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Primer: The Kalecki Profits Equation (Part I)

The Kalecki turn a profit equation -- named after the economist Michal Kalecki -- describes how aggregated profits are determined past times national accounting identities. (Note that Jerome Levy came upwardly with a similar approach earlier; the equation is sometimes referred to equally the Kalecki-Levy turn a profit equation.) The results are maybe non obvious if nosotros expression at profits from a bottom upwardly perspective. From the perspective of concern cycle analysis, the fundamental signal to banking concern notation is that internet investment is a source of profits. Meanwhile, since firms invest inward club to grow profits, nosotros instruct a self-reinforcing feedback loop. From a policy perspective, nosotros reckon that governmental deficits also add together to profits, which implies that increasing deficits add together to profits inward a recession, helping seat a flooring nether activity.

Given the length of this discussion, it volition live broken into a multi-part article. (Link to purpose 2.) This get-go article volition hash out the purpose of savings in addition to the distribution of income on profits. My objective is to explicate the practical importance of the turn a profit equation, in addition to I brand a number of assertions nigh concern cycle conduct to practice so. Other articles volition expand upon this analysis, in addition to render a stronger justification of these assertions. I also wishing to add together a disclaimer that I am non specially concerned nigh the details of national accounting; I am writing nigh a simplified accounting organization that would reverberate the outcomes of economical models. There may live some details around diverse definitions that I am glossing over.

If nosotros wanted to apply the turn a profit equation to existent the world national accounts data, the lastly equation contains a corking number of terms. This complexity distracts from the basic principles of the equation. Instead, this handling volition start off with the equation for real uncomplicated model economies, in addition to and so add together terms equally nosotros add together complexity to the models. The usefulness of the Kalecki turn a profit equation is for agreement the model dynamics that transfer to existent the world behaviour, rather than playing with national accounts identities. We tin create upwardly the equation term-by-term, in addition to so nosotros tin take away hold an intuition of the purpose of each term.

This handling is largely based on the ane industrial plant life inward Section 5.3.6 of Marc Lavoie's Post-Keynesian Economics: New Foundations (link to review). I would also banking concern notation the historical give-and-take industrial plant life inward "Profits: The Views of Jerome Levy in addition to Michal Kalecki" past times S. Jay Levy; Levy's tended to live to a greater extent than focused on the details of the national accounts.

Given my aversion to the theoreteical concept of "money," I usage "cash" inward discussion. Cash tin refer to whatever instruments that are used exchange, which may or may non live formal monetary aggregates (although all the instruments inward monetary aggregates are undoubtedly cash).

Model 1: Simplest Two-Sector Model

We volition start with the simplest case: an economical model with only ii sectors (the concern sector in addition to workers), in addition to no investment. Furthermore, nosotros volition assume that the concern sector does non pay dividends. In club to eliminate investment, nosotros volition assume that the concern either provides services or highly perishable goods; in that location are no inventories. We volition refer to this is model #1, in addition to it has an associated turn a profit equation.

We volition process the concern sector equally if it were a unmarried employer. If in that location are multiple employers, nosotros powerfulness reckon that some are profitable in addition to others run at a loss; what nosotros are interested inward is aggregate profit, so that distribution does non matter.

The concern sector's profits are equal to revenue minus expenses.
  • Revenue equals purchases from households.
  • Expenses are equal to reward paid to workers.
We tin straightaway reckon that if households pass 100% of reward (and take away hold no other source of spending), revenue equals expenses in addition to profits are equal to zero. There is a circular flow of cash out of the describe of piece of work solid to workers which in addition to so returns equally revenue, in addition to no cash drops out of the loop. However, if workers relieve some of their income, revenue volition live less than expenses; cash has dropped out of the loop. This gives us a version of the turn a profit equation with only ane term:

(Model 1 Profits) = - (Household savings).

Even this simplest version of the turn a profit equation has a span interesting theoretical properties.

