## Sunday, January 19, 2014

### 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 growth rate of firm value is akin to maximising its present value. In a world of scarce resources, maximising the growth in value can be achieved by maximising the rate of return on those resources.

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 in the manner of monopolistic competition. 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.

 Comparison of profit-maximising and return-seeking firm choices

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 usually 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.

1. Suppose you are a farmer. You use land, labour, and tractors, to produce wheat. Would you maximise the rate of return per acre, per worker, or per tractor? Would it matter whether you owned or rented the land, labour, or tractors?

1. i don’t know if it is a very stupid answer, but I guess you would maximise the monetary profit over monetary cost, i.e. the monetary rate of return.
I think this is the only safe way to aggregate heterogeneous factors.
BTW, it seems a good way to give some importance to nominal quantities in micro

2. Not sure exactly what you are getting at Nick.

The short answer is you maximise the rate of return on all costs, regardless of what those costs are. And it wouldn't matter if you owned or rented, because for either entity (the land owner or the agricultural business that rents land) they maximise the value of their business by maximising their rate of return.

Maybe you were going somewhere with this example.

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4. Having a second try at getting my calculus right! (I was always bad at math, and it's early here in Canada).

Cameron: I'm not going anywhere yet. Just trying to understand your model, and see where it leads.

So your firm maximises (TR-TC)/TC ?

Taking the derivative wrt output, and setting it to 0, we get:

[(MR-MC)TC - MC(TR-TC)]/TC^2 = 0

Which implies it sets output where (MR-MC)TC = MC(TR-TC) ?

Or, MR = MC + MC(TR-TC)/TC

(Or did I screw up the math again?)

It's that second term on the RHS that differentiates it from the standard profit-maximising model.

When maximum profits are zero, that second term disappears.

5. Why not just simplify and say it maximizes TR/TC?

(TR-TC)/TC = TR/TC - 1 after all...

6. Anon,
Sure you can do that. And I did in early drafts when I was fleshing out the idea. But we didn't, and chose to stick to the complete formulation.

Nick,
Equations 6-12 in the paper work through the optimal conditions.

Also, yeah, you screwed up the maths.

"Which implies it sets output where (MR-MC)TC = MC(TR-TC) ?"

Correct

"Or, MR = MC + MC(TR-TC)/TC"

No. You can cancel the MC.TC term on each side, then you get MR.TC=MC.TR

Or, MR = MC.TR / TC

Which is our equation 12 (cancelling the q)

MR = MC.P / ATC

2. It seems you have reached EJMR

1. I'm going to have a beer and celebrate! (Actually it's just a coincidence, I'm already drinking a beer)

Despite the nonsense that goes on their, sometimes good discussions take place.

2. "If you feel like I do, you would like to kill yourselves. This guy has just exploited f**king low hanging fruit"

This was exactly what I thought when I first read it (not that I wanted to kill myself, but "seriously? Nobody has done this before?")

Great job Cameron!

Also, I'm not really sure what Nick Rowe is getting at. Surely you'd seek returns of all of those things? EG if a farmer buys a new tractor, he'll want a sufficient return to the investment, but he'll simultaneously want returns on his land. Maybe there's room for expansion in the factors of production, but there's no problem that the current theories don't already have. After all, does the farmer maximise *profits* from his land, labour or machinery? It's a nonsense question as they're all part of the whole!

3. There are fruit on a tree. Each fruit can be sold for $100. It costs$1 to pick a fruit that is 1 foot high, $2 to pick a fruit that is 2 feet high,$3 to pick a fruit that is 3 feet high, etc.

The standard model says you will maximise profits and pick fruit up to 100 feet high.

To maximise (TR-TC)/TC, you should only pick the lowest-hanging fruit.

4. Now suppose you have already picked the lowest-hanging fruit. You take a second look at the tree. Would you say that "bygones are bygones", and pick the second-lowest fruit, because that is now the lowest-hanging fruit? If so, and you keep on repeating, you get the same solution as the standard model. You pick all fruit up to 100 feet high.

