Time for a new theory of the firm

I don’t know how best to say it, so here it goes – the current mainstream theory of the firm is dodgy. Real dodgy. Put simply, the theory of the firm that we all know and love tolerate, is a neat mathematical construction contrived to support an already established, but flawed, theory of markets.

If we want to make real progress in economics we need a new theory of the firm upon which we can build a theory of markets; fully informed by empirically observation and able to generate realistic predictions about production, trade and prices.

Is that too much to ask?

I stumbled into this challenge. In first year economics, when the supply curve was shown as upward sloping, the annoying undergraduate in me asked: why? When we get on to exactly why the supply curve is upward sloping, lo and behold, it is simply a representative firm’s marginal cost curve. Amazing!

But wait. If that’s true then firms operate at a point where there are diseconomies of scale. Yet didn’t most goods come down in price as output increased? What happened to the whole idea of economies of scale?

Oh what’s that? You’re getting confused between the short, medium and long run young grasshopper, of course there’s economies of scale, but we don’t lose anything from the analysis by assuming they exist only in the long run.

Tell me more Obi-Wan.

It was far too ad hoc for my liking. The contrived concept of short, medium and long run, is to all accounts quite inconsistent, since all periods of time must be part of all ‘runs’. But as a good economist-in-training I shoved my doubts back into the suppressed deviant skeptic part of my mind and accepted that marginal costs probably slope up. Surely the chaps with all those PhDs must have some empirical insight about this ‘fact’.

Except they didn’t. And they don’t. Alan Blinder made that clear after surveying firm managers about their cost structures and operations. He said

The overwhelmingly bad news here (for economic theory) is that, apparently, only 11 percent of GDP is produced under conditions of rising marginal cost. … firms typically report fixed costs that are quite high relative to variable costs. And they rarely report the upward-sloping marginal cost curves that are ubiquitous in economic theory. Indeed, downward-sloping marginal cost curves are more common…

If these answers are to be believed … then [a good deal of microeconomic theory] is called into question…

There are numerous other studies showing this to be the case – that flat or rising marginal costs are the exception rather than the rule.

So do I trust the contrived theory of the firm? Or do I trusted the empirical record? Personally, I prefer to start from observation, so I’m siding with the empirical record.

Which altogether leads to another conundrum – the heart of economic theory, that equilibrium is found where marginal cost equals marginal revenue, can no longer be accepted. Some other mechanism must be at play in the determination of prices generally.

My own experience in business, and the repeated challenges to the theory of the firm, finally revealed to me what was missing from the theory.

Returns.

It’s strange to think how in economic commentary the rate of return and profit are terms used almost interchangeable. Even Milton Friedman did this from time to time, saying that ‘firms behave as if they were seeking to maximise their expected returns’. He did a poor job of clarifying what he meant by returns, only that he uses the term profits as the realised ex post version of the ex ante expected profits, which he labels returns. Strange but true.

The foundation of economic theory is actually centred on profit-maximisation, being the maximisation of revenue minus costs. Returns, by every definition apart from Milton Friedman’s, are profits divided by costs. Colloquially, profits are ‘bang’, and returns are ‘bang for your buck’ – and I’ve never heard of anyone trying to get the best bang without trying to economise on the buck.

Just think of Milton Friedman assessing a production plan before a company board:

MF: This project will earn a return of $10m! 

Board member: Great! But a return of $10m on what?

All the more strange is that Avinash Dixit and Robert Pindyck made the astute observation twenty years ago that in the real world of uncertainty, and where investments in new businesses and expansions are risky and costly (meaning firms have a real option to delay incurring costs to increase production levels), that maximising the firm’s overall rate of return maximises its value.

So if maximising the rate of return is ubiquitous in financial analysis, and has strong foundations in economic analysis under realistic market conditions, why hasn’t our theory of firm production been updated to address this? Well, today it has.

We – myself and co-author Brendan Markey-Towler – have released a working paper outlining a new theory of return-seeking firms. And to our surprise, what seems a rather minor change in the firm’s objective function leads to a variety of results consistent with the empirical record, and with many alternative theories of firm production and pricing (such as mark-up pricing).

What did we do?