The get-go thing to banking concern notation that since identify savings subtract from profits, rising savings "all else equal" has a negative cyclical effect. Variants of this concept present upwardly throughout discussions of uncomplicated monetary models; for example, the wishing to hoard money could allegedly atomic number 82 to a recession. However, in that location does non seem to live whatever prove of such an outcome inward marketplace position economical analysis. From my perspective, the emphasis on identify savings equally a cyclical factor past times academic economists caused me to sentiment their operate equally existence unrealistic. The employment is the overly simplified near-barter economies academics usage to illustrate their models -- the number is non changes inward what households sentiment equally "saving," rather the willingness to incur debt.

If the identify sector borrows inward aggregate during the accounting period, it could eat to a greater extent than than it earns from wages. That is, if identify saving is negative, profits are positive.

Within this ii sector model, in that location are ii avenues to allow this borrowing.
  1. The concern sector tin lend to households; for example, past times offering financing on purchases. The concern sector could terminate upwardly with an unchanged cash balance, but it volition gain fiscal assets -- the debt-like claims emitted past times identify sector.
  2. Individual households tin lend to other households. However, this tin entirely live sustained for equally long equally lending households agree cash instruments.*
Household consumption patterns seem to live fairly stable across the cycle (during the expansion, at least). However, the willingness to incur debts is to a greater extent than cyclical, specially with respects to housing in addition to auto purchases.** We require to driblet the parables nigh Farmer Bob buying apples from Farmer Alicia, or Bob's wishing to agree golden coins, rather the number is whether their kids Cynthia in addition to Doug are buying a condo inward the large city.

The side past times side thing to banking concern notation is that ane could sentiment the equation equally implying that identify frugality is a negative. This is inward stark contrast to the conventional story that nosotros require to increase identify savings to boost growth. ("Farmer Bob needs to agree dorsum some of his corn to industrial plant life side past times side year!") This model stacks the deck against frugality past times assuming that investment is zero; I volition render to this when investment is added into the model.

Model 2: Dividends

The side past times side add-on to the model is to add together dividends into the mix. Neoclassical models take away hold a hard fourth dimension with dividends, for reasons that volition live discussed below. However, the inclusion of dividends into the equation has some major theoretical in addition to political economic scheme effects.

H5N1 dividend is a payment past times a describe of piece of work solid to its owners, in addition to dividend income is unremarkably the objective for capitalist firms. The normal supposition is that dividends are paid out of profits (current or historical) -- although the private equity manufacture has mucked that belief up.

Dividends in addition to reward are the ii primary cash flows from the concern sector to the identify sector inward economical models. (In the existent world, some individuals either are self-employed or purpose of private partnerships that terminate upwardly existence lumped inward the identify sector inward the national accounts. As a result, existent the world information could reckon to a greater extent than types of interactions than the tidy the world of economical models.) Although the cash flows may live fungible, they take away hold real dissimilar implications for profits: dividends are non an expense.

If nosotros assume that the identify sector has nil savings, all concern cash outflows render inward revenue. So if 20% of outflows are dividends, entirely 80% of outflows are wages. This agency that profits (revenues minus expenses) are 20% of revenue -- or equal to the dividend payments. However, the identify savings is by in addition to large non-zero, in addition to nosotros terminate upwardly with the turn a profit equation #2, with an added term:

(Model 2 Profits) = - (Household savings) + (Dividend payments).

(In other words, nosotros added some other term to the equation.)

One typical way to introduce Kalecki's model is to add together some behavioural information that acts to constrain outcomes. The supposition is that workers in addition to capitalists are distinct sets of households, in addition to that workers pass 100% of their reward (and practice non dis-save). This has the implication that that identify sector saving is just equal to the savings of the households that have dividends.

This implies a dissimilar turn a profit equation:

(Kalecki Assumption Profits) = (Dividend payments) - (capitalist savings),

which past times Definition of savings implies:

(Kalecki Assumption Profits) = (Capitalist consumption).

 This explains Kaldor's aphorism***:
Capitalists earn what they spend, in addition to workers pass what they earn.
Once again, this version of the equation entirely holds inward models with the constraint that workers' aggregate savings are just equal to zero; this volition non live truthful inward existent the world information (except equally a statistical fluke). Furthermore, since workers in addition to salary owners tin also ain equities (courtesy of the motion to self-directed retirement schemes), nosotros take away hold a blurring inward the distinction betwixt "workers" in addition to "capitalists." Nevertheless, it does seem prophylactic to struggle that dividend income is largely received past times the upper income quantiles, in addition to those quantiles take away hold a greater propensity to save. Therefore, the behavioural constraint powerfulness live a reasonable approximation of reality.

