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Economics and Kepler’s Angels Defending the Law of Marginal Utilities

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### Economics and Kepler’s AngelsDefending the Law of Marginal Utilities

Barry Schwartz, Ph.D.

For the Mises Society

March 2011

Law of Marginal Utilities

- Price reflects Value at the Margin of “need” …
- 1862
- Discovered separately by
- Jevons, UK
- Walras, France
- Menger, Austria

Comparison … LMU vs Law of Gravitation

- Kepler’s laws described planets
- Mathematical precision
- Causal connection to local events – UNKNOWN
- Newton’s law
- local (falling apples) large-scale (solar system)
- Same law governs two realms
- Classical Economic laws described supply & demand
- LMU
- local (personal) utilities large scale (market) prices
- LMU deserves to be regarded as a Universal Law

“let’s ask Newton …” @1690’s

- Question:

British treasury officials asked Newton how to price the Pound Sterling …

- Answer:

“ in applied mathematics,

you must describe your unit.”

It took 175 years for economists to define their unit

- LMU dissolved the “Central Paradox”
- 1687 – Philosophiæ Naturalis Principia Mathematica
- 1862 – Law of Marginal Utilities

Challenge: Relating two unlike kinds of valuation

- The personal utility of a good
- e.g. ice-cream
- Scarcity has no intrinsic value, and yet …
- in the Marketplace – scarcity means higher price
- Is a diamond more useful for being rare?

“Central Paradox of Economics”

- Water is essential for life, diamonds are not, so Why are diamonds costlier than water?
- Do personal values contradict market prices?
- Are markets irrational?
- Are preferences un-economical?

The LMU insight

- Error – valuing the whole world’s supply
- Value depends on available supply in relation to needs that remain unsatisfied
- Goods are valued at the margin of subjective scale of utilities
- Last satisfied need
- or first unmet need

How LMU Solves the Water/Diamond Paradox

- Before buying a diamond, many uses for water have already been met
- The 1stuse of a diamond is typically greater than the next(27th ) use for a gallon of water
- In a lifeboat: $ water may > $ diamond

LMU Basic tenets – defining the unit of action

- #1 Two people trading two goods
- Trading is done among “consenting” people
- “Rational” = capable of choosing freely
- #2 Every economizing trader has a personal hierarchy of wants
- Both sides expect more utility after the trade
- (They don’t have to achieve it!)

Newton’s development of units

- F = G*m1*m2 / r2
- F= gravitational force
- Point masses - to define “r” precisely
- Infinitessimals to describe curved motion
- Integral and Differential Calculus
- Two inventors – Newton & Leibniz

Fundamental unit of action

- Two people, two goods, two quantities
- Two actors A1 & A2
- trade an amount q1 of good G1
- for an amount q2 of good G2

Mixed economy sandwich planning mentality

- Does either A or B know about global supply of peanut butter or jelly?
- Can an outside agency determine the right p-b/j ratio for everyone’s lunch?
- Is there enough aggregate demand for jelly without a federal stimulus?

The properties of local individual units

2 masses m1 & m2 at a distance r

2 actors A1 & A2 trade an amount q1of good G1 for an amount q2of good G2

The dynamics

of the system

Moons & planets in Orbit & local motions of pendulums, falling apples

Market Prices, Supply, Demand

‘unit of action’ – 2 systemsgravitation

economics

LMU and free markets

Voluntary trades are sufficient to explain the market laws of Classical Economics

No external or collective influences are needed

No coercion is needed

HELP WANTED

No Angels Need Apply

Angels & Demons

- Kepler’s Angels went unemployed
- But the angels of Economics had allies
- In universities, treasuries, and legislatures
- Many arguments to dismiss or ignore LMU
- Consider one set– challenges to its Universality

Meeting Objections

- Objections (from various books) to the UNIVERSALITY of LMU

“LMU might work for simple trades with only economic goods but …not in real life .”

