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I´m trying to fully understand the basic circular flow and the equivalence among production, income and expenditure, but considering the accumulation of inventories (still the most basic version, without financial sector or government).

When there´s the hypothesis that the firms sell everything they produce, the equivalence among product, expenditure and income is obvious, but what if the firms don´t sell everything and inventory (either planned or unplanned) is formed?

Product Y is the value of everything that is produced even if it isn't sold. All of the output is consumed either by the household sector or there is accumulation of inventories which is interpreted as an investment done by the firms, so that Product = Expenditure. So far, so good, but this value must turn into income (wages, since the model considers just work as a production factor) and now there is less income than product (because less output was sold, which leads to lower wages) and the equality between product and income doesn't hold anymore. Would inventory somehow generate this missing piece of income? Is it impossible to maintain the model as simple as this and still keep the equivalence? If not, what´s the minimum amount of information necessary to add?

Also, if it´s true that a flow of real goods in one direction must accompany a flow of money in the other direction in this simple model, is there an interpretation for the "acquisition" of inventories that fit in this idea or it should be abandoned?

EDIT. Some additional thoughts:

As I understand, the idea of circular flow contains 3 direct causalities (which are equalities):
1. Production -> Income
2. Income -> Expenditure
3. Production -> Expenditure
All of these happen in the same period of time. The next causality connects 2 different periods and it is not necessarily an equality. The production here is the level of production of the next period:
4. Expenditure -> Production (a behavioral relation and not an identity like the previous ones)

"3" analyzes the destiny of the values of all produced goods. Everything that is produced ends up with someone. If there´s inventory, the "trick" that considers unsold goods also as an expenditure (by the firms) leads to the equality Y = C + Inventory. There isn't a monetary counterpart in the "acquisition" of inventory by the firms, so it really seems just an exception to balance the identity.

"2" analyzes what people do with their incomes. If inventory is formed, it means the workers didn't spend everything and there's some savings S inside their houses. They're the only ones who receive income, so that wages are the only form of income. Income = C + S. Comparing with the previous equation, it makes sense that the value of inventory is the same as the amount of money under the mattresses of the household sector.

Now I´m struggling only with "1", which seems like a philosophical relation and not mathematical like the others. The factors of production "turn into" a finished good. The firm begins the period with a plan to produce N items and spends a certain amount to achieve that. The resultant payment of the factors acts as a definition of "value of production" Y? Is payment of factors in some sense the same thing as "costs of production"? Is the equality production=income a tautology?

About "4", without creation of money, it seems that in this simple example the production has an upper limit because just a certain amount of income can be paid. So, the production of the next period can only be lower. In this next period, if workers decide to spend their savings, the production can raise again later.

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The statement

and now there is less income than product (because less output was sold, which leads to lower wages)

misses that the workers are paid to work a certain number of hours in production, and that production happened, so current wages are unaffected.

Meanwhile, the firm’s income is unaffected by the inventory build, since it is a form of investment, and thus the wages used to produce the inventory are effectively capitalised on the balance sheet.

Incomes might only fall in subsequent periods, as production is lowered in response to the unplanned growth in inventories.

As such, there is no real mystery to be explained.

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  • $\begingroup$ Hi, tks for the answer. I´m thinking about an extremely simple scenario of 1st page of econ book. As such, the money to pay the workers must come from the sales. The inventory can´t turn into payment and there´s no financial sector. Since the firm receives less money than the value of all its production, this is the mathematical unbalance I try to solve. It´s a weird situation where the wages would have to adjust every time to the product (if this is the only source of income). $\endgroup$ – Rick Jun 8 at 2:46
  • $\begingroup$ The firm has to run down its cash balances. If there is an unplanned rise in inventories, there is an unplanned drop in cash levels. This may be hard to fit into a neoclassical model, but that’s an issue with the strategy. $\endgroup$ – Brian Romanchuk Jun 8 at 11:26
  • $\begingroup$ I made an edit to the question. I believe I've found most of my errors of thought, everything is almost clicking. $\endgroup$ – Rick Jun 13 at 1:04
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You had got the right intuition: <<is there an interpretation for the "acquisition" of inventories that fit in this idea>>. In fact, if you consider that there is a sale of those commodities from the production firm to itself, with the counterbalance payment in money (a payment to itself, with a net result of zero), as any capital-goods purchase, you arrive easily to the solution of your paradox.

In the other hand, you have to realize than the firm has a loss in cash, true, but compensated by a gain in commodities in its warehouses.

Regarding your "additional thoughts", my advise is that you forget the idea of causalities as long as considering GDP computing: the GDP flow contains (or, more accurately, is computed by means of) 3 equalities. The triggering of new production by expense (then introducing the new concept of demand) is another matter, one of "economic behaviour" (as you again correctly intuitively felt), which in turn involves the matter of the transformation of income in expense, the matter of the identity of both, side by side with the indentity fo savings and investments, the creation of credit-money by banks therefore affecting the creation of true (though provisional) purchase power...

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An online article lists these assumptions associated with the circular flow of income in a two sector economy:

  1. There are only two sectors in the economy - households and firms.
  2. Households spend all of their income on goods/services without accumulating financial savings.
  3. Firms spend all their revenues on factors of production with no profits.
  4. There is no government.
  5. The economy is closed - no international trade.
  6. All outputs produced by firms is purchased by households. There is no surplus.
  7. There are no injections of income or additional investments - no financial sector.

In this model one can consolidate the production sector into one firm. Call it the Consolidated Production Corporation (CPC). The CPC makes a mix of items called Investment goods and Consumption goods. If I put the government functions and banking/finance functions on the books of the consolidated production sector then all transactions occur on the books of the Company Town Corporation (CTC).

Ignore government activities and foreign trade. Also allow for household financial saving and inventory accumulation in the CPC. There would no longer be a circular flow if income on the books of the CPC and consolidated household sector. One must split the households into Owners (capitalist) and Workers, and assume that the Consolidated Production Corporation issues money when it spends, and cancels money when it collects payments. If the CPC provides credit to workers then it can sell goods at a profit despite the accumulation of inventory and the Owner households can accumulate equity claims against inventory and other assets in the CPC.

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