First, we relaxed the assumptions about market conditions. Rather than the unrealistic free entry and exit and perfect knowledge of the future which define most models, in our world firms face uncertainty, have irreversible costs, and can delay investment to future time periods. As per real options theory, these conditions give rise to our firm objective of return maximisation.

Next, we allow competition to enter the model via the shape of the firm-specific demand curve. The firm specific demand curve can be specified to include the supply of other firms producing substitute goods, and the parameters of the curve can be varied to reflect differing intensity of competitive pressures.

We do this because the usual model condenses similar products into a single market, yet there are almost no examples of markets where the goods produced by different firms are perfectly interchangeable. Hence, competition is a process of return-seeking between firms competing in close substitute goods.

This conception of competition also predicts non-price competition which aims to reduce the price sensitivity of customers, such as loyalty schemes and other incentives, and of course, product differentiation. Because of the way market competition is conceived in our new model, there is no need for the arbitrary conceptual leap between a downward-sloping market demand curve, and a horizontal curve faced by a firm in a competitive market. All firms operate in their own markets, whose demand schedule is influenced by the offerings in substitute markets.

One thing that is consistent with the traditional model of markets is that the more competitive a market the firm faces, in terms of having a flatter demand curve (more price sensitive customers who have more substitutes available), the greater their output with a specific level of capital.

I show this in panel (c) of the figure below, where competitive (q*c) and monopolistic (q*m) outputs are chosen when the same firm faces a competitive demand curve, p(q)c, or a monopolistic-type demand, p(q)m using the same capital inputs. grid1 Third, firms choose their inputs and output level to maximise their rate of return. This means that the price is above the marginal cost (and above average cost) such that mark-ups over cost are a feature of firm accounting structures. It also means that there must exist some economies of scale for firms to produce at all.

In the special case reflecting a traditionally perfect market (firms face a horizontal demand curve), return-maximising firms do not respond to changes in demand. They produce at the point of minimum cost at all times, as long as prices are above costs (shown as point q* in panel (a) of the above figure). Hence there is no supply curve as such in this market.

Indeed, even under imperfect markets, where firm-specific demand curves are downward sloping, the path of a firm’s supply response to a change in demand depends both on the shape of their cost curve and the shape of their demand curve. Hence, there is no supply curve, merely a response to changing market conditions conditional upon a firm’s cost structure. This has implications for long run trends in the relative prices of different goods. For example, goods limited natural supply, such as land and mineral resources, will increase in price relative to manufactured goods where economies of scale dominate.

In panel (d) we show that the emergent supply response can lead to what some might call a downward sloping demand curve (following a rightward shift of the demand curve from p(q) to p(q)delta).

Fourth, we make the input and output space of the firm discrete, meaning firms can only produce goods in discrete quantities, or batches, and can only choose capital inputs in discrete amounts. This is highly relevant to the capital debates, which demonstrated the inadequacy of capital aggregation. In our model firms face discrete choices in their capital investment, allowing ‘lumpy’ capital units, and various production techniques to be exclusive choices for firms.

The discrete nature of firm choices also means that firms are almost never going to be at their optimal point – they will be seeking to get there but typically they will be unable to because the optimal point is between two discrete choices. Hence we call the model one of return-seeking, rather than maximising, firms.

Such a disequilibrium approach allows for interactions between investment paths of firms across the economy as each firm’s slightly imperfect decisions cascade into those of other firms, resulting in a business cycle driven by capital investment choices. For example, a large firm in a region undertakes a capital project, thereby increasing the income of the workers, who in turn increase the revenues of other businesses, who in turn undertake return-seeking capital investment choices based upon expectations of continued growth in revenue.

Fifth, in our model there is no need to invoke a ‘normal’ rate of return on costs, since all real returns are driven by investment and output decisions in markets. Rates of return emerge from the market, rather than being fed into the market and emerging from some deep group psychology.

Sixth, the existence of a firm relies on both economies of scale and uncertainty – both of which must feature in our model. This shouldn’t be a surprise, since some rather hard-hitting economists have also made this point. Here’s Ronald Coase – “It seems improbable that a firm would emerge without the existence of uncertainty.” And not forgetting Frank Knight – “Its [the firm’s] existence in the world is a direct result of the fact of uncertainty”. We simply add that economies of scale are also necessary, since output would be infinitesimally small for any firm if that wasn’t the case.