5. Well, in that case the choices are not mutually exclusive. If the fruit went rotten after one period then you'd definitely go for the lowest - similarly, when faced with 3 different investment choices that cannot all be taken, (the argument is that) your average firm would go for the one with the highest returns, not profits.

6. In theory, Nick’s argument is right. The point is that in practice there are two issues:
1- While costs are known, returns are not. Therefore it seems to me that trying to maximise returns is an heuristic managers use to avoid the situation in which they jump too high and then they are not able to catch the fruit
2- The performance of the manager is judged in terms of returns. While it is optimal for the firm to take every project until MC=MR, this will cause the ROI or the ROE to decrease.

7. I understand you fruit tree example Nick. However they way you describe it is a very rare case indeed, and not the conditions where return-maximisation is at play.

In your example there is no ability to delay. The tree is already there, the fruit is there. If it doesn't get picked today I can't pick it tomorrow (or maybe I can, and then my interpretation holds and you leave some fruit on the tree for a later date).

But this is not usually the case. Usually I will have to decide when and what type of trees to plant in the first place. I make this decision by considering how best to maximise my rate of return on costs.

Further, you seem to imply that the revenue from selling fruit occurs instantly. But what if that is not the case. What if I have to incur the costs today, but don't sell for a year (I'm making jam). And in the mean time I will have the opportunity to pick fruit many times?

Lastly, the model does explicitly show that there needs to be some returns to scale of firm production to take place. If the real world is like my model suggest, then a situation such as your example would be extremely rare, to the point where no farmer would invest in creating such conditions.

3. "yet there are almost no examples of markets where the goods produced by different firms are perfectly interchangeable"

I'm not really understanding this. It appears to me that in lot's of markets (household goods, cosmetics, electronics) firms basically produce the same goods (washing up liquid, shampoo, washing machines) and that although 'features' are a form of differentiation (scent, vitamin B whatever, cycle times) when it comes down to it most people base their decisions on the price of what are essentially interchangeable products.

Although I might have got the wrong end of the stick here.

1. Yeah, that's basically right. A lot of stuff is very similar. But I can't think of one example where they are identical.

I a world of similar goods we have a continuum of products, where any market definition will arbitrarily draws a boundary.

2. Price is important, but availability, brand preference and a host of other factors come into play otherwise supermarkets wouldn't even carry non-generic products.

4. Why would anyone try to maximize anything besides profits or expected profits with some sort of risk aversion?

I'm not saying there isn't a reason, but the theory for profit maximization explanation is simple. They maximize profits to maximize payoffs.

Why would firm owner's want to maximize revenue? Unless we are in a world with a principal-agent problem, where the firm owner incentives the manager to maximize revenue, thus still maximizing the owners' profits. But that is not the direction you appear to be going.

1. I'm going to just assume you haven't read the post or the linked working paper. The new theory is that firms maximise their rate of return on costs, not their revenue. I also explained that the basis for such as theory is the work on real options, which you are also welcome to read up on, that demonstrates that this is a firm value maximising condition under very realistic conditions of irreversible investment, uncertainty, and an ability to delay.

5. Assuming a firm has a fixed amount to invest at any one time surely maximising the total size of the return (profit) and the rate of return (return) are the same thing. It is true that when new expenditure is considered in a firm there is a close scrutiny of the return on investment but surely this is because each new potential expenditure is usually for a different amount (a different fraction of the total available) so rate of return is a better relative metric than absolute level of return.

The distinctions I suppose is risk. A company might choose to invest less than all its available cash because the potential rate of return available does not warrant the necessary risk where as a lesser project might have a better risk/reward ratio.

1. "Assuming a firm has a fixed amount to invest at any one time surely maximising the total size of the return (profit) and the rate of return (return) are the same thing."

