Onion Eater
Well-Known Member
- Joined
- Jun 28, 2008
- Messages
- 65
At the Physics and Physicists Blog, Pedro J has asked an interesting question regarding Jean-Philippe Bouchaud’s essay, Economics Needs a Scientific Revolution.
I reply that my economic theory is based on three assumptions:
1) One's value scale is totally (linearly) ordered:
i) Transitive; p ≤ q and q ≤ r imply p ≤ r
ii) Reflexive; p ≤ p
iii) Anti-Symmetric; p ≤ q and q ≤ p imply p = q
iv) Total; p ≤ q or q ≤ p
2) Marginal (diminishing) utility, u(s), is such that:
i) It is independent of first-unit demand.
ii) It is negative monotonic; that is, u'(s) < 0.
iii) The integral of u(s) from zero to infinity is finite.
3) First-unit demand conforms to proportionate effect:
i) Value changes each day by a proportion (called 1+εj, with j denoting the day), of the previous day's value.
ii) In the long run, the εj's may be considered random as they are not directly related to each other nor are they uniquely a function of
value.
iii) The εj's are taken from an unspecified distribution with a finite mean and a non-zero, finite variance.
In my Non-Mathematical Explanation of the Axioms, I explain the reasoning behind and the applicability of my three axioms.
Socrates and Hume at Billiards is a simulated dialogue between Socrates and David Hume over a game of billiards in heaven. They are visited by a swami and a physicist, both of whom counsel Socrates on where his billiard ball will go after he hits it with his cue ball. Then, Socrates and Hume contrast these two quotations:
David Hume: "When I see, for instance, a billiard ball moving in a straight line toward another,... may I not conceive that a hundred different events might as well follow from that cause?... All these suppositions are consistent and conceivable. Why then should we give preference to one which is no more consistent or conceivable than the rest?"
Cristobal Young: "Milton Friedman, torchbearer for the ‘free market’, insisted that the realism of background assumptions is not important. ‘In general, the more significant the theory, the more unrealistic the assumptions’. Good theory may well make use of ‘wildly inaccurate’ assumptions, and proceed ‘as if’ the assumptions held true. The purpose of theory is to generate testable implications."
Here I am quoting Cristobal Young’s review of Robert Nelson’s book, Economics as Religion, which JP Bouchard mentions in his paper.
Pedro J asks, “¿What about the great physical principles? For example, conservation of energy happens because you assume your laws of motion are the same today and tomorrow.”
This paper specifically answers Pedro J’s question. I have my hypothetical physicist explain to Socrates and Hume:
“Two of the principle axioms of physics are that momentum and energy are both conserved. If you measure the momentum (mass times velocity) and the energy (mass times velocity squared) of the cue ball before the collision and compare these numbers to the sums of the cue and object balls’ momentum and energy after the collision, then, within this axiomatic system, they must be equal. Thus, you can answer your question by solving two simultaneous equations in two unknowns.”
Socrates then illustrates how these axioms are applied in the simple case of hitting an object ball directly with the cue ball:
Let Vc be the cue ball’s velocity and Vo be the object ball’s velocity. Before the collision, Vc = 10 cm/sec and Vo = 0 cm/sec. So adding up the total momentum and the total energy defines two equations:
Vc + Vo = 10 momentum
Vc^2 + Vo^2 = 100 energy
I then have Socrates claim:
“The identity, Y = C + I + G + X, national income equals consumption plus investment plus government spending plus net exports, is an axiom. How else would you describe such a statement? Economics majors who go on to take an upper-division macroeconomics course will be given another equation, D = M/P, the demand for money equals the stock of money divided by the price level, and another variable, R, the interest rate.”
Hume responds, “I thought upper-division macroeconomics courses were about IS-LM Analysis.”
Socrates replies:
“They are. IS-LM Analysis is a system of two equations in two unknowns, just like the physical system we just discussed, except that the equations are Y = C + I + G + X and D = M/P with unknown quantities, Y, national income, and R, the interest rate.”
So, in answer to Pedro J’s question, we see that physics and economics both employ axioms that are used to set up systems of simultaneous equations which can be solved to answer practical problems.
Zapper Z is wrong when he states, “If and when it doesn't work anymore, we will revise it.” It is impossible for the identity Y = C + I + G + X to “not work” because the terms are defined in a way that it must work. Similarly, physicists are not looking for the conservation of momentum and energy to “not work.” That is just how the concepts are defined.
Of course, some axiomatic systems are more useful than others. I believe that my axioms, stated at the top of this post, are more useful than those of IS-LM Analysis. But I would certainly not deny, as Zapper Z does, that the income identity is not an axiom or that, if we look hard enough, we may someday find that consumption, investment, government spending and net exports do not add up to national income.