Lastly, we need not invoke any special notions of short, medium or long run to understand markets. At all points in time firms are investing in new capital – it is a continuous process in the macro economy, even if at a firm level these lumpy capital investments are undertaken intermittently.

Phew.

We never expected that the small changes we made to ‘what firms do’ in a model would capture so many features of reality that had so far been treated in an ad hoc manner.

One important question concerns the value in this new theory. What can it tell us that existing theory cannot? I’ve thought about this a lot, and the answer is ‘a great deal’. It may take a number of posts to cover the important ones, such as; regulation of private monopolists, analysis of competition and market structures, the dynamics of market power and innovation, the ability to define economic rent broadly, the impact of regulations on competitiveness, competition via market share, and more. But let me just give you an example that I think is extremely important.

Housing supply.

The usual approach is to suggest that rising home and land prices have some connection to town planning regulations that determine location and density limits for new housing. If prices are rising, then according to our mainstream theory there must be a regulatory or physical constraint on the ability to shift the supply curve.

But the theory of return-seeking firm suggests that for many land owners the optimal choice is to withhold their land from development. Because there is an ability to delay investment, deferring capital improvement maintains the option value to develop at a later date to a much higher density. It may currently seem optimal to develop a 3 storey apartment building, but if I delay investing, I might be able to develop a 10 storey building in five years time and increase my return on the land.

In fact land development is a core example in real options theory.

If a government wanted to intervene in this market to increase housing stock compared to the status quo under existing regulations, our theory of return-seeking firms suggests that any policy that reduces the rate of return of the land owner when they delay will be effective at bringing housing investment forward in time. One idea is to announce a future restriction on development density, or implement a land value tax, which will reduce the potential rate of return from delaying investment.

Again, the working paper is here for those who wish to review our approach. I appreciate all responses and criticisms. Please share this article. Tips, suggestions, comments and requests to [email protected] + follow me on Twitter @rumplestatskin

Comments

  1. migtronixMEMBER

    Fantastic piece! That got my brain working early this morning 🙂

    I always thought the idea of fungible widgets (this guy makes green widgets that one red, it’s all the same…) was off too but that really put a lot of economic theory into perspective.
    Cheers.

  2. Many thanks, Rumples. We need more thinking on the optionality of investment choices and your example of land supply and time is on the money.

    Economies/diseconomies of scale is a field that has always interested me. Does a firm facing sharply lower returns on higher output hand customers to competitors? Only sometimes.

    On the notion that firms are always progressing toward optimum returns rather than arrived at, I am reminded there are at least three coherent answers to any complex problem. Firms do change their objectives and for some, scale and complexity add to the options available.

  3. Don’t forget the other types of analysis that firms do:
    1 NPV analysis
    2. IRR
    3. Payback period
    4. Sensitivity analysis of each of the above
    5. Effect on competitors of early investment (ie lock competitor out of a market by investing too early and get super profits over time)
    6. Extaction of long term monopolistic or oligopolistic profits through short term profit reducing industry concentration.

    Strategy and tactics also have a place in determining the behaviour of firms.

    • Yep. All of these are measure of return (apart from raw npv)

      The way we construct our model is to say that firms will undertake strategies that maximise their return (your no. 6). Because time becomes explicit when you think in terms of returns, short terms losses, delaying investment etc can all be optimal strategies, as long as you generate profits within your feasible planning horizon.

  4. Great work, I’d only add one concept:

    Disruptive technology.

    In markets where some technology advancement occurs it is often obvious to all players that the old ways are dead and the future belongs to the new. Logically in such a market the old players should just roll over and die as their profits disappear, yet many years of experience tells me that they dont do this, rather they act like little children and refuse to acknowledged the obvious,

    waw waw waw…I cant hear you.

    These firms enter their own parallel reality, their investors and capital suppliers are also often trapped in this reality. Who do they trust the new guy with unproven technology or their customer of 15 years?