The add-on of the dividend term to the turn a profit equation has express existent the world significance inward terms of cyclical analysis. Over brusque spans of time, dividends are stable, in addition to so this term is non likewise pregnant a source of volatility when compared to the other terms to live added. Over multi-decade periods, the changes inward dividend policy would presumably present upwardly inward secular turn a profit trends, in addition to so assertions nigh the long-term would require to convey dividend changes into account. However, the add-on of dividends to the turn a profit equation is real of import from a theoretical perspective, equally good equally for political economy.

(The electrical current popularity of stock buybacks powerfulness soiled the theoretical waters. In a stock buyback, the concern sector outflows are inward telephone substitution for fiscal assets, in addition to the seller volition non count the sales proceeds equally normal income. At most, in that location volition live working capital alphabetic quality gains. Trying to analyse this properly would require something similar a stock-flow consistent model that takes into concern human relationship equity marketplace position valuations in addition to working capital alphabetic quality gains. Those models are complex, in addition to enhance a corking number of thorny questions. I may render to this question, but I practice non reckon an obvious respond equally to the macro effects of a switch from dividends to stock buybacks.)

The theoretical employment with dividends existence a source of profits is that is creates a self-reinforcing feedback loop betwixt profits in addition to dividends, equally greater profits allows for greater dividends. For simpler models similar stock-flow consistent models, this is non a especial issue. However, if ane believes that model outcomes are inward some sense the resultant of optimising behaviour, this creates difficulty. If the concern sector (or capitalists) were really aiming for optimal outcomes, the solution would probable live pathological, with extremely high dividends that are non saved. Neoclassical models avoid these problems past times avoiding actual optimisations, instead sectors follow heuristics that are sub-optimal relative to choices that are implied past times taking into concern human relationship the total macro model. (See this article for a longer explanation of that assertion.) This accords with my previous sense inward applied mathematics: for practical problems, optimisations almost ever resultant inward pathological outcomes.

Even if nosotros take away hold that economical outcomes are non inward whatever sense optimal, in that location are of import implications of the purpose of dividends. The implication is that the grade of profits inward an economical organization are essentially arbitrary; for whatever grade of output, nosotros tin split the output betwixt workers in addition to working capital alphabetic quality in addition to take away hold a organization that respects cash flow constraints (accounting identities). An economical model needs to pivot downwardly the distribution of income using some assumptions nigh conduct inward club to take away hold a unmarried solution.

Neoclassical models shroud distributional questions nether the carpet past times assuming that workers in addition to working capital alphabetic quality have their only desserts: marginal contributions decide the levels of reward in addition to profits, in addition to so the income shares. As a result, it is possible to ignore the politics of income distribution. By contrast, the post-Keynesian tradition explicitly notes the arbitrary nature of income distributions. To live fair, "mainstream" economists are at nowadays to a greater extent than willing to hash out the effects of income distribution (at to the lowest degree the leftward terminate of the mainstream).

From a short-term perspective, distributional questions are a mo club effect. I take away hold seen arguments to the outcome that the structural lethargy of recent decades is due to a lower wage portion of national income, but I am agnostic on the validity of that view. Investment trends are much to a greater extent than of import for turn a profit determination, equally I hash out next.

Model 3: Investment

I volition conclude this purpose of the article with the add-on of investment, which is arguably the most of import cyclical factor during an expansion. For those who are novel to economics, ane needs to maintain inward heed that the Definition of "investment" inward economic science does non jibe the way the intelligence is oft commonly used. For example, people volition oft usage "investing inward the stock market" equally a way of describing the purchase of shares; this does non fit the Definition used inward economics. Instead, "investment" hither refers to spending past times firms that creates non-financial assets that presumably volition generate futurity profits. The fox is that this tin either live fixed investment, or investment inward inventories. The issues around inventory investment volition live discussed later.