This is certainly true, but the existence of a cost curve implies that firms do not have a fixed amount to invest, and that they can change their investment along the cost curve. Thus, in this sense the objectives of profits vs returns, as we show, lead to different output choices.

6. It looks like an economist has actually read a 10K filing or corporate press release. I took a couple of terms as an undergraduate and found a huge disconnect between how individuals, investors and corporations made their decisions and what they were teaching me in class. I was familiar with accounting, so it was a shock to find so many conflicts between basic accounting concepts and how people used them in decision making and economic theory. It's great to see a few economists examining their assumptions and trying to incorporate real world knowledge. Even the quantum theorists realized that they had to predict classical physics at the statistical extreme.

7. Your use of the terminology "Theory of the Firm" is misleading. Most microeconomists use that term to mean "theory of the boundaries of the firm", which investigates why firms should exist at all and focuses on limitations of contracting or complimentarities between factors. Although, I should say that it is typical (not universal) to assume that the firm's objective is profits, no one views this as foundational to the theory, but just a simplifying assumption.

What you are doing, on the other hand, is a new theory of competitive markets based on a new (more accurate?) understanding of firm incentives. That's something different. I will say that I need to think whether I like your formulation or not: it sounds a lot like some theories of imperfect competition, such as monopolistic competition which I am in fact a fan of.

1. "Although, I should say that it is typical (not universal) to assume that the firm's objective is profits, no one views this as foundational to the theory, but just a simplifying assumption"

Not sure what you are getting at here. Remember, models are merely an assembly of assumptions - the assumptions are the model so to speak. Therefore if there is a fairly radical change in behaviour from a change to the assumption of firm objective, then clearly it is a foundation of the theory, for it determines all the predictions.

"What you are doing, on the other hand, is a new theory of competitive markets based on a new (more accurate?) understanding of firm incentives."

Thanks, I hope so. The aggregation question here is interesting. We obviously plan to do more work on this. But as far as the existence of a firm, and firm boundaries, the contribution here is that there must exist some economies of scale for a firm (a production unit of any type) to exist at all. That seems pretty important.

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9. So, if I understand this correctly, the whole point is that firms maximize p(q)*q/c(q) instead of usual p(q)*q - c(q). This is followed by lots of needlessly complicated calculus (e.g. what's the point of time integral in equation 1, when everything afterwards is static?).

Why should this be the firm's objective? Do you really claim that in a static setting, facing exclusive choice between two projects, one with cost 1$and payoff 2$, the other with cost 1 million $and payoff 1.5 million$, a firm should/would choose the first? I see absolutely no reason for that to be true.

As for other criticisms of mainstream theory, sorry but they're mostly false. Few examples:

* Returns vs. profits - we usually speak of returns in dynamic setting, with payoffs coming later than investments. In such case, standard theory says that firms should maximize their value (i.e. discounted sum of future profits), not just immediate profit.

* Real options are presented as disproving standard theory, but in fact are perfectly consistent with it, once one explicitly adds irreversibilities to the standard model (with value maximization, Bellman equations and everything).

* You say that in your model "All firms operate in their own markets, whose demand schedule is influenced by the offerings in substitute markets." - yet that's exactly what formal models of monopolistic competition such as Dixit-Stiglitz (1977) are about. Nothing new here.

1. "what's the point of time integral in equation 1, when everything afterwards is static?"

The point of doing so is to make it clear the the firm makes forward-looking decisions at all time. The whole nature of the rate of return is that it is a measure per period of time. We simplify to Eq (6) because decisions are made at all points in time. Maybe we could treat p(q) as an expectation, but I don't think that changes much.

"Why should this be the firm's objective? Do you really claim that in a static setting, facing exclusive choice between two projects, one with cost 1$and payoff 2$, the other with cost 1 million $and payoff 1.5 million$, a firm should/would choose the first? I see absolutely no reason for that to be true."

