Suppose, Adam Smith writes (and I paraphrase)
Adam Smith sets out to show that these assumptions are plausible. After all, considering assumption 1, if you, as a consumer can choose between buying the same thing more and less expensive, what will you do? Would not most, if not all consumers be like you? And, considering assumption 2, is not the whole idea of entrepreneurship that you invest in means of production in order to have a profit? Why else would you do it? And if you can choose between investing in something more and something less profitable, would not you choose for the most profitable investment? What reasons could you have to act differently? Would not most entrepreneurs be like you when you imagine yourself to be an entrepreneur?
What will happen in a country where people are free to choose from whom to buy and to
whom to sell? One could start by assuming that some good, say, coal, yield a price such a
to render a higher rate of profit to coal producers than producers of other goods, say
bricks, receive.
As everybody knows, entrepreneurs have invested their money in stocks and equipment. The
coal producer's money is invested in coal heaps (paid labour), buildings, tunnels, rail,
wagons. The brick producers money is invested in heaps of brick, buildings, drying houses,
furnaces.
So far the coal producer just has more luck than the brick producer, profiting from better
prices.
But while the equipment wears out the entrepreneur saves money to replace it when it will
finally be worn out. At that critical moment of the replacement decision, an entrepreneur
can choose for buying different equipment. Equipment designed to produce different, more
profitable goods. Sooner or later, the brick producer has his investment money free to
reinvest. Then, he can look around. If he is rational, and strictly preferring the highest
rate of profit, he will now invest in coal producing equipment rather than brick producing
equipment.
Coal production will increase. To sell the increased amount of coal to the consumers
completely, its price should be lowered. But that reduces the revenue of the coal
producers, and thus their rate of profit goes down in the direction of the previously
lower rate of profit in the brick industry..
Meanwhile, less bricks are produced, because the brick industry lost the investor who
shifted to coal. Consumers compete for a smaller quantity of bricks supplied, brick prices
will rise, brick revenue will rise, and thus the rate of profit in the brick industry will
rise in the direction of the previously higher rate in the coal industry..
Summarising: by making their excess or insufficient demand felt through market prices offered, consumers "direct" entrepreneurs investment money to the most profitable industry. However, after sufficient entrepreneurs have shifted their investments from below average profitable industries to above average profitable industries, they will all end up having just the average profit. Below average profit rates tend to rise, above average profit rates tend to decline, until the average is reached by all. That is an equilibrium: there will be no more unrest, no more desire of entrepreneurs to shift from one industry to another. Profit rates tend to equalise.
Methodological analysis of the invisible hand story
The amazing thing is that the story follows basically from the two assumptions 1 and 2.
Who would see these implications by himself, without having read Adam Smith's explanation?
Not many. That proof is Adam Smiths theoretical achievement. It is very
convincing to everyone who subscribes the two assumptions.
The method of deriving theoretical conclusions form plausible assumptions, and defending
the validity of the conclusions deductively, is called the method of apriorism.
Apriorism has later been developed into the Method of Deductive Model Exploration (dme).
Does the conclusion of Adam Smith imply that profit rates will be equal? NO! The invisible hand theory decries how entrepreneurs follow changes in consumer demand by shifting the the most profitable industries. But consumer demand changes all the time, so do market prices, so do industry profit differences. The system has no time to settle, to come to rest in a simultaneous equilibrium on all industry markets that would make everybody satisfied or at least too lazy to change for some little advantage. The system is shaken all the time.
The tricky thing is that an a priory theory is a plausible reasoning about imaginary situations of systems that are settling in an equilibrium. Real economic systems never do.
How to judge the adequacy of such a theory, or at least, how to judge which one of several such theories, if inconsistent, is the best? What is the use of such theories? There is a vast methodological literature about that subject, because it has always been a challenge to discuss plausible but untestable theories.
[planned addition links to literature]