(The usual convention inward the national accounts is that investment is largely an activity of the concern sector; identify spending is usually classified equally consumption. This is an artefact of the nature of the way that national accounts are measured. For example, national statisticians cannot say whether my purchase of a figurer is to back upwardly consulting activities -- an investment -- or to play the latest video games -- which is a shape of consumption. The give-and-take hither follows the convention that entirely the concern sector invests.)

Investment is some other cash fountain past times businesses that is non an expense. As a result, circular flows resultant inward revenue that is non matched past times a wage expense -- profits.

The Model 3 equation at nowadays reads:

(Model 3 Profits) = (Net Investment) - (Household savings) + (Dividend payments).

The transactions for investment are to a greater extent than complicated than the previous models. We tin imagine 3 basic channels for investment inward this simplified framework. (If nosotros add together to a greater extent than sectors, in that location are to a greater extent than possibilities.)
  1. The describe of piece of work solid pays workers $100 to create a working capital alphabetic quality good. The $100 payment is non treated equally an expense, it is instead "capitalised." From the workers' perspective, it does non brand a departure whether the $100 is expensed or not; it is a identify income-producing cash flow that tin live spent. The identify cash flow in addition to so recirculates through the organization equally before. Profits are higher since nosotros are at nowadays no longer deducting some of the cash flows from revenue.
  2. The describe of piece of work solid pays workers $100 to create products that are non sold. The unsold products volition terminate upwardly inward inventory. The inventory volition live held on the residual canvas at the production cost (which is equal to to wage payments require to create the goods). The promise is that the goods inward inventory volition live sold inward a futurity accounting period, in addition to the profits on the sale are equal to the sales cost less the cost of the goods equally valued inward inventory. (Under most circumstances firms cannot grade the value of inventories equally equal to their lastly selling price, equally firms could generate "profits" past times only producing goods that cannot live sold in addition to dumping them into inventory.) This in addition to so leads to some other observation -- selling the goods out of inventory represents disinvestment (negative investment), in addition to this amount would live subtracted from gross investment inward the side past times side accounting catamenia to instruct internet investment. (Note that the turn a profit equation specifies internet investment, non gross investment.) 
  3. Firm H5N1 purchases a working capital alphabetic quality proficient for $100 from Firm B. Firm B held the proficient inward inventory, with a value of $80. The $100 cash fountain for Firm H5N1 is non an expense; in addition to so the transaction is turn a profit neutral. For Firm B, the turn a profit on the transaction is equal to the selling cost ($100) less the cost of goods sold ($80) -- which implies a turn a profit of $20. The internet investment for the aggregate concern sector is also $20. Firm H5N1 has a novel fixed investment of $100, spell Firm B has an inventory disinvestment of $80. It is tardily to reckon that cash flows tin instruct quite complicated ane time nosotros allow for intra-sector cash flows (e.g., concern to concern flows). For example, an investment projection could take away hold a mixture of purchased inputs equally good equally worker pay. The fundamental is that investment creates outflows that are non matched to an expense. 
Depreciation adds some other wrinkle to the concept of internet investment. Most working capital alphabetic quality goods take away hold a finite lifespan, in addition to their value is written downwardly over time. The decrease inward property value is known equally depreciation, in addition to it shows upwardly equally an expense (the cost of capital). Depreciation is subtracted from other investment inward club to instruct internet investment. That is,

Net Investment = (Gross fixed investment) - (Depreciation) + (New goods added to inventory) - (Value of goods sold from inventory).

If nosotros had a static economic scheme with fixed nominal prices, depreciation expense would converge to equal gross investment. For example, assume that all working capital alphabetic quality goods depreciate past times 10% of their initial value every twelvemonth for 10 years. If firms invest $100 per year, that would create an expense of $10 per twelvemonth for 10 years. After doing this for 10 years, the grade of depreciation expenses would equal the novel investment. However, the usual status for modern economies (outside Japan) is that prices in addition to volumes of investment are rising over time, so the novel investment is larger than the depreciation of before investments (which take away hold a lower nominal value).

The internet investment factor of the turn a profit equation is much to a greater extent than of import from a cyclical perspective than identify saving in addition to dividends. The argue is that investment is pro-cyclical: firms invest if they hold back higher futurity demand -- in addition to profits. Since investment itself generates profits, expectations of higher profits tin live viewed equally self-fulfilling. This agency that expansion is the natural nation for capitalism; the employment is that other factors tin derail profits in addition to investment, in addition to and so the self-reinforcing feedback depresses activity.

