- carlob 11y ago
  True, but still how many broke musicians and actors should be considering this month's zero income a fluctuation and get into credit card debt and how many should just be more conservative with their spending?
  - yummyfajitas 11y ago
    If you look at my example, the person with peak income of $10 spent a bit under $5.5/month. Both time periods were "fluctuations" from his average income of $5.5.
    - carlob 11y ago
      Yeah but the first one was 1 the second was 10, not the other way around. After one month at 1 how do you know you're going to average out at 5.5?

cperciva 11y ago

If I use credit, I can have utility log(5.5 / (1+r)), with r the interest rate. At 10% interest, that's 3.2. At 20% interest that's 3.0. At 50% interest that's 2.6. Correct idea, incorrect math. The optimum is found with (11+r)/(2 + 2r) consumption in year 1 and (11+r)/2 consumption in year 2, for a total utility of 2 log(11+r) - 2 log(2) - log(1+r); at (10%, 20%, 50%) interest rates this yields (3.33, 3.26, 3.09) total utility.

yummyfajitas 11y ago
Good catch, I wildly oversimplified. That's what I get for doing arithmetic before coffee. Key idea is that since utility is concave, smoothing it out is a win. Now just trade off the gains from smoothing against the losses from financing, and you are golden.
- infinite8s 11y ago
  Why is utility modeled concavely?
  - nordsieck 11y ago
    https://tgmstat.wordpress.com/2014/01/22/declining-marginal-utility-and-the-logarithmic-utility-function/ https://tgmstat.wordpress.com/2014/01/22/declining-marginal-...
  - TJSomething 11y ago
    Due to the Law of diminishing marginal utility.
  - yummyfajitas 11y ago
    My utility from eating (in one time period) $800 worth of food is less than 2 x utility of eating $400 worth of food. Doubling my consumption doesn't double my happiness. Concavity is a way of formalizing this intuition; it means, roughly speaking, that f(2x) <= 2f(x). Econ uses log(x) as a simple model, but the same idea would apply to any convex function albeit with different arithmetic.

_yosefk 11y ago

I suspect that the average person - actually, make it 99.5% of the people - is better off with advice along the lines of "if you can possibly help it, don't get into debt to buy anything that can't be used to make enough money to offset the interest, and be very careful even " then "get into debt as long as the utility offsets the interest." I think so because I doubt that most people (regardless of how good they are at math) can trust their current selves to compare utility from consumption to disutility from having to pay back (meaning that their future self will often disagree strongly with their current self.) This is not to say that someone else should be trusted with decisions about savings and loans other than the saver/borrower (forcing someone to put money into a pension fund on the grounds that they're irrational and then not really paying the pension back is a bit too common for my taste), just that "by default, don't get into debt" is good advice. More generally, IMO quite often clever utilitarian maximization works worse than simple rules designed to keep you out of trouble first, and seek "utility" later. (I guess I don't quite believe in people being utility-seeking machines, not to mention ones having stable preferences, nor do I believe that a person is truly better off having achieved more utility per unit of time.) I realize it's not a satisfactory argument, of course, if one does believe in utility maximization as a good way to think about these things, and I really wish I could back this up so it's more than a hunch...

imgabe 11y ago

In the scenario where you can predict with certainty that your income will increase by tenfold in one year, sure, that's rational. That is not a realistic situation for most people.