    To give an example. In 2001 it was obvious to all in the consumer electronics field that Flat screen LCDTV would win out over all other technologies. Yet even leading firms in the space such as Samsung, Sony and Panasonic refused to invest accordingly.

    Samsung had a huge program to construct very thin CRT’s (6 inch deep for about 40 inch CRT screens) required heavy duty video processing to correct for the distortions inherent in such a thin CRT. When directly asked which market these products would sell into there was always a lull before someone mentioned India, S. America ….Africa, naturally they knew better than to suggest this was the trend in the US or Europe, which are far more transparent markets.

    OK so the end result is that enormous amounts of capital were wasted on a dead technology Thin CRT’s.

    Sony is a similar story of internal division and company wide dysfunction. Panasonic was just a basket case .

    I’m mentioning this because in my world, new technology ALWAYS faces this absurd counter intuitive behavior and it is exactly this behavior that bankrupts many bleeding edge technology companies because they expect that rational profit seeking will be the name-of-the-game.

    I’ve modeled this in the past with non-linear hysteretic models of the different segments market behavior. The real trick to accuracy is correctly defining the I-give-up points. Interestingly the first clear signals usually come form the capital side rather than the technology side.

    .

    • migtronixMEMBER

      Marketing and stick to what you know explains a lot of this. If all you’ve ever known for the 50 years of life before becoming a product manager is large, bulky, heavy as a ship’s anchor CRTs, thin CRTs are a no brainer!! What’s this LCD sh*t? Like my calculator? No thanks.

      Management is often the bottle neck

    • To give an example. In 2001 it was obvious to all in the consumer electronics field that Flat screen LCDTV would win out over all other technologies. Yet even leading firms in the space such as Samsung, Sony and Panasonic refused to invest accordingly.

      Well, there was also the problem that early LCDs had horrendously poor image quality compared to the alternatives and were shunned by high-end purchasers because of it, and were also relatively quite expensive, putting them out of the reach of low-end purchasers.

      Even today, a plasma will generally deliver a better picture than a low- to mid-range LCD, albeit with a much higher power budget – though LCDs have completely dominated the cheap & nasty end of the scale.

  5. Interesting. It concerns me that your description and the actual paper contain some key differences, for example you state ” in our world firms face uncertainty” yet the paper appears to have no treatment of uncertainty.

    Some points you might find interesting:
    – I believe there’s a large number of homogenous products (where the only differentiator is price) in most people’s daily lives, for example electricity, gas, water, milk, petrol, mortgages…I’m sure I could think of many more. Yes, producers try to product differentiate but a determined consumer can usually cut through to the core product across multiple suppliers in these markets and compare on a pure price basis. This doesn’t actually impact your analysis so it seems your desire to make a big deal of this is to allow your formulation to dovetail into the residual demand literature?
    – For a given capital stock, I think there are many cases where there are clearly upward sloping marginal supply curves (where the curve is defined as marginal cost as a function of output, not average total cost). For example, every plant I’ve looked at in the stationary energy and industrial processing sectors have exhibited this trait. The reason? A given plant is similar to a car, it has an efficient output level that minimises the marginal cost of a unit of output , the car analogy is highway driving using least fuel. You can run a plant harder and produce a larger quantity in absolute terms (speeding near a car’s red line) but you use your inputs less efficiently (petrol, wear and tear on engine, tires, etc) so marginal costs go up. Therefore, energy and industrial plant have increasing marginal costs for a given plant as you go from optimal to higher levels of output (they also increase as you go from optimal to minimum levels). You can of course build a new, more efficient plant, but it too will have increasing marginal costs, just around a different (lower) level. In aggregate for a firm (of one or n plant) you get increasing marginal costs. I’d also note that if a firm owns a single plant (with some marginal supply curve) and then invests in a new, more efficient plant (with lower but still increasing marginal supply curve) then the aggregate supply curve for the firm will comprise two ‘steps’ that reflect the operating range and increasing marginal costs of the two plant. In this case it’s likely that the original (less efficient, higher costs plant) will be marginal in any markets.
    I’ve personally done studies looking at historical information for such plant and they definitely have increasing marginal costs (above optimal levels), I believe there is similar outcomes for manufacturing plant with regard to energy consumption, failure rates and other parameters.
    If it’s not new build of more efficient means of production (e.g. capital investment), then what drives the economies of scale you mention that give you decreasing marginal costs for a firm’s aggregate curve?
    – You are maximising the net present value of the time dependent Lerner Index (marginal profit of the firm, [p – c]/c). There is a classical result that shows that the Lerner Index is equivalent to the inverse negative price elasticity of demand of a firm’s residual demand curve. It seems like you are aware of this (e.g. you repeatedly talk considering the “demand curve for the firm” rather than for the market) without having made it explicit in your paper/post?
    – You would want to be careful about your analysis of market competition issues if you are implicitly using a residual demand formulation. For example, many inferrances only hold in the case of continuous decision variables.
    – I haven’t looked through in detail, but I have a feeling that your formulation may not hold after you’ve discretised the objective function (both output and capital). You rely on a number of differential conditions that may not hold once you discretise.

