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COSTS
 

 

by Valentino Piana (2003)

     
 
 

Contents


 
 
1. Significance
 
 
2. Cost categories
 
 
3. Production costs
 
 
4.Total and average costs
 
 
5. Marginal costs
 
 
6. A manufacturer's perspective
 
  7. A retailer's perspective  
  8. A building business perspective  
 
9. The temporal profile of costs: investment, cost of operations, sunk costs
 
 
10. Profitability and shut down rules
 
  11. Is refusal to sell a marginal cost issue?  
  12. Spatial differentiation of production costs  
 
13. Formal models
 
 
14. Data
 
 

 

Appendix: Some simple relations between marginal costs and average costs

Link to a paper on Activity Based Costing
quoting the present paper on costs.

 
 
A related paper: The production function of students' grade
 
 
A related paper: Firm-specific fixed costs and variable costs: a model of market dynamics
 
 
 
 

Significance

The burden sustained in order to perform a certain activity, to carry out a certain production, to achieve certain goals.

In a balance sheet, costs raise commercial liabilities to be settled. They should not be confused with money outflows.

By contrast, in economics, most formal models ignore this distinction between costs and payments.

Cost categories

Actual costs refer to real transactions, wherease opportunity costs refer to the alternative taken into consideration by decision makers who might want to choose the line of activity which minimise the costs. From an external point of view, it is difficult to ascertain which are the alternative considered.

Discretionary costs are not strictly necessary for current production but correspond to strategic goals (e.g. improving the firm's image through an advertising institutional campaing).

Attributed costs are computed values from accountancy that are conventionally attributed to products as part of the process trying to establish profitable prices by appropriate routines.

Production costs

Given a specific product version, production costs are usually classified according to their responsiveness to different levels of production attained.

Fixed costs are simply not responsive to production levels.

If there are only fixed costs, the total costs follow this rule:


For instance, the cost of renting an office is a fixed cost, since usually the contract fixes it for a certain period of time (say one year), without any reference to the income produced by the operations that take place in the same office.

The firm deciding to rent this office, however, will have usually expected to be able to afford it as well as to be reasonably sure that it will not be too small for the kind of operation it intends to carry out.

This brings us to an important conclusion: a very common situation is that of quasi-fixed costs. They are flat in a certain range of (expected) production but they are forced to jump to higher levels if certain thresholds are overcome. Near these thresholds, in fact, quality deterioration of output and other negative phenomena take place.

Symmetrically, below other minimum thresholds in level of activities, the same costs become unaffordable and will probably be reduced. Here you have the graph of total costs when there are only quasi-fixed costs:


Variable costs grow with higher levels of production (proportionally or not). If there are only variable costs, at zero production the total costs will be zero. Total costs will follow for instance this rule:


In particular, economies of scale describe situation when the total costs rise less than proportionally to production increases, as you see in the following diagram:


Dis-economies of scale represent the opposite situation:


Constant return to scale are the intermediate situation in which the growth in production is exactly matched by the same percentage increase in total costs, i.e. elacticity of costs to production levels is 1:

In this case, productivity is constant.

To understand the sources of economies of scale is helpful to consider that total costs for production inputs depends on two components: the quantity and the price of the inputs.

Accordingly, it is often useful to distinguish two broad reasons for cost to rise: an increase of the input quantity or a soaring price for input. This allow for distinguishing different reasons for costs behaviours in reaction to changes in production levels.

In particular, economies of scale can be due:

a) to savings in average physical quantity of input when the production is higher (e.g. electricity dispersion is lower in percentage when the electricity throughput is high);

b) to reduction in prices paid when buying larger quantities (e.g. because of stronger power in purchase negotiation).

If sales increase, variable costs rise and fixed costs remain the same. To make experiments with different situations, you can use the free Costs software, distributed by the Economics Web Institute.

Total and average costs

Total costs are the sum of all costs. By dividing the total costs by the quantity produces, one gets the average costs: how much a unit of production costs ("unit cost").

Average costs can be directly compared with price to compute profitability: if the price is higher than average cost, the production is profitable.

