Thursday, November 28, 2013

Price, Average Total Cost, Average Variable Cost and Marginal Cost

The graph below illustrates the cost curves of a typical real world firm as understood in the Post Keynesian theory of the firm. Such a firm is also a mark-up pricing firm.

We have the firm’s marginal costs (MC), average variable costs (AVC), total average unit costs (UC), point of full capacity (FC), and point of theoretical full capacity (FCth).

It is assumed that average variable cost is a reasonable proxy for marginal cost (an assumption widely held, as in, for example, the Areeda-Turner predation rule [Areeda and Turner 1975]).

It is furthermore assumed that marginal cost is constant (which is supported by the finding of Blinder et al. 1998: 103 that 88% of businesses reported that marginal costs are constant or declining).

Between full capacity (FC) and theoretical full capacity (FCth), marginal costs and average variable costs will increase, because of overtime payments, cost of increased maintenance of machines, and possible increased costs of replacement for machines whose operation life will be decreased (Lavoie 1992: 120, 125–126).

However, firms generally do not produce beyond the point of full capacity, so that the rising cost curves to the right of the point FC are mostly irrelevant to real would firms (Lavoie 1992: 121).

Empirical studies have confirmed that the U-shaped cost curves of neoclassical analysis are irrelevant for many real world firms, because firms prefer to avoid production beyond the point FC. Therefore realistic total average long-run cost curves for such firms are L-shaped and average variable (or direct or prime) cost curves are constant (Lavoie 1992: 122, citing Johnston 1960; Walters 1963; Lee 1986). Marginal cost is also found to be generally constant up to full capacity (Lavoie 1992: 122).

Reserves of capacity are the norm in many firms and the actual rate of capacity utilisation will be below FC and normally within the 80–90% range (Lavoie 1992: 122). The reason for this is that firms have excess capacity available to deal with unexpected increases in demand, and full capacity itself might be increased in line with demand (Lavoie 1992: 124, citing Kaldor 1986). Thus excess capacity is a way for firms to reduce the uncertainty related to demand fluctuations, and in this sense firm demand for excess capacity is analogous to the precautionary demand for money and other highly liquid financial assets (Lavoie 1992: 124–125).

The effective use of excess capacity can also deter other firms from entering a market, and can therefore function as a barrier to entry (Lavoie 1992: 124).

Neoclassical price theory holds that firms equalise marginal revenue and marginal cost: price tends towards marginal cost.

One of the neoclassical responses to heterodox mark-up pricing is to argue that it is compatible with standard marginalist theory. A standard view is that, in imperfectly competitive markets, firms will set a price that is a markup over marginal cost (Fabiani et al. 2006: 16).

Yet mark-up businesses normally use total average unit costs to calculate prices, not marginal cost or average variable costs. In fact, marginal cost is a concept some business people have difficulty even understanding (Blinder et al. 1998: 216–218, 102; Fabiani et al. 2006: 16; Ólafsson et al. 2011: 12, n. 8), and most do not use it in calculating prices (Hall and Hitch 1939: 18; Govindarajan and Anthony 1986: 31; Shim and Sudit 1995: 37). These findings simply refute the idea that firms in general are using marginal cost (or only average variable costs) in calculating prices.

Another attempted neoclassical explanation is that, if marginal cost and total average unit costs roughly coincide, then a profit maximizing firm will use total average unit costs as a proxy for marginal cost. But, as we have seen, it is generally thought that average variable costs are the best proxy for marginal cost, not total average unit costs. In addition, many firms report that total fixed costs (an important part of total average costs) can be very high: as much as 40 percent of total costs on average (Blinder et al. 1998: 105, 302; and cited by Keen 2011: 126).

And if firms really are so concerned with the concept of marginal cost, then why do they show such a lack of interest in it or even confusion in understanding it? This is simply inconsistent with the second purported explanation.

