### Cars and capacity

More careful thinking in the field of accountancy is bringing it closer to economics

Every student of economics is taught that the essential first step in deciding the price of an item is to determine its marginal cost. But in reality, calculations of marginal costs play almost no role in business decision making. When firms calculate the costs of the different items they sell, they use a management accounting system which allocates the total costs of the business to individual products.

And there seems to be good reason for this. Virtually every calculation by a firm of its marginal costs that I have seem comes up with a figure that is extremely low. Pricing by reference to marginal cost is a sure fire recipe for going bust.

But this should not be true. The same economic theory explains the relationship between average and marginal costs. That relationship is determined by the extent of economies of scale. Marginal costs are below average costs if these costs fall as output increases, and vice versa. And, the mathematics also defines the extent of the divergence. Suppose, for example, increasing output by a factor of five would lead to a halving of unit costs. This is an extreme case of scale economies. You might get up to this sort of figure in the manufacture of large aircraft, but not in many other businesses. Certainly there could be no industry in which scale economies were as extensive as that and where both large and small firms survived. But even there, marginal costs would only be around 15% less than average costs. If scale economies were less extreme, the divergence would be much smaller.

So why do people often come up with such low numbers? It is quite common – in a manufacturing process for estimates of the marginal cost of output to be no more than half the number that management accountants would attribute to the same output through their cost allocation system. In some of network industries, like rail or telecom, where regulation and price control has made it important to reach good estimates of marginal cost, the answers that are derived are as low as 10% or 20% of the costs the business needs to recover in order to pay its way.

There are two explanations of this inconsistency. Each of them points to mistakes in the way these calculations are typically made. The analysis that describes the relationship between average and marginal costs assumes that the firm has set its capacity correctly. If there is too much capacity, then the distinction between short and long run marginal costs becomes important. Long run marginal cost is a measurement of marginal cost that takes account of the increased capacity that increased demand requires in the long run. Short run marginal cost simply looks at the direct costs of additional output. If you can produce that additional output within additional capacity, then short run marginal cost appears to be very low.

But that situation is really much less common than it seems. There are very few firms in which it is sensible to plan to run a plant at full capacity all the time. You need additional capacity to cope with fluctuations in demand, to provide for breakdowns and contingencies, to accommodate growth in demand. That security margin brings a benefit, and imposes a cost. If you factor into your calculation the costs of eating into the security margin, you find that short run marginal cost is much higher, and is once more equal to long run marginal cost. The reason you incur expenditure on extra capacity in the long run is that the costs of having it are less than the benefits of having that margin of flexibility in your operations.

There is an apparent paradox there. Most economists would tell you that short run marginal cost is what you should really look at in thinking about prices, and they are right. But long run marginal costs are actually often a better guide to the true level of short run marginal costs than the calculations of short run marginal costs which are made.

Then there is a second reason why average cost seems to be higher than marginal cost. The way you usually calculate average cost is from the top down – you start with the total costs of the business and you allocate them to individual products. But when you calculate marginal costs, you do it from the bottom up – you look at the costs of each individual element and you make your estimate by reference to that. The first of these is typically characterised by errors of inclusion – you put too many things in. The second is typically characterised by errors of exclusion – you leave too many things out.

Take the chairman\’s car, for example. When you measure average costs across the business, you simply lump expenditure on that with other overhead costs and allocate them across all the products the firm makes. But no one calculating marginal costs ever thinks \”if output increases the chairman will probably buy himself a bigger car and I\’d better attribute some of the costs of that to the model 330 widget\”. So expenditure on the chairman\’s car gets included in estimates of average costs and excluded from estimates of marginal cost. If common costs which are not immediately related to specific outputs are large – which is often true – then this is a major issue.

Reality, of course, lies somewhere in between. Obviously the chairman does not need a bigger car to enable the firm to make more model 330 widgets. But companies with a larger overall scale of business have – and genuinely require – a large level of these central overhead costs. One of the helpful contributions of activity based accounting to modern management thinking is that it requires you to think much more carefully about the things that cause overhead expenditures to be incurred. And when you do that, you include more in marginal costs, less in average costs, and the gap between the two starts to narrow. And that might start to narrow the gap between accountants and economists as well.

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