I would summarise the post-Keynesian sentiment of how firms operate during an expansion equally follows. (I volition fill upwardly inward references inward later.) It is a error to believe that firms endeavour to solve some optimisation employment inward club to innovation their activities; they are missing likewise much useful information to fill upwardly inward the optimisation parameters. Instead, they require to usage rules of pollex (heuristics), such equally extrapolating past times growth trends. Obviously, they practice a corking bargain of analysis of their market, but in that location is an obvious corking amount of uncertainty nigh the direction of the overall economy. They volition in addition to so come upwardly up with some baseline forecast of demand for their products.
  • They volition innovation production to encounter demand, in addition to to grow their inventories inward describe with sales. That is, they typically wishing to maintain the ratio of inventory to sales at some target ratio, such equally belongings ane month's sales inward inventory. (Since inventory is a stock in addition to sales are a flow, the ratio has units of time.)
  • They volition launch fixed investments if they believe that they require to add together capacity to encounter projected demand.
The implication is that if firms are projecting demand growth over their planning horizon, they volition by in addition to large innovation on both increasing inventories equally good equally increasing fixed investment. 

The futurity does non ever encounter past times projections. Two competing firms may take away hold ramped upwardly capacity beyond the demand for their products, in addition to so sales terminate upwardly below their projections. If they are producing goods that are held inward inventory, they volition terminate upwardly with a higher inventory-to-sales ratio than desired. By itself, the higher inventory levels practice non campaign a loss. However, the unplanned inventory create represents a striking to cash flow -- they paid cash to create the inventory. Their residual canvas weightings shift from cash to inventories -- in addition to they require cash to encounter expenses in addition to repay debts. The inventory create has to live reversed -- which implies a reduction inward investment.

This agency that "investment" is non an unalloyed positive, equally it is sometimes portrayed inward economical parables. One real oft encounters stories nigh Robinson Crusoe economies, or economies that consist of barter alongside diverse proprietors (fisherman, shoemakers, etc.). In such an telephone substitution economy, investment is represented equally frugally abstaining from consuming output to add together to productive capacity. However, inward a monetary economy, "investment" may only live the piling upwardly of unsold goods at firms -- in addition to those firms volition become bankrupt if that inventory create is non reversed. This explains why "Keynesian" economists oft emphasise the purpose of demand inside the economy.

Concluding Remarks

The give-and-take of the Kalecki Profit equation volition conclude with the add-on of ii extra terms, which convey into concern human relationship the authorities in addition to external sectors.

Link to the mo part.

Footnotes:

* These sorts of complicated intra-sector transactions tin intermission overly simplistic analysis that wants to develop mechanistic models of cash flows inward the economy. As a resultant of things similar intra-sector borrowing, measured gross debt levels tin motion around without resulting inward changes inward measured GDP. Conversely, if ane assumes that debt is entirely issued to purchase goods in addition to services, ane tin incorrectly believe that in that location is an Fe police relating debt changes to gross domestic product changes.

** The purchase of an existing theatre does non itself add together to GDP, whereas it volition inflate identify debt (in the typical instance where the buyer volition terminate upwardly with a larger mortgage than the seller). This makes sense, equally nosotros practice non consider the proceeds of a theatre sale to live income. That said, in that location are fairly large income effects inward a typical housing transaction. Things similar realtor fees, mortgage insurance, legal fees, welcome tax, in addition to moving expenses stand upwardly for income for the providers of services, in addition to are oft rolled into the mortgage. As a result, a portion of the increase inward mortgage debt does direct enhance GDP. This matches upwardly with the sense of housing booms: they buoy economical activity, but the outcome is smaller than the alter inward mortgage debt would imply.

*** N. Kaldor, "Alternative Theories of Distribution," Review of Economic Studies, 23 (2), pages 83-100. The quote itself is inward page 96. I got the reference from Marc Lavoie's Post-Keynesian Economics: New Foundations. He notes that this quotation is oft mis-attributed to Kalecki.

(c) Brian Romanchuk 2018

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