Furthermore, if we turn back to the graph above, while total average unit costs fall towards average variable costs, the total average unit costs will not equal average variable costs (which is taken as a proxy for marginal cost).

And of course the actual price of a mark-up pricing firm will be some point above total average unit costs. If the firm reduces its price as total average unit costs fall, then the price will appear as a curve-like line above the total average unit costs curve. If, however, the firm maintains a fixed price above total average unit costs, then the price will be a vertical line above total average unit costs and profits will increase as total average unit costs fall.

Either way, it follows that mark-up prices will permanently tend to be set above marginal cost. When the price remains fixed, even with falling total average unit costs, price will not converge to marginal cost, but will be stable and well above it. When industries decide to reduce price given falling total average unit costs and competition, even here price will still be set in the long run above marginal cost.

I repeat some definitions of key concepts below.

Average cost
This is total production costs per unit of output produced by a business. This equals (1) total fixed (overhead) costs plus (2) total variable costs divided by the number of units of output produced. Given that many businesses can use economies of scale and increase their output over time, average costs may fall too, because average fixed (overhead) costs fall, since they are divided by more units of output.

Fixed costs or overhead costs
Fixed costs (or overhead costs) are short-run costs that do not vary with the changing volumes of output produced, including rents, depreciation of fixed assets, marketing, etc. Average fixed costs will fall as output increases. Also called indirect costs.

Variable costs
Costs that vary with the rate of output, usually labour and raw materials costs. These are sometimes called operating costs, prime costs, on costs, or direct costs.

Marginal cost
The cost accruing from an additional unit of output.

Areeda, Phillip and Donald F. Turner. 1975. “Predatory Pricing and Related Practices under Section 2 of the Sherman Act,” Harvard Law Review 88.4: 697–733.

Blinder, A. S. et al. (eds.). 1998. Asking about Prices: A New Approach to Understanding Price Stickiness. Russell Sage Foundation, New York.

Fabiani, S., M. Druant, I. Hernando, C. Kwapil, B. Landau, C. Loupias, F. Martins, T. Mathä, R. Sabbatini, H. Stahl and A. Stokman. 2006. “What Firms’ Surveys tell us about Price-Setting Behavior in the Euro Area,” International Journal of Central Banking 2.3: 3–47.

Govindarajan, V. and R. Anthony. 1986. “How Firms use Cost Data in Price Decisions,” Management Accounting 65: 30–34.

Johnston, J. 1960. Statistical Cost Analysis. McGraw-Hill, New York.

Kaldor, N. 1986. “Limits on Growth,” Oxford Economic Papers 38.2: 187–198.

Keen, Steve. 2011. Debunking Economics: The Naked Emperor Dethroned? (rev. and expanded edn.). Zed Books, London and New York.

Lavoie, Marc. 1992. Foundations of Post-Keynesian Economic Analysis. Edward Elgar Publishing, Aldershot, UK.

Lee, F. S. 1986. “A Post-Keynesian View of Average Direct Costs: A Critical Evaluation of the Theory and the Empirical Evidence,” Journal of Post Keynesian Economics 8.3: 400–424.

Ólafsson, Thorvardur Tjörvi, Pétursdóttir, Ásgerdur, and Karen Á. Vignisdóttir. 2011. “Price Setting in Turbulent Times: Survey Evidence from Icelandic Firms,” Working Paper Central Bank of Iceland‎

Shim, Eunsup, and Ephraim Sudit. 1995. “How Manufacturers Price Products,” Management Accounting 76.8: 37–39.

Shipley, D. D. 1981. “Pricing Objectives in British Manufacturing Industry,” Journal of Industrial Economics 29.4: 429–443.

Walters, A. A. 1963. “Production and Costs: An Econometric Survey,” Econometrica 31.1–2: 1–66.