Yeah they will choose the first. When they have made their return due to the increased value of their business, they will look at more investments. Or do you believe these types of massively high return (but small) investments are merely left hanging?

"Returns vs. profits - we usually speak of returns in dynamic setting, with payoffs coming later than investments. In such case, standard theory says that firms should maximize their value (i.e. discounted sum of future profits), not just immediate profit."

Yeah sure. If you have a fixed amount to invest then maximising profits and the rate of return is the same. However, the existence of a cost curve for a firm implies they can vary the amount they choose to invest in any production activity. Thus, if they can vary their choice of the size of their investment - meaning cost curves exist - then they will do so at the point that maximises the rate of return.

Again, the existence of these curve really relies on relaxing the assumptions free entry and no ability to delay. None of these assumptions make any sense in almost every real life setting. That's the standard theory. By not imposing these assumptions you get return-seeking as a value-maximising proposition.

"Real options are presented as disproving standard theory, but in fact are perfectly consistent with it, once one explicitly adds irreversibilities to the standard model (with value maximization, Bellman equations and everything)."

Nor did we say that standard theory is disproved - only that it is not generally applicable, and relies on the special case when maximising profits does maximise the rate of return. All the evidence points to firm behaviour being consistent with conditions of real options, rather than on the standard model. Thus we question the usefulness of the standard model, and note that no alternative has been explored in detail.

We make the point that under conditions of real options that value maximisation occurs when firms maximise their total rate of return. So why hadn't this entered a model of firm production choices yet?

"* You say that in your model "All firms operate in their own markets, whose demand schedule is influenced by the offerings in substitute markets." - yet that's exactly what formal models of monopolistic competition such as Dixit-Stiglitz (1977) are about. Nothing new here."

Actually, the free entry and exit assumption in monopolistic competition rules out conditions of irreversibility, ability to delay etc (which is why it maintains the MR-MC condition of profit maximisation). This assumption about market conditions is, in my view, a rather gargantuan conceptual leap.

If we rule out the standard rather restrictive assumptions about market conditions then we fall back on to return-maximising as the value maximising objective of a firm, as per real options.

2. To be more clear, we do not claim that a firm-specific demand curve is new, but that is useful for our model because it allows us to vary a single parameter to represent the degree of competition.

How firms respond to this, under the less restrictive assumptions about entry etc, is what is new.

3. "The point of doing so is to make it clear the the firm makes forward-looking decisions at all time."

But it doesn't, because there's nothing that links individual time periods together. If you added let's say capital accumulation with some adjustment costs, then you would have truly forward-looking behavior - but even then, the objective function (discounted average of static within-period rates of return?) makes little sense.

"Thus, if they can vary their choice of the size of their investment - meaning cost curves exist - then they will do so at the point that maximises the rate of return."

Again, I don't see why that should be the case. Even when firm can adjust continuously its inputs, it's possible that return-maximizing choice will result in small-scale operation with large relative return but low absolute profit, as in my example (in fact it's pretty much a mathematical necessity that it will operate at smaller scale than profit-maximizing firm). Moreover, if financial markets evaluate firm's value as discounted sum of future profits, any other strategy than period-by-period profit-maximization in your model will decrease, not increase the firm's value.

"Again, the existence of these curve really relies on relaxing the assumptions free entry and no ability to delay."

Cost curves are derived from the firm's dual problem (minimize cost of input factors given required level of output and technological constraints), and as such doesn't require any assumptions about free entry, delay, etc. Since your model is static and doesn't deal explicitly with any of those either, I must confess I don't understand what you're getting at here.

"All the evidence points to firm behaviour being consistent with conditions of real options, rather than on the standard model."

But real options ARE part of the standard model, once dynamics and irreversibility are properly added to the model. In real options literature, the objective function is typically to maximize discounted sum of profits. I'm not sure what you mean by "under conditions of real options that value maximisation occurs when firms maximise their total rate of return." In these models, value maximization occurs when discounted sum of profits is maximized, by definition. It's true that one way of presenting the intuition behind real options is to say that given the option to wait, the required return for the project to be undertaken is higher than the one given by vanilla NPV criterion. That's not the same as maximizing "total return".

