Thermodynamics of Economy?

[ipaps]

Let me put it this way, just for fun.

A variable e := production efficient, is changed from a lower value to a higher, causing a closed economic system to shift into a equilibrium with high jobless rate.

In order to bring the system to a new equilibrium with low jobless rate we can change e back to it's previous lower value, but that sounds stupid.

We can also change work time per week per person to a lower value because, assume employers prefer full time employees, number of man needed = total work hour*man needed / total hours per man. But this is not really a must, we can also start constructing the colony on moon.

The fun point is the resemblance of ideas in economics to that in thermodynamics.

The assumption that a market, if left untouched, will work it's way to the highest efficiency in production and distribution is a statement that there exists one and only one state of equilibrium a given economy system will approach. This is what the second law of thermodynamics says about a closed system and that state of equilibrium is said to have the highest entropy.

 

[oldfart]

The fun point is the resemblance of ideas in economics to that in thermodynamics.

The assumption that a market, if left untouched, will work it's way to the highest efficiency in production and distribution is a statement that there exists one and only one state of equilibrium a given economy system will approach. This is what the second law of thermodynamics says about a closed system and that state of equilibrium is said to have the highest entropy.

The crucial question in general equilibrium theory concerns whether a given equilibrium is static or dynamic, stable or unstable, and global or local. Each of these has an analog in physics, but the idea of a unique equilibrium is a special case in both.

Consider a system where the problem is to maximize px ST Ax<=b, x>=0, A being a matrix and b a vector. The solution set of this optimization problem has four possible outcomes:

1. The solution set is the null set, i.e. there is no solution meeting the conditions.

2. The solution is unbounded, i.e. px can be increased within the constraint set to infinity.

3. There is a unique solution for the vector x.

4. There are multiple solutions all of which are within the constraint set and yield the same value for px.

It's called optimization theory (linear programming) and has been the backbone of mathematical economics for the last sixty-five or so years. Historically general equilibrium analysis has been associated with Leon Walras, welfare functions with Vilfredo Pareto, and input-output methods with Wassily Leontieff.

P.S. There are protocols like the original Simplex algorithm that guarantee a solution given enough computing power. It does not require calculus, thus it answers questions without an assumption of continuous twice-differentiable functions. There is a mirror solution that automatically pops out that gives the opportunity cost values for the b vector inputs.

No need to reinvent the wheel.

 

[ipaps]

The fun point is the resemblance of ideas in economics to that in thermodynamics.

The assumption that a market, if left untouched, will work it's way to the highest efficiency in production and distribution is a statement that there exists one and only one state of equilibrium a given economy system will approach. This is what the second law of thermodynamics says about a closed system and that state of equilibrium is said to have the highest entropy.

The crucial question in general equilibrium theory concerns whether a given equilibrium is static or dynamic, stable or unstable, and global or local. Each of these has an analog in physics, but the idea of a unique equilibrium is a special case in both.

Consider a system where the problem is to maximize px ST Ax<=b, x>=0, A being a matrix and b a vector. The solution set of this optimization problem has four possible outcomes:

1. The solution set is the null set, i.e. there is no solution meeting the conditions.

2. The solution is unbounded, i.e. px can be increased within the constraint set to infinity.

3. There is a unique solution for the vector x.

4. There are multiple solutions all of which are within the constraint set and yield the same value for px.

It's called optimization theory (linear programming) and has been the backbone of mathematical economics for the last sixty-five or so years. Historically general equilibrium analysis has been associated with Leon Walras, welfare functions with Vilfredo Pareto, and input-output methods with Wassily Leontieff.

P.S. There are protocols like the original Simplex algorithm that guarantee a solution given enough computing power. It does not require calculus, thus it answers questions without an assumption of continuous twice-differentiable functions. There is a mirror solution that automatically pops out that gives the opportunity cost values for the b vector inputs.

No need to reinvent the wheel.

Thanks for the information.

I may have gotten too literal in the first place.

The idea of free market should probably be giving individuals enough room to optimize themselves. Not really perfectly comfortable, but each is reasonably comfortable himself. Forming a stability that probably also takes the least energy to maintain.

But this idea is probably also ages old, how would I know? Next I'll probably be told to read more. Ok, I'm zipping it.

 

[waltky]

Granny says, "Dat's right - we ain't even seein' the light at the end of the tunnel yet...

US economy may be stuck in slow lane for long run
9 Feb.`14 WASHINGTON (AP) — In the 4½ years since the Great Recession ended, millions of Americans who have gone without jobs or raises have found themselves wondering something about the economic recovery:

Is this as good as it gets? It increasingly looks that way. Two straight weak job reports have raised doubts about economists' predictions of breakout growth in 2014. The global economy is showing signs of slowing — again. Manufacturing has slumped. Fewer people are signing contracts to buy homes. Global stock markets have sunk as anxiety has gripped developing nations. Some long-term trends are equally dispiriting.

