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  • Writer's pictureEmily Dow

ExplainedByED: the loss making firm and the long run

A firm operating while making a loss was always nonsensical to me. The first time I was told there are firms who consciously operate while their profits are negative genuinely hurt my head. Despite this, it was the economic concept which hooked my curiosity and made me fall in love with the subject. Economists can quickly evict any dubiety surrounding a concept - no matter how abstract or far-fetched it initially seems - with simplification, logic, and of course, a graph. The theories underpinning economics which concisely explain society's and market complexities rely on generalisations, assumptions and firms and consumers acting in the predicted manner. Although some roll their eyes and debate this is exactly why economic theories are futile, they allow governments and important policy makers to predict future outcomes and trajectories of indicators with (a lot of the time) precision. Theories are undoubtedly an indispensable component to the running of nations. Now, back to the theory which tormented my 13-year-old mind: why does a firm remain trading when they are making a loss?

This particular economic situation, known as the shutdown position of a firm depends on the conceptual idea of the short and long run. Although intangible, the short run is where firms (and individuals) are experiencing some form of economic constraint such as fixed costs, while other factors are variable. The long run, however, is putatively where there are no economic constraints and all costs and more widely factors of production are variable; although with no definitive time scale there is an expectation of autonomy and businesses experiencing no curtailment of their preferences by fixed factors. A fixed cost or factor does not adjust with the level of output, with the important thing to take from this definition being the cost of this factor does not change if the output of a firm is sky high or zero. Examples of such are buildings, land, capital equipment, some bills such as a mortgage, etc. On the contrary, variable costs - you guessed it - adjust with output. This includes raw materials used in production, labour, energy and the like. You may be thinking, but can't a firm just buy another machine or more land? Well, yes they can, but not in the short run. I couldn't decide today I needed more land and have it ready to be used in production tomorrow. But in the long run, this, and anything else for that matter, is feasible. Total variable costs are variable cost per output multiplied by the quantity produced whereas fixed costs per output and total fixed costs are the same value. Here's an example for clarification:

Fixed costs                = £100    
Variable costs             = £50
When the quantity produced is 10, fixed costs remain £100 and variable costs are £500.
When the quantity produced is 0, fixed costs remain £100 but variable costs are £0.

Another important cost to a firm is its marginal costs which is the cost a firm incurs to produce an extra unit of output. The relationship between marginal costs and average variable costs are vital to a firm's decision-making and the analysis of their association is the backbone to many economic theories, particularly in market structures. A common slip up is to assume marginal costs are equivalent to variable costs per output, and although this can be the case, it rarely is. For this to be true, one factor of production would need to produce one unit of output, always. However, due to the concept of economies of scale (which will be investigated later, another aspect of economic theory which depends on the segregation of the short and long run) and the general knowledge that it's unlikely one input will produce one unit of output exactly, marginal costs do not equal variable costs per output. To understand why marginal costs (calculated as the change in T divided by the change in Q below) even in the short run is not simply the variable costs per output (defined as the change in V divided by the change in X), here is an example:

Factor    Output    Fixed    Variable    Total    Marginal
(X)        (Q)       (F)        (V)       (T)        (M)
1           10       100        50        150         5
2           35       100        100       200         2
3           54       100        150       250         2.6
4           68       100        200       300         3.6
5           78       100        250       350         5
6           85       100        300       400         7.1

Below is a rough graph I drew which exemplifies the data above in terms of average costs (i.e. total and variable costs divided by output).

The takeaways from this graph are all average costs initially decrease due to increasing returns to the variable factor, reach a certain minimum point, and then start to increase again due to diminishing returns to the variable factor. The marginal cost curve intersects the average variable and total cost curves at their minimum points, as displayed on the diagram.

All of these components are important when discussing the point at which a firm will exit an industry because it separates the idea of the shutdown point of a firm and the breakeven point of a firm. The argument that these two points for a firm are equal is often mistakingly assumed cogent. Take a look at the added annotations on the graph below:

Firstly, notice the addition to the Y axis of 'price'. This means that when the price is equal to the minimum average costs, and at this point equal to marginal costs, the firm is breaking even - they are making no profit or loss. Now to the interesting part: when a firm's price drops below average total costs but remains above average variable costs, they continue to operate in the short run. This is because regardless of production levels, a firm will always have the obligation to fulfil their fixed costs. If they choose to stop production completely when their price falls below average total costs, they have guaranteed a loss equal to fixed costs. However, if the firm continues to operate when the price lies betwixt ATC and AVC, they will reduce their short run losses. This is because as long as the firm's price covers at least the average variable costs, any additional revenue can be allocated to paying the short run fixed costs, thus reducing the firm's losses. Here's an example:

Peach operates a fruit farm. Her land and machinery are fixed factors and create fixed costs of £80. her variable costs of her labour are £40. This means that Peach's total costs are £120. If Peach was to produce nothing, she would total a loss of £80 in the short run. If Peach was to produce at, say, price per ton of £50, Peach would total a loss of £70 instead. This is because, although the price is less than the cost, £40 is allocated towards paying off the variable costs and the remaining £10 can be used to contribute to the fixed costs. Thus, although Peach's fruit farm is making a loss regardless, by producing where the price is above average variable cost it is always profitable her to activate production in the short run. Only at a price below £40 would Peach be better off not producing in the short run. Note at £40, Peach is indifferent.

This demonstrates why there is a difference between when a firm will shutdown and when they are merely breaking even. To emphasise, as long as a firm is more than covering their average variable costs it is within their interest to produce in the short run to ensure they can contribute to their fixed costs, even if this does result in a loss. This links to the perfectly competitive market structure - which will be explained in depth in a coming article - where no abnormal profits are made, all firms in this market structure produce where the price = marginal cost.

Back to our notional time scales, all of the above applies in the short run exclusively. Regardless of production choices in the short run, any loss incurred should signal the firm to exit the market in the long run when the economic constraints of fixed factors have been removed. This leads me to the next concept I'll explain: the long run is derived by joining the minimum points of the short run average costs. This is illustrated in the graph below with SAC for short run average costs and LAC for long run:

The long run average cost curve creates a curve which resembles the parabolic shape of the short run average cost curves, however joins the minimum points of these short run average cost curves to determine its journey. This is because, as explained earlier, in the long run a firm has no economic constraints. This means that a firm can not only alter their variable factors but they can also adjust the scale of production. This is a unique feature of the long run and epitomises a firm's liberation to make decisions in this time period. In the short run, a firm will stop increasing production at the minimum point as beyond this point there will be diminishing returns to the variable factor. In the short run, I have reached my optimal level of output. However, in the long run the scale of production can be increased and a new short run time period is entered when a fixed factor has been adjusted. This process continues and creates the long run trend shown in my graph above. The decrease in costs observed in the long run uses different terminology than that of the short run. Instead of calling these reduced average costs as diminishing returns, we define them as economies of scale. Beyond the long run optimal point of production the firm would experience diseconomies of scale as their average costs begin to increase. This is illustrated below:

The relationship between the optimal production levels in the short run, followed by a change in production scale (alteration of fixed factors) in between these short run states creates a long run optimal level of production where a firm takes full advantage of economies of scale and is experiencing no diseconomies of scale.

A comprehensive example is provided below:

Ralph owns his own coffee shop called Ralph's Roast. Ralph opens his coffee shop with one machine which can produce three coffees at a time. He begins producing coffees by himself, but quickly realises although his machine can produce three coffees at once, he can't when working alone. He employs another person to make coffees - increasing the variable factor. Ralph continues to employ individuals until three coffees can be made at one time, but ensures nobody is ever sitting idle. This is the short run optimal level of output where the addition of any variable factor, which would subsequently increase average variable costs, would not be 'worth' the increase in production they would bring. In the long run, however, Ralph could increase the fixed factor by adding a second coffee machine allowing him to produce six coffees at once. The key here is that in the short run, regardless of how many people Ralph employs, he cannot produce more than three coffees at once due to the constraint of the machine.

Economies of scale are associated with a reduction in per unit cost as the scale of a firm increases. These can be financial such as preferential loan rates, purchasing such as bulk-buying discounts, division of labour allowing specialisation, to name a few. Once a firm fully utilises their economies of scale potential, a further increase in the scale of operation will trigger diseconomies of scale which slow down the productivity and efficiency of a firm. It should be noted that these graphs and examples provided are internal economies of scale. There are things such as improved infrastructure or legislation which can create economies of scale externally, thereby impacting an entire industry which would be reflected in vertical shifts in the average cost curves for an industry.

COVID-19 has placed a lot of firms in a difficult loss making state, however due to the global impacts and prolonged lockdowns, many firms were unable to even trade and had to exit their industries when paying their fixed costs became too large of a financial burden. Schemes such as the newly introduced Scottish legislation requiring only 28 days notice to terminate private leases has helped 'compress