  1. Price is only equated to marginal revenue for the perfect price taker, with effectively infinite elasticity of demand & therefore a nil or negligible profit maximizing mark-up over marginal cost. For firms with substantial market power and sufficiently low firm elasticity of demand, the profit maximizing mark-up on marginal cost, the profit maximizing position is often below the designed full capacity point. Where the PK analysis really bites into the standard story is for monopolistic competition, where firms often produce within designed full capacity even though marginalist profit maximizing would indicate producing between designed full capacity and theoretical full capacity.

    1. "For firms with substantial market power and sufficiently low firm elasticity of demand, the profit maximizing mark-up on marginal cost"

      That is untrue: marginal cost is largely irrelevant.

      Firms use total average unit costs.

      See the edit above.

    2. I'm not saying that the marginalist theory correctly models firm behavior, I'm rather saying that your description of the marginalist model, that price tends to marginal cost, is only strictly true for perfect competition among the three classical marginalist price/production-period models, because price and marginal revenue are not identical in either monopolistic competition or monopoly.

      The fact that firms typically do not make price/production-period decisions on production-period marginalist profit maximizing grounds does not modify what the profit maximizing mark-up on marginal cost IS, it rather reverses the role of the profit marginalist profit maximizing mark-up on marginalist cost on highlighting long falsified predictions that price/production-period marginalist profit maximizing models make, by simplifying comparing those falsified predictions more directly to mark-up pricing models that perform more robustly.

      But I do not want to dwell on where I feel you missed a step, as the important point is where you bring out the tacit false information that the marginalist price/production-period building the model upon: "Thus excess capacity is a way for firms to reduce the uncertainty related to demand fluctuations, and in this sense firm demand for excess capacity is analogous to the precautionary demand for money and other highly liquid financial assets." If the price/production-period marginalist profit maximizing model is built on a premise of no uncertainty regarding demand, then its not an ACTUAL profit maximizing model, but a profit maximizing model for some world other than the one we live in, and so all of the evolutionary arguments regarding, "experience of successes and failures in the marketplace will ensure that firms will come to behave as if they made decisions in this way" fall over in a heap.

  2. In Austrian models (and I suspect in neo-classical ones also?) average costs will tend to equal marginal costs. So firms who use marginalism to set prices will not necessarily end up with different prices to those that use average costs.

    Put in a different way: Even if all firms use cost+markup pricing and use quantity adjustments to match supply to demand then the fact that average costs are used for pricing does not disprove the theory that prices in such an economy end up the same as if marginal-ism was used.

    1. "In Austrian models (and I suspect in neo-classical ones also?) average costs will tend to equal marginal costs. "

      And is it your belief that those models are accurate?

      And why is it that average variable cost -- not total average costs -- is widely considered a good proxy for marginal cost?

    2. I think Austrian models are logically consistent at least as far as price setting is concerned.

      And I think the intuitions on which this part of their model is based (the fact that firms will vary the mix of inputs so that MR is the same for all inputs, and that investment will be structured across an economy so that profits will tend to be standardized between different industries) seem likely to hold empirically.

      I think the fact that most firms claim to practice administered pricing actually indicates that prices are set as if marginal ism holds. If that was not the case there would be arbitrage opportunities for firms that did practice marginal pricing to exploit and make above average profits. Marginalism is not only a theory of how prices are set but actually a description of the optimum way a firm should set output and price if it wished to maximize profit.

    3. That last arbitrage argument assumes that profit maximizing pricing as if the firm had perfect information will approximate profit maximizing pricing if the firm has strategically incomplete information. There is, however, no reason to believe that to be true unless the argument is made.

      Also, the idea that MR will be the same for all inputs ignores neo-Ricardian insights into general complementarity ~ it would be a rare real world production system where the MR of each input can in reality be disentangled, where the argument regarding equalization of MR of inputs presumes at the outset that they can be disentangled.

    4. I don't think firms need perfect knowledge - they just need to be able to spot opportunities where current pricing allows above average profits to be made. Such opportunities will only exist if cost+markup pricing set prices to something different to marginal pricing.

