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Econ: for comments: GE example with indivisible (dis)utility

  1. Jan 13, 2008 #1


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    Simple Robinson Crusoe (RC) economy.

    There are 2 periods.

    Price level p is given exogenously (e.g. through trade).

    RC is the "capitalist," he earns competitive profits (=0) so he is indifferent between producing and not producing. He doesn't have to eat to live.

    Friday is the laborer, he has a family and a (high) fixed disutility of labor: his disutililty as a function of hours worked H is C1(H) = f + c1 H for f > 0 and c1 > 0.

    If the Friday family survive the first period then in the second period, Friday Jr. will be the laborer. He is much more efficient than his father. His disutility is C2(H) = 0 + c2 H where c2 < c1.

    Friday's total utility is U = Y - C1 = wH - c1 H - f, where Y = income = consumption = wage x hours worked.

    Suppose if Y < C1 then the Fridays cannot survive to the second period, in which case their utility will have become -infinity.

    First-period neoclassical equilibrium is at dC1/dH = c1 = w; suppose c1 = 1 = w. At w = 1, suppose Friday works H = 1 hr. and earns Y = $1.

    Further suppose f = $2 > $1.

    Given these parameters, Friday works 1 hr. At the end of period 1, all Fridays die. In period 2 there is no production. Their total utility over two periods is then -infinity.

    This is an inefficient outcome. Had Friday Jr. survived the first period, production would have folded by a factor of k > 1 in period 2 (i.e., Friday Jr. would have worked many hours more than his father). Total utility over two periods would then have been > 0.

    Ends that can be tied together:

    1. The minimum level of income necessary to survive period 1 can be tied to p.

    2. The linear part of C(H) can be made into a backward-bending labor supply function, c(H), such that there are two equilibrium wage levels, w and W, where W > w. With a downward-sloping labor demand curve, W is an unstable equilibrium but w is stable. If equilibrium selection rule includes "stability," then W would be ruled out. This can further be tied to a low-wage equilibrium that ends up being dynamically inefficient because it does not generate sufficient income to survive the first period.
    Last edited: Jan 14, 2008
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  3. Jan 13, 2008 #2
    I'm still un undergrad, so I haven't taken any grad level micro yet, and therefore I am not the best with this stuff.

    However, it seems that the results of your model may rely mostly on the part I quoted above. It could very well be that in order to maximize the present value of long run profits "the capitalist" would want to increase the productivity in both periods, and would therefore pay the first Friday enough to survive (in order reap the benefits of Friday Jr).

    Lastly, I'm unsure if this model is supposed to "prove" anything, because we can always derive many strange results from theoretical models that we never find occuring in the real world. There are plenty of theoretical economic models which show that free-trade can be bad, however, these models are never supported by the empirical results. The main reason we have models in economics is to derive refutable propositions that we can then go out and test in the real world.
    Last edited by a moderator: Jan 13, 2008
  4. Jan 14, 2008 #3


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    Firstly, I think most of your posts include well-crafted arguments for an undergrad, so keep up the good work.

    Secondly, you are bang-on with the phrase you have quoted from my example. If the "capitalist" believed that he could earn positive profits by supporting the Fridays' livelihood in the first period then he would have, provided that he also has the means to do so. The two problems are: (i) in a truly competitive market, each firms is constrained to zero profits, and therefore do not have "excess profits" to "lend to" the Fridays,* and (ii) a perfectly competitive market also implies that each firm is just indifferent between producing and not producing -- so really, there is no reason for them to care.

    As to your last paragraph, you are correct (and courageous!) to point to testable propositions as the mainstay of meaningful economic science. I have two points:

    First, if I am presented with a formal model that "proves" X implies Y (e.g., "all competitive equilibria are Pareto optimal"), I have the right and responsibility to think about the assumptions "buried" in that model. If any of the assumptions can be violated then the model should be "served" (and taught) with that caveat attached to it.

    Second, there are at least three types of experiments in science. The first type of experiment is the controlled ("lab") experiment that is common in natural sciences. This type of experiment is usually designed by a team of scientists. The second type of experiment is the "natural" or "historical" experiment that is more common to social sciences. This type of experiment isn't consciously designed by scientists, but it occurs naturally or has occurred historically; all the scientist has to do is to collect the data and understand the conditions under which the experiment has occurred. An example is a labor strike in a production plant that shut down that plant for two months. If the orders in another plant producing a similar (but not identical) product has increased during that two-month period, then we can conclude that the two products are good substitutes form the buyers' point of view. Of course, there may be other reasons why the demand at the second plant has increased during that period, and it is the scientist's responsibility to know about and control for these alternative reasons for a surge in demand in the second plant. A formal, mathematical model can help the scientist to "predict" alternative reasons as to why the demand may have surged during that period.

    A third type of experiment is the thought experiment, which is commonly used in theoretical sciences. This type of an experiment is abstract but can be quite useful. For example, it can be and has been used to challenge or refute a theory, by discovering an internal contradiction (inconsistency) or an absurd (unrealistic) axiom. If a theoretical model that starts with the assumption "a planet is flat," and concludes "the planet cannot have more than one tectonic plate," then its conclusion is testable, but pointless. It is just a waste of time to take it seriously and try to measure the number of tectonic plates on any planet. It is not that the theory doesn't have testable predictions, but it is too simple a theory, and hardly applicable even as an approximation. Time would be spent more efficiently if one replaces the assumption "flat" with "spherical," then show (through mathematical modeling) that a spherical planet can accommodate multiple tectonic plates. Now, unless and until a geologist collects underwater sonar data and painfully turns those data into visual maps, the second theory is not tested, and it remains hypothetical. But what the second theory accomplishes, even untested, is to show that the first theory is not a particularly useful theory, because it is not very general at all. This is a somewhat extreme example of a thought experiment, but deliberately so because it makes the point clearly.
    *One way for the capitalist to subsidize the labor in the first period is to sell part of his capital. This assumes that the capital is "fungible," i.e. at the very least, not specialized (and can be sold for a positive price). It also assumes certain conditions apply to the production process.
    Last edited: Jan 14, 2008
  5. Jan 14, 2008 #4
    Thanks a lot! I want to get a PhD in Economics, and I hope to start a program in September of 2009. It sounds like you are (or maybe used to be) a grad student in Economics. What degree (Masters or PhD)? What school? I'm guessing it's somewhere in Europe, right?

    I see what you're saying, and these are good points.

    These are also good points, and it seems to me that good Economists (whether American, European, or any other Nationality) try to understand and teach models in this way.

    Yeah, I used to plan on majoring in Psychology, so I've taken many Psychology classes. Psychology mainly uses experiments to test their hypotheses. I wish they would start doing more regressions though because I don't know the degree to which some of their lab findings (under very controlled conditions) will generalize to the real world. One reason they might not run regression analyses is because it would appear to be very difficult with the subjects and specific variables they study.

    How do you feel about Economists who are starting to use experiments to test hypotheses? You probably already know this, but Vernon Smith won the Nobel Prize in Economic Sciences a few years back for his work on Experimental Economics. I didn't know a lot about the field, nor Dr. Smith, until I listened to the podcast below. It's very interesting and you should listen to it. Dr. Smith is a lot more interesting and entertaining then I thought he'd be. He also has a pretty big critique of a specific thing still taught in Economics, that is not supported in his experiments. Namely, that you need a large number of buyers and sellers in order for prices to reach the equilibrium level (he spends a few minutes talking about this, and it's pretty interesting).

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