Total profits will be given by multiplying the average profit with the quantity produced and sold.

Identically, total profits can be obtain as total revenues less total costs.

The relationship between total revenue and total costs depending on the production level is analysed by the so-called "break-even analysis".

Let's see mathematically what component crucially influences average costs at two widely different levels of production.

In the simplified situation of a production process characterised by a fixed cost (F) plus a proportionally-growing variable cost (VC), total costs (TC) are described by the easy formulas below:


TC = F + VC×q

where q is the quantity of good.

Average costs (AC) are thus the following:


AC= TC/q = F/q + VC

The first term of the right side (F/q) decreases systematically the higher the production level (q). At low production levels, this reduction is quantitatively relevant wherease for a high q it is not.

In fact, for high q, the average cost is practically equal to variable cost VC.

A numerical example of fixed, variable and total costs:


F = 100
VC = 5

First case: q = 10

TC = 100 + 5x10 = 150
AC = 150/10 = 15 = 100/10 + 5

Second case: q = 100
TC = 100 + 5x100 = 600
AC = 600/100 = 6

For low levels of production, fixed costs are major determinants of average costs whereas for high levels of production, variable costs dominate.

The percentage composition of total cost is, in our example, the following:

Cost component q = 10 q = 100
F 66% 16%
VC 34% 84%
Total 100% 100%

To investigate what happens if many firms are competing with different combinations of fixed and variable costs, see this paper and the related software.

Marginal costs

Marginal costs indicate by how much the total costs changes because of modification in the production level by one unit.

When there are only fixed costs, marginal cost will be zero: any increase of production does not change costs.

If there are only proportionally-growing variable costs, marginal costs will be equal to variable costs.

To see which are the relationships among marginal, average and total costs, you can use the free Costs software, distributed by the Economics Web Institute.

A manufacturer's perspective

The main costs that a manufacturer faces can be summarised in the following table:

Cost item Cost category Justification
Raw materials to be processed Variable (proportionally) Production recipe: any un-proportional change would impact the features of the product
Semi-manufactured components to be assembled Variable (proportionally) Production recipe
Energy Variable (less than proportionally) Physical properties produce economies of scale
Personnel (direct labour) Variable (proportionally)

Constant productivity of people directly involved in production

Particularly flexibility-oriented legal contracts with the labour force

Personnel (indirect labour) Quasi-fixed The size of necessary administrative personnel (and of other indirect labour) doesn't change so much if production incrementally changes. Discrete jump will happen when the overall scale of production drastically changes.
Plant rent Fixed The typical contract of rent makes no reference to effective production levels
Amortization of capital goods Fixed Fiscal and accountancy rules
Policy costs (advertising, R&D,...) Fixed or quasi-fixed Discretionary costs
Distribution cost Variable (proportionally) plus a fixed component

Sale representatives usually are paid in percentage to success plus a fixed fee.

Sometimes supermarkets would require a "listing fee" to be admitted on the shelves and require a rebate at the end of the year, based on the amount of sales done.

Shipping and transport Variable (more or less proportionally) Shipping is proportional to volume sent and packed. Transport would also depend on the distance to be covered (and speed of delivery). Both elements alternate randomly across orders.
Participation to trade fairs and promotion materials Fixed Discretionary cost, whose effectiveness depend on many elements.

The above-mentioned table is just a rough and conditional description. It is only meant for easy introduction to the problem - often implicitly assuming many specific hypotheses.

For instance, the labour costs can be fixed costs, quasi-fixed costs or variable costs depending on the legal contracts of employment and the rules governing wages.

General firm strategies have deep impact on costs. For instance, if a firm in a high-wage country exports a lot in a low-wage country, it may consider a Foreign Direct Investment to setup a factory there where to carry out the final - or most labour-intensive - phases (e.g. assembly or labelling).

Taxes are not costs in accountancy terms: they are paid out of added value, i.e. the difference between turn-over and costs. They reduce the profits earned by the firms.