  3. LK:

    I just found a giant bibliography of articles on management/accounting views on pricing decisions. It struck me as something you might find useful. :)

  4. What determines output?

    1. Of a typical firm as above? The level of demand for their product and even expected demand, as in present sales volume and orders, and their expectations about what this will be.

  5. Dear Lord Keynes,

    as a self-decribed Austrian I read your blog with great interest and get a lot of insights.

    However, since you started your inquiry into post-keynesian price theory, I feel the urge to ask you a question:

    Are you awars of Armen Alchians paper on the marginal pricing controversy? (Alchian, Armen A., 1950: "Uncertainty, Evolution, and Economic Theory", The Journal of Political Economy 58 (3), pp. 211-221)

    In your posts you often make it seem as if neoclassical, marginalist economists actually believe that firms consciously set P=MC. You then refute this view by correctly showing, that few businessmen are aware of the concept of marginal costs (which itself is only meaningful in a world of near-perfect information and calculablecost curves).

    This however is a strawman argument. No marginalist economist actually believes, that firms set P=MC. Rather, P=MC is the evolutionary winning rule in competitive markets. Firms use various heuristics (like mark-up full cost pricing) in daily business. In the !competitive! long run however those firms which use a heuristic which is close to P=MC tend to generate positive profits (or non-negative), while firms with irrational or "bad" pricing strategies leave the market.*

    P=MC therefore is not a pricing strategy consciously used by businessmen, but rather a prediction which economists make about the long run winning strategy in a competitive market. To put it another way: Economists dont know how an individual firm sets its market price. But economists know which pricing strategies are outcompeting the alternatives in the long run - depending on the market design and especially the intensity of competition in the given market. Thus they can use the formula P=MC as a proxy for real world firm behavior, even if in reality no single firm knows what MC is.

    Surely you can find good arguments against this view. Also Alchians argument does not touch post-keynesian insights into the macro-economic consequences of fixprices. However your suggestion that neoclassical economists require, that businessmen know the concept of MC seems to be a strawman argument.

    That said, Im looking forward for many more new posts on this interesting topic, which is also of interest for those of us who lean to the Hayek-Kirzner-Lachmann view on real-world markets.

    *This argument obviously only applies to competitive markets (which need not be perfectly competitive), but this is well-known among mainstream economists.

    1. You are aware of Steve Keen's (with Standish and incorporating Stigler) critique of neo-classical perfect competition which says that even in a theoretical perfect competition context equating MC = MR is not a profit maximizing strategy?

      There are some criticisms, which should also be looked at, but I don't see any which implies MC=MR is a winning strategy, when other firms are not following MC=MR (even for perfect competition).

    2. (1) yes, I am aware that neoclassical theory from the 1950s has tried to argue that mark-up pricing is consistent with marginalist analysis.

      I am in fact reading the history of the debate as we speak, as described in this symposium in the Journal of Post Keynesian economics.

      (2) "In the !competitive! long run however those firms which use a heuristic which is close to P=MC tend to generate positive profits (or non-negative)"

      But that is simply incoherent.

      How can a firm be accurately using average unit costs as a proxy for MC if they cannot properly estimate their MC, and they are simply unconcerned with MC?

      A mark-up price is permanently well above average variable costs, which is often taken as a proxy for MC.

      Even Rothbard appears to think -- wrongly -- that real world markets have a tendency for prices/marginal revenue to tend towards marginal cost, even though all prices will never reach MC (Man, Economy, and State with Power and Market, Scholar's Edition, p. 696).

      As Keynes said long ago,

      “Indeed, it is rare for anyone but an economist to suppose that price is predominantly governed by marginal cost. Most business men are surprised by the suggestion that it is a close calculation of short-period marginal cost or of marginal revenue which should dominate their price policies. They maintain that such a policy would rapidly land in bankruptcy anyone who practised it.” (Keynes 1939: 46).

      Real world firms are greatly concerned with recovering overhead/fixed costs including sunk costs.