    Good luck

    • Good spotting. Excellent comment.

      No we don’t say the word uncertainty in the paper, because we have a real problem with the way uncertainty is treated as some perfectly quantifiable distribution of future outcomes in most of economics.

      Uncertainty, to us means uncertainty. We are tying to avoid the debate entirely by simply noting the consistency with real options, where uncertainty is a condition.

      What you say about economies of scale is really the point we try to make with the discrete input space. When you make the decision to build a new plant you attempt to build one at a size that minimises the unit cost. If demand shifts during the lifetime of that plant, then because the choice to shift to a new plant is such a costly leap, or perhaps there are physical an institutional barriers to investment in new capital, you ‘temporarily’ produce at a point with increasing marginal costs if you want to maintain market share until you can invest in new capital. That ‘temporarily’ might be many years in the case of large plant like electricity generation, especially where there are major constraints.

      Lerner was a smart fellow. Actually our plans are to expand this idea and borrow his (and others) measure of market power to generate our parameter inputs for a firm.

      When we discretise we explicitly note the conditions for shifts between choices. The cost curves exist because we don’t take labour to be discrete (you can have a continuous amount of labour time devoted to a set of capital equipment). There is a field of these curves which firms make choices about being one.

      • Hmmmm…this will sound harsh but for someone who teaches at UQ that is a weak response. I think it is intellectually dishonest to present a theory of the firm that contains no treatment of uncertainty (your residual demand and production functions are defined explicitly for all periods and contain no shocks, your optimisation occurs under perfect information) as one that does and then, when questioned, present a bespoke and circular definition of uncertainty that is completely at odds with any standard definition. Surely, as a professional economist teaching at one of the best Unis in the land you know full well how the majority of your audience would interpret the phrase “in our world firms face uncertainty”.

        Your theory is interesting without these kind of tricks, why not sell it on its merits? It doesn’t include uncertainty, at best it accounts for the time value of delaying investment decisions under perfect information. It is substantially different to real options where multiple paths through the investment decision tree are considered (not just the optimal path) and decisions are made with respect to expectations across multiple future states of the world.

        My view is Lerner’s measures of market power are flawed for many industries…basically for suppliers of any good with a common clearing price. I could be the lowest producer of a good with a high market clearing price, for example a 10 MW wind farm in the NEM (which is ~45,000 MW total supply). The Lerner Index would say that I have more market power than a 4500 MW coal fired generator solely because my production cost is lower. Is that right? This argument applies to many, many goods. So beware.

        Again, best of luck and I’ll be interested to see how your theory develops.

      • Ha! You are probably the least harsh, and most constructive commenter in the blogosphere. You get thick skin after blogging for a while. I appreciate your frank opinions.

        Im any case, we could easily change the term p(q) and c(q) to E[p(q)] and E[c(q)] and make everything an expectation, and therefore capture our meaning of uncertainty.

        I’m open to the suggestion of doing this for a more complete explanation, but I’m not sure what the subsequent analysis gains from it.

        Just remember, however, that under perfect competition is there is no option to delay. You are already there in the end-of-time equilibrium.

  6. And ——when & where are you all building your spacecraft — – – – – ordinary mortals need to know 🙂