"Actually, the free entry and exit assumption in monopolistic competition rules out conditions of irreversibility, ability to delay etc (which is why it maintains the MR-MC condition of profit maximisation)."

Monopolistic competition doesn't require free entry (e.g. in many DSGE models, you have fixed number of monopolistically-competitive firms making positive profits), and definitely doesn't imply MR=MC. In fact, it leads to mark-up pricing, with mark-up determined by the demand elasticity of substitution between individual goods (the more likely are consumers to substitute between goods, the lower is markup).

10. If we restrict our problem to commodity markets and firms dealing with commodities (metals for example), we would see a far more complex picture emerging. MR=MC is actually meaningless here, as one would notice that commodity prices in this part of the cycle has a drooping nature over a five year horizon and still investments are happening all over the world, which is essentially shifting the supply curve further to the right while the demand curve isn't making any change. The firms are stuck in the middle as taking out capacity which is less efficient or less productive takes time and sometimes not possible (like a whole town's livelihood would change if a large plant is shutdown). So the overhang of capacity stays while new investments are being made unabated largely due to the current financial conditions. The impact of all this on prices is bad, but the firms are stuck in the middle.

11. Maybe the accountants already have a theory of the firm. If that is so than economists ignorant of accounting could only come up with some thing bastardized version.

12. Ahhh, but what kind of firm? There are different kinds of firms. Two examples are manufacturers and banks. Both are firms.

13. IRR is not valid criterion when choosing among exclusive projects (every textbook, and even even Wikipedia says so). And when the firm chooses output, it is essentially choosing from mutually exclusive "projects".

14. "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."

Can you point to cases where the pattern of land development requires this model of behaviour to explain it? Do landowners ever have the option to redevelop existing land, so being able to go from 3 storey to 10 storey buildings?

15. The reason why bang for your buck matters more than bang alone is the uncertainty, I think. The bang on an investment only actually becomes known for definite at some point in the future. Buck is committed prior to fruition. This is why, contra to the example given in comments above, firms often (but not always to the fullest degree) opt for cost minimization and rent seeking.

16. I need to have another look at the paper but to get these results you seem to need a strong limit on gearing- either via credit constraints or risk aversion. Otherwise, maximizing return on equity would entail near standard behavior- so long as marginal returns are above the cost of credit, borrowing to fund capacity expansion will increase return on equity. Now if there is a fixed gearing ratio then your result holds but conversely if credit is available subject to average or marginal returns being above some (perhaps increasing in gearing) threshold then high return projects which decrease average return on capital may increase return on equity if marginal returns are above the threshold value and the capacity expansion is then largely funded via credit. Modelling credit constraints using some realistic formula may provide ambiguity in firm behavior such that standard, and non-standard results as developed in your paper are possible.

1. Good comment. Yep. All of what you said is true.

I certainly have considered the effect of gearing. Your point about a fixed gearing ratio does rescue our model.

Although it is probably not clear in the linked working paper, in our model a firm chooses capital inputs and the output level simultaneously. We might consider they choose the maximum risk-adjusted leverage as well. Thus to expand output, and in the process increase input costs, requires additional input of equity at the previous leverage ratio.

I discussed our rough approach (that we have since refined and incorporated in the paper) here
http://ckmurray.blogspot.com.au/2014/02/the-firm-existence-puzzle-and-how-we.html

The whole idea of a capital constraint becomes obviously crucial to our model. Which is strange, because economics is apparently the study of scarcity, yet in partial equilibrium analysis we often forget that. We typically invoke arbitrary time periods to handle scarcity (short run models etc).

If you haven't read my other follow up post, you might find it interesting
http://ckmurray.blogspot.com.au/2014/01/why-is-return-seeking-optimal.html