  6. Thanks for your comments. However I am not sure if they really capture the essence of Alchians argument.

    My point is very simple: To accuse neoclassical economists of bad science because they allegedly think, businessmen consciously set prices equal to MC, is to attack a strawman. No neoclassical economist ever thought this way. This also means, that no neoclassical economist ever required firms to know the shape of their cost curves, especially their MC. In fact, they dont even need to know what MC is.

    The neoclassical prediction P=MC is not empirically founded, was never meant to be empirically founded and need not be empirically founded. It is deduced from assumption over a given market. Give them another market design and they deduce you different pricing strategies. In the case of perfect competition however, the simple neoclassical prediction is, that those firms, which set prices near or equal to MC will outcompete their competitors. This prediction does not rest on any behavioral assumptions. To refute it by treating it as if it was meant to be a behavioral assumption is to create a strawman.

    This said, the neoclassical view of course can be attacked on several lines. For example it often assumes well-behaving cost curves or a high level of competition. These problems are well-known.

    @Nic the NZer: I was not aware of this paper. Thanks.

    1. "To accuse neoclassical economists of bad science because they allegedly think, businessmen consciously set prices equal to MC, is to attack a strawman. No neoclassical economist ever thought this way."

      Your last sentence is straightforwardly untrue, as any reading of Hall, R. L. and C. J. Hitch. 1939. “Price Theory and Business Behaviour,” Oxford Economic Papers 2: 12–45 would show.

      The Oxford economists who did this early survey were precisely expecting to find firms calculating MC and setting price by equating price with MC.

      “In fact severe questioning by the Group failed to uncover any evidence that the businessmen paid any attention to marginal revenue or costs in the sense defined by economic theory, and that they had only the vaguest ideas about anything remotely resembling their price elasticities of demand. The Oxford economists were shocked, to say the least. But what caught their attention even more was the relative stability of prices over the trade cycle, and this became the phenomenon which really needed to be explained.” (Lee 1998: 89).

      I'm sure I could plenty of other evidence, but this alone is enough to refute your statement above.

    2. " To accuse neoclassical economists of bad science because they allegedly think, businessmen consciously set prices equal to MC, is to attack a strawman. "

      An additional point: Hall and Hitch 1939: 13 make it clear that they though business people would at least be trying to set prices in a way that **tends to move prices towards** MC -- even if only in perfect competition in equilibrium all prices would be at MC.

      As I have just told you above, even Rothbard appears to think precisely that -- but wrongly: real world markets have a tendency for prices/marginal revenue to tend to move towards marginal cost, even though all prices will never reach MC, since the world can never reach or be in a general equilibrium state or the ERE or Mises's final state of rest (Man, Economy, and State with Power and Market, Scholar's Edition, p. 696).

      And please don't tell me that no Austrian in human history has ever argued -- falsely -- that most real world businesses really do set their wages by equating them with marginal revenue product of labour: I've seen videos where Austrians do exactly that.

      Steve Horwitz does it right here in the video:

      It is untrue. This form of wage setting is mostly irrelevant.

      Now if my Austrians interlocutors are reasonable and make a good faith attempts to argue, and acknowledge their errors, I am willing to continue the arguments and conversation.

      But are you willing to admit your error graciously, I wonder?

    3. That, however, presumes that the Alchian "as if" argument suffices as a theoretical cover for using a known-false model of business behavior.

      It does not. Alchien presents an evolutionary theoretical hypothesis, but the hypothesis does not hold. Firms that engaged in administrative pricing that have mark-ups that are "as if" they are profit maximizing on the basis of available information will not be including prudent consideration of intrinsic uncertainty, and firms that do take prudent consideration of intrinsic consideration of intrinsic uncertainty will set prices that are biased from the view of profit maximizing prices based on all available information. Alchian's argument is based on a premise that profit maximizing prices based on all available information are the most evolutionary fit, and that would seem to be a false assumption.