The conventional ‘upward sloping’ supply curve is known by everyone from an econ101 student to a professional economist. The curve posits a positive relationship between price and quantity supplied – in order to increase the quantity supplied, a higher price must be offered. What is less commonly known, however, is that an upward sloping supply curve is actually incredibly hard to justify, both in theory and in practice.
Behind the curve lies the proposition that production costs per unit increase as output increases. This makes the ‘upward slope’ a necessity: since an item costs more to produce, a higher price must be charged as production increases. Microeconomic theory posits that this relationship holds in both the short and long run. However, all signs say this can’t be true.
The Short Run
The neoclassical idea is that firms can only increase one factor in the short run, which gives birth to the increasing marginal cost argument – returns to production diminish as more and more is ‘squeezed’ out of the fixed input. Is this how production behaves?
I have previously commented on Piero Sraffa’s excellent critique of the idea of increasing marginal costs in the short run. Sraffa’s argument was two pronged, depending on how we define a ‘firm’ or ‘industry.’
Sraffa argued If we define an industry narrowly, such as a single firm, it turns out firms generally have a lot of spare capacity and can quickly employ previously idle resources to expand all inputs at once. This belies the traditional justification for decreasing returns – if we expand inputs simultaneously, we should expect roughly constant increases in output as a result.
Sraffa went on to argue that we could define an industry broadly enough that it’s reasonable to say a factor is fixed in the short run. This would be because, for a large industry, a new factor would have to be converted from other uses before it could be employed. Hence, diminishing returns may be possible. However, at this point it is no longer possible to neglect the collateral effects caused by changes in firm’s expenditure and output: the partial equilibrium method becomes contradictory, and the various curves – demand, supply, average cost – cannot move independently, which is a key assumption of the theory. So the theory as a whole is no longer appropriate.
So the idea doesn’t hold up in the short run, except in the extremely small number of cases that lie between the ‘narrow’ and ‘broad’ definitions. But what about the long run?
The Long Run
If you learn producer theory from the bottom up, one of the assumptions you start with is that inputs and outputs are infinitely divisible; in other words, they are like clay. They are also homogeneous, and available at a set price. Based on these assumptions, it is reasonable to assume that in a short run – when one factor is fixed – there may be increasing marginal costs. At this point I would defer to Sraffa’s above critique.
However, when we move to the long run, it’s incredibly hard to justify increasing MC even within the confines of the theory. Textbooks will generally assume the standard production function, which looks like this:
The downward sloping portion – for which costs fall as output rises – will generally be justified by ‘Economies of Scale (EoS).’ But what causes EoS? Bulk buying is one example, but this can’t apply because prices are taken as a given. Another is indivisibilities - if you buy a big machine it takes a while before you fully utilise it – but this quite clearly contradicts the assumption of perfectly divisible inputs. Yet another, the increasing returns to the division of labour, contradicts the assumption of homogeneous inputs.
Similarly, the upward sloping portion is then justified by ‘Diseconomies of Scale (DoS).’ Examples of this are generally few and far between – DoS is, after all, the strange proposition that firms simply become incompetent at some level – but again they tend to contradict our assumptions. One example is managerial difficulties – who is the manager if labour is homogeneous?
In fact, it turns out that few, if any, of the explanations for either EoS or DoS hold up under the available assumptions. If you increase a homogeneous perfectly divisible mass of inputs a certain amount, there is no reason to expect anything other than a constant, proportional increase in put: in other words, constant returns to scale.
Unsurprisingly, it is true that the overwhelming majority of firms report constant or falling returns to scale. Walking down a high street in a capitalist country, it’s hard to deny that firms have the available goods to accommodate an increase in demand without a rise in cost; factories are designed in a similar fashion. Furthermore, in the long run a firm is likely to respond to an increase in demand by opening up more branches, rather than simply increasing prices.
So what’s the problem? The proposition that demand determines outputs and supply determines price is logically, intuitively and empirically reasonable in any time period and for most industries. Why can’t economists just tilt their supply curve 45 degrees to the right?
Well, at this point a few things become apparent. The theory of the firm becomes indeterminant: one of economist’s beloved negative feedback loops that allows the economy to self-equilibrate is gone, as firm size is not limited by production costs. Hence, the marginal theory of the firm goes from explaining everything – from firm size to income distribution – to explaining very little. This also makes explicit the idea that output in the economy is driven by demand, both in the short and long run, which contradicts conventional macro theory, where demand only matters because prices are sticky.
Overall, a flat supply curve turns the conventional story told in neoclassical economics, where the economy is self-equilibrating, bar a few frictions, to one where many key variables – wages, output, firm size – go from being at the equilibrium or ‘natural’ level, into one where they are largely arbitrary. It’s easy to see why economists would resist this.