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COSTS
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by Valentino Piana (2003) |
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A related
paper: The production function
of students' grade
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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. 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). 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:
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). To make experiments with different situations, you can use the free Costs software, distributed by the Economics Web Institute. 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:
where q is the quantity
of good. Average costs (AC) are thus the following:
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:
First
case: q = 10 TC
= 100 + 5x10 = 150 Second
case: q = 100 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:
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 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. The
main costs that a manufacturer faces can be summarised in the following
table:
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). The
basic costs that a family-run small shop pays are the following:
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. 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 (for a performance-based exit analysis see here). 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. 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.
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 Return to scale: an empirical estimation in Pakistan Decreasing return to scale in fishery: an estimation in New Zealand Costs in manufacture from aggregated balance sheets
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