The Congressional Budget Office foresees growth picking up through 2016, only to weaken starting in 2017. By the CBO's reckoning, the economy will soon slam into a demographic wall: The vast baby boom generation will retire. Their exodus will shrink the share of Americans who are working, which will hamper the economy's ability to accelerate. At the same time, the government may have to borrow more, raise taxes or cut spending to support Social Security and Medicare for those retirees.

Only a few weeks ago, at least the short-term view looked brighter. Entering 2014, many economists predicted growth would top 3 percent for the first time since 2005. That pace would bring the U.S. economy near its average post-World War II annual growth rate. Some of the expected improvement would come from the government exerting less drag on the economy this year after having slashed spending and raised taxes in 2013. In addition, steady job gains dating back to 2010 should unleash more consumer spending. Each of the 7.8 million jobs that have been added provided income to someone who previously had little or none. It amounts to "adrenaline" for the economy, said Carl Tannenbaum, chief economist for Northern Trust.

And since 70 percent of the economy flows from consumers, their increased spending would be expected to drive stronger hiring and growth. "There is a dividing line between a slow-growth economy that is not satisfactory and above-trend growth with a tide strong enough to lift all the boats and put people back to work," said Chris Rupkey, chief financial economist at Bank of Tokyo-Mitsubishi. "That number is 3 percent." The recovery had appeared to achieve a breakthrough in the final quarter of 2013. The economy grew at an annual pace of 3.2 percent last quarter. Leading the upswing was a 3.3 percent surge in the rate of consumer spending, which had been slack for much of the recovery partly because of high debt loads and stagnant pay. Yet for now, winter storms and freezing temperatures, along with struggles in Europe and Asia, have slowed manufacturing and the pace of hiring.

MORE

 

[percysunshine]

"The fun point is the resemblance of ideas in economics to that in thermodynamics"

The analogy holds together fairly well. The word 'work' has both a formal physics definition as well as a formal economics definition.

And they both require energy.

 

[william the wie]

Let me put it this way, just for fun.

A variable e := production efficient, is changed from a lower value to a higher, causing a closed economic system to shift into a equilibrium with high jobless rate.

In order to bring the system to a new equilibrium with low jobless rate we can change e back to it's previous lower value, but that sounds stupid.

We can also change work time per week per person to a lower value because, assume employers prefer full time employees, number of man needed = total work hour*man needed / total hours per man. But this is not really a must, we can also start constructing the colony on moon.

The fun point is the resemblance of ideas in economics to that in thermodynamics.

The assumption that a market, if left untouched, will work it's way to the highest efficiency in production and distribution is a statement that there exists one and only one state of equilibrium a given economy system will approach. This is what the second law of thermodynamics says about a closed system and that state of equilibrium is said to have the highest entropy.

I would suggest reading Brian Arthur. Increasing marginal returns due to formal and informal network economies do not have good and simple physics analogs. Areas of increasing returns include:
ICs
optronics
bio-tech
nano-tech
superconductors
space launch

And many others, which is why there is no proof of equilibrium using finite math. Lorenz's "The Essence of Chaos", Mandelbrot's "The (Mis)behavior of Markets" and Minsky have all presented arguments that cast doubt on the whole idea of equilibrium.

 

[oldfart]

I would suggest reading Brian Arthur. Increasing marginal returns due to formal and informal network economies do not have good and simple physics analogs. Areas of increasing returns include:
ICs
optronics
bio-tech
nano-tech
superconductors
space launch

And many others, which is why there is no proof of equilibrium using finite math. Lorenz's "The Essence of Chaos", Mandelbrot's "The (Mis)behavior of Markets" and Minsky have all presented arguments that cast doubt on the whole idea of equilibrium.

The conditions for equilibrium in finite math are a lot less limiting than calculus (we avoid producing 73% of a battleship, for example). In addition finite math (game theory) provides solutions for a range of problems that calculus does not address well. I think if you review my four possible outcomes for the general optimization problem, the theory at least comprises all possible outcomes. This is not the result you get with "proofs" of the existence of a solution in Walrasian general equilibrium theory.

I am familiar with the work of the three gentlemen you mentioned and have had the pleasure of meeting Hyman Minsky. Their work is excellent, but it is directed to exposing problems with Walrasian general equilibrium theory, and the stability of dynamic equilibria, not finite mathematical modeling and optimization theory.

 

[william the wie]

Actually I agree with pretty much all of your points OF but the constraint slack exceeds zero runs straight up against normal economic assumptions:

Inflation = negative slack (Some big bank economist on Bloomberg's Asia Edge about a month ago made the most blatant use of this impossibility I have ever seen. He was explaining how the lack of infrastructure in India caused inflation without reference to increasing marginal costs of transportation, bribery or other Indian inflation drivers.)

That the double or triple peaks found in incidence graphs of say UE are not a slice of a strange attractor.

Or for that matter given the microscopic budgets for job creation/destruction and UE surveys the data generated are used with a level of confidence that hardly seems justified.

I think part of the problem is that premature lock in is more common than Equilibrium theory permits also we lack the math circuits in our brain to actual describe what is observed. A day laborer can use the spoil from square footings as backfill but the math to explain how he takes the square root for the footing is lacking.