- Real life economics is more complex
- Groups (corporations) change everything
- There are non economic “Externalities”
- It’s not mathematical enough for science
- People are not rational

1.Real life economics is more complex

- Objection: LMU – just 2 actors, 2 goods – never occurs
- Answer: abstraction
- Trade with many goods & parties can be broken down conceptually …
- Separate trades need not really exist
- Comparison with Gravitation
- There are no cases with 2 isolated masses, and point masses don’t really exist either
- You need to use an abstraction to apply the unit
- Irony – the 3 body problem

2. Groups (corporations) change everything

- Objection: corporations are not like 2 actors
- Answer: use abstractions
- As long as combinations are voluntary, the same abstraction applies …
- Comparison with Gravitation
- Point masses don’t really exist either, but the law still applies to complex planets with moons, and asteroid fields … all are combinations of “point masses”
- You need to use an abstraction to apply the unit

3. There are non economic “Externalities”

- Objection: “not everything reduces to economics and price—there are passions and there are natural disasters too”
- Answer: LMU describes economic action, not all of psychology. Other forces don’t cancel out economic ones.
- Comparison with Gravitation
- Newton’s law does not claim that Gravitation is the only force. The equation refers only to the force due to the effect of gravity.
- Other forces (momentum, magnetic fields) will alter the position of two masses, but once you know mass and distance, you can calculate the gravitational force perfectly well.
- You need to use an abstraction to apply the unit

4. It’s not mathematical enough for science

- Objection: “LMU is too qualitative. Real economists use numbers.”
- Answer:
- Numbers without the right units are empty. LMU is the BASIS for using numbers.
- It’s wrong to throw out a law because it doesn’t deliver predictions in one step. When observed conditions are added, one can make quantitative conclusions.
- Comparison with Gravitation
- Newton’s law was much simpler and less numerical than the Ptolemaic wheels within wheels model of the solar system.
- To apply the law, one must add in specifics of mass, velocity, position and other forces. The law doesn’t generate ellipses in one step.
- You need to use an abstraction to apply the unit
- GIGO

5. People are not rational

- Objection: “Do you really believe that myth about the rational economic man? Not with this crazy economy!”
- Answer:
- The objection uses “rational” to mean “wise, logical” – economists don’t say that man is wise…it’s naïve and irrelevant.
- LMU assumes “rational” in the sense of “capable of choosing”
- LMU requires no specific degree of logical consistency.
- The “myth” rests on a crude equivocation on the term “rational”
- Comparison with Gravitation
- Is there a “myth” of a perfect planetary system with no explosions, collisions, comets or disasters? That has nothing to do with the law of gravitation.

Ceteris Parabis

- All extraneous variations are held constant
- The expression is just
- a form of method of JS Mill’s joint method of agreement and difference
- Applied to economic questions

Bring on the Angels

- Physicists
- were wise enough to test and adopt Newton’s universal laws of gravitation
- Economics
- borrowed the solution to the economic paradox,
- but combined it with “classical” economics – ie NO THEORY OF VALUE AT ALL …
- Neoclassical economics is like …
- F = G*m1*m2 / r2+ Angels

LMU is Scientific because…

- Subject to empirical tests
- Needs to be employed in context of data
- Universal to economic phenomena
- Like Evolution is to biology, Gravitation to physics
- Can be challenged but not dismissed
- Unless there’s a contradiction or contrary prediction
- Or unless there’s a more universal and parsimonious theory to take over

The Austrians

- Austrian economics – adheres to LMU
- Extended LMU to … money, interest, business cycles, employment, and so on…
- Don’t ask whether economists support the free market …
- ask they agree with LMU

Non Marginal Economics?

- Any factor “added to” Marginal Utilities
- Joker in the deck – arbitrary and unscientific
- prevents economists from making accurate predictions
- It’s a step backwards

New Rule

- If you don’t adhere to Marginal Utilities
- Then, you can’t claim to solve the earlier “economic paradox”
- You can’t have angels AND science.
- You have to choose

Conclusions

- LMU got the units right
- It can claim to be scientific
- No other system has made a serious attempt to formulate its units of action
- Newton said he saw further because he “stood on the shoulders of giants”
- He didn’t step in their faces!

Questions?

- Barry Schwartz, Ph.D.

Topics for Questions

- Does LMU deny that Economics is value free “Wertfrei” ?
- Is LMU un-mathematical?
- Is numerical math valid in economics?
- Does using money change anything?
- Does LMU still work if people are irrational?

Topics for Questions

- Does LMU deny that Economics is value free?
- No—values are factored out via ceteris parabis
- The only value is presupposed: trade assumes non aggression
- Is LMU un-mathematical?
- It is mathematical… Ordinal Scale vs Interval and Ratio scales
- Parallel in Psychophysics (Thresholds)
- Is numerical math useful in economics?
- Yes in application to Catallactics - (but only if the units are right!)
- Does using money change anything?
- No – real $ is a commodity
- As a medium, it is an intermediary exchange
- Does LMU still work if people are irrational?
- Rationality determines how much wealth you get, just the way altitude determines how far someone falls – it doesn’t CHANGE the law!

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