A retailer's perspective

The basic costs that a family-run small shop pays are the following:

Cost item Cost category Justification
Goods in sales Variable (proportionally) Price list of wholesaler or producer
Shop space (if rented) Fixed Proportional to square metres, not to items sold
Shop space (if in ownership) None There is the opportunity cost to use this space otherwise but this does not lead to transactions
Lighting Fixed Proportional to the number of light bulbs in the shop, not to items sold
Heating, cooling and ventilation Fixed Largely determined by the climatic conditions, opening hours, target level of comfort, energy prices; no relation with sales

Total revenues less all these costs constitute a gross profit, comprehensive, however, of the time the owner and the family spend working there and of the shop space (if in ownership). This logically heterogeneous aggregate is in fact indivisible because it is received by the same people and does not vary according to the external markets of labour and commercial spaces. The market of a good where seller and buyer are the same person is not perfectly competitive, nor linked to others.

Large retailers chains (including supermarkets and hypermarkets) negotiate the purchasing prices with producers, often achieving rabates in function of the sold quantities, to the effect that goods in sales are less-than-proportional variable costs. Logistics is a major cost component, largely dependent on its spatial organization and distances travelled by wares. Personnel is usually hired as in manufacturing sector. Other cost components are somehow similar to the abovementioned analysis.

A building business perspective

In the building industry, it is not uncommon that the delivered product is "one" building, not many replicas as in manufacturing. So sales are "one" and this prevents the conventional categories of variable costs to apply (since sales are not many). In this case, variability can be looked for with respect of other quantitative parametres, but the conventional analysis remains severely limited.

The basic costs that a building firm pays to build one residential building are - as a very simple approximation - the following:

Cost item Cost category Justification
Legal right to build Fixed Dependent on the law; in certain countries linked to the value of the building, in other independent from in.
Land Proportional to land area Land is purchased depending on the quantity. However, land has a hugely differentiated price depending on its location, legal status and year of purchase.
Raw materials and building components Fixed (e.g. for foundations) and variable (e.g. for number of floors) Established parametrically in the final project of the building, separately for each component. Usually the building company participates to a bid, where has to express its (lowest) aggregate price for delivering the building, then negotiates with sub-contractors the actual prices of purchase. Very different costs depend on the quality and technology applied.
Personnel (direct labour) Variable (proportionally) to time of use

Many uncertainties surround the duration of building works. Depending on the work contract, this variability will impact the business or the worker.

Personnel (indirect labour) Quasi-fixed The size of necessary administrative personnel (and of other indirect labour) doesn't change so much if production incrementally changes.
Financial costs

Variable but not in respect to the "quantity" produced but to its economic value and many more elements

Proportional to the economic dimension of the construction, to the financial leverage used, to the (fixed or variable) interest rate paid, to the time of construction and payback (which in turn depends on seleability of the building spaces)

More in general, urban transformation and regeneration requires not only new buildings but accessibility, mobility services, new infrastructure and many components to be financially, economically, socially, envioronmentally and culturally sustainable.

The temporal profile of costs: investment, cost of operations, sunk costs

In most cases, a firm has first to sustain certain costs (investment) before any production takes place (e.g. R&D, machinery investment). These costs are called investment costs.

These costs should be recovered within a reasonable period of operative activity (production). In certain cases, after the full exploitation of production opportunities there is a further una-tantum revenue for asset sale.

For instance, when a firm buys an office, it invests a certain amount of money. It will use it for a certain period, say 10 years, during which it saves the rent it would have paid if it didn't own the office, thus (totally or partially) recovering the initial cost. At the end of the 10-years period, it can decide to shut down operations and it will be able to sell the office (una-tantum revenue).

Sunk costs are investment costs incurred before a certain activity takes place which cannot be recovered by the possible sale of the asset they produced.

Highly specific investment (e.g. R&D) are usually sunk costs.

Sunk costs represent barriers to exit. A firm which has incurred in high sunk costs will have difficulties in deciding to exit the market even if it sees good opportunities outside.

Conversely, a firm that is deciding whether to enter into a certain business will have to consider with a particular attention the sunk costs and the risk that during the operations period they might not be recovered. Sunk costs, in this perspective, represent barriers to entry.

In the case of an exporter, an example of sunk costs could be the costs of analysing the market and of exploring opportunities and seeking commercial partners.

"The more the setting up of an activity is innovative, the more is it likely to involve long periods of gestation, and thus higher sunk costs" states Prof. Sergio Bruno in "The economics of ex-ante coordination".

High sunk costs makes an investment irreversible, what, couple with uncertainty about the future, impacts the level of investment by industry, as this empirical analysis points out.

A narrative example of sunk costs in a real-world situation is given here.

Profitability and shut down rules

In one period of time, total profits are given by total revenue less total costs. If they are negative, the firm will look into the future and see whether there is a possible reversal of this situation. Perhaps it is carrying out investments that are large now but that can produce effects later on. But it can also take into consideration the possibility of shut down operations and exit the market. It will, for instance, evaluate the average variable costs and the current price. If the price is lower, then for every units of production the price doesn't recover even the direct costs. A very critical situation.

But exiting a market is a strategic decision that cannot be taken wholehearted and it should be put into the more larger picture of industrial dynamics, where exit dynamics is related to more than just cost considerations, as for instance empirically demonstrated in this paper.

To see the balance between entry and exit in a market where fixed costs and variable costs are firm-specific see this paper and the related software.

In particular, cashflow and debt problems play a crucial role in increasing the risk of default, because firms take credit to fund both current business activities and investment (e.g. in fixed assets). The availability of credit depends on creditworthiness, which in turn is linked to real and perceived risk in the specific market and country-wide. In other terms, bankruptcy can happen even if the price cover the costs, but the firm has become, for other reasons, unreliable and nobody provides necessary credit.

In a less drammatic condition, multiproduct firms (selling more than one product) might decide to sell some of its products at a price lower than unitary cost (or of marginal cost), recovering the losses by selling more of the others. This is very common for large retailers and supermarkets which promote (temporarily or permanently) their overall sales by demonstrating exceptionally cheap some reference products (be they well known industrial brands or phantasy brands of their own). Far from being a critical situation, this competitive strategy is a sign of strength.

Indeed, if below-cost prices are used to eliminate competitors (for which the product at hand represents a very substantial share in sales), this predatory price strategy is effective in two versions: either the price bounces back to higher-than-cost after the competitor has shut down or it is kept constantly lower-than-cost to keep competitors out of the market (and balancing the losses on it with margins on the other products sold).

Is refusal to sell a marginal cost issue?

The neoclassical theory of costs assumes that marginal costs are rising and that producers will refuse to sell a further unit after the equilibrium quantity because the price does not cover the larger marginal cost it requires. An exploration of this case and of realistic reasons to refuse to sell is here.

Spatial differentiation of production costs

The cost of production can be widely different in geopolitical areas where the labour cost, the energy cost, the land cost, interest rates, and other prices are different (thus violating the Purchasing Parity theory). In principle quantities should be the same (material input needed, intermediate goods, hours of labour, etc.). In fact, the productivity of people and machine is largely dependent on historical reasons, with path dependency and place-dependency, to the effect that also quantities can widely vary across areas.

Appendix: Some simple relations between marginal costs and average costs

If to an average of 5, you add a 6, the new average will be higher than 5. If the cost of a further unit is higher than the average cost of all preceding units, the average cost will rise. If marginal costs are higher than average costs, the "average cost curve" will be upward sloping.

You can experiment with these relationship through this MS Excel file.

 

Formal models

Costs: a software to understand cost structures

Cost structures and their impact on prices in a monopoly market

R&D, advertising and other costs in dynamic competition

Marginal and average costs: a spreadsheet to understand relationships

Isoquants: a software for understanding the neoclassical production choice theory

Return to scale: an empirical estimation in UK

Data

Costs in manufacture from aggregated balance sheets

 

 

 
 
 
 
Key concepts
  Industrial dynamics  
  World trade  
 
 
 
 
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