Zapper Z, who owns the Physics and Physicists Blog, deleted my reply to Pedro J so, if anybody knows Pedro J, please tell him that I have replied to his query here.
I reply that my economic theory is based on three assumptions:
1) One's value scale is totally (linearly) ordered:
i) Transitive; p ≤ q and q ≤ r imply p ≤ r
ii) Reflexive; p ≤ p
iii) Anti-Symmetric; p ≤ q and q ≤ p imply p = q
iv) Total; p ≤ q or q ≤ p
2) Marginal (diminishing) utility, u(s), is such that:
i) It is independent of first-unit demand.
ii) It is negative monotonic; that is, u'(s) < 0.
iii) The integral of u(s) from zero to infinity is finite.
3) First-unit demand conforms to proportionate effect:
i) Value changes each day by a proportion (called 1+εj, with j denoting the day), of the previous day's value.
ii) In the long run, the εj's may be considered random as they are not directly related to each other nor are they uniquely a function of
value.
iii) The εj's are taken from an unspecified distribution with a finite mean and a non-zero, finite variance.
In my Non-Mathematical Explanation of the Axioms, I explain the reasoning behind and the applicability of my three axioms.
Socrates and Hume at Billiards is a simulated dialogue between Socrates and David Hume over a game of billiards in heaven. They are visited by a swami and a physicist, both of whom counsel Socrates on where his billiard ball will go after he hits it with his cue ball. Then, Socrates and Hume contrast these two quotations:
David Hume: "When I see, for instance, a billiard ball moving in a straight line toward another,... may I not conceive that a hundred different events might as well follow from that cause?... All these suppositions are consistent and conceivable. Why then should we give preference to one which is no more consistent or conceivable than the rest?"
Cristobal Young: "Milton Friedman, torchbearer for the ‘free market’, insisted that the realism of background assumptions is not important. ‘In general, the more significant the theory, the more unrealistic the assumptions’. Good theory may well make use of ‘wildly inaccurate’ assumptions, and proceed ‘as if’ the assumptions held true. The purpose of theory is to generate testable implications."
Here I am quoting Cristobal Young’s review of Robert Nelson’s book, Economics as Religion, which JP Bouchard mentions in his paper.
Pedro J asks, “¿What about the great physical principles? For example, conservation of energy happens because you assume your laws of motion are the same today and tomorrow.”
This paper specifically answers Pedro J’s question. I have my hypothetical physicist explain to Socrates and Hume:
“Two of the principle axioms of physics are that momentum and energy are both conserved. If you measure the momentum (mass times velocity) and the energy (mass times velocity squared) of the cue ball before the collision and compare these numbers to the sums of the cue and object balls’ momentum and energy after the collision, then, within this axiomatic system, they must be equal. Thus, you can answer your question by solving two simultaneous equations in two unknowns.”
Socrates then illustrates how these axioms are applied in the simple case of hitting an object ball directly with the cue ball:
Let Vc be the cue ball’s velocity and Vo be the object ball’s velocity. Before the collision, Vc = 10 cm/sec and Vo = 0 cm/sec. So adding up the total momentum and the total energy defines two equations:
Vc + Vo = 10 momentum
Vc^2 + Vo^2 = 100 energy
I then have Socrates claim:
“The identity, Y = C + I + G + X, national income equals consumption plus investment plus government spending plus net exports, is an axiom. How else would you describe such a statement? Economics majors who go on to take an upper-division macroeconomics course will be given another equation, D = M/P, the demand for money equals the stock of money divided by the price level, and another variable, R, the interest rate.”
Hume responds, “I thought upper-division macroeconomics courses were about IS-LM Analysis.”
Socrates replies:
“They are. IS-LM Analysis is a system of two equations in two unknowns, just like the physical system we just discussed, except that the equations are Y = C + I + G + X and D = M/P with unknown quantities, Y, national income, and R, the interest rate.”
So, in answer to Pedro J’s question, we see that physics and economics both employ axioms that are used to set up systems of simultaneous equations which can be solved to answer practical problems.
Zapper Z is wrong when he states, “If and when it doesn't work anymore, we will revise it.” It is impossible for the identity Y = C + I + G + X to “not work” because the terms are defined in a way that it must work. Similarly, physicists are not looking for the conservation of momentum and energy to “not work.” That is just how the concepts are defined.
Of course, some axiomatic systems are more useful than others. I believe that my axioms, stated at the top of this post, are more useful than those of IS-LM Analysis. But I would certainly not deny, as Zapper Z does, that the income identity is not an axiom or that, if we look hard enough, we may someday find that consumption, investment, government spending and net exports do not add up to national income.
Zapper Z, who owns the Physics and Physicists Blog, deleted my reply to Pedro J so, if anybody knows Pedro J, please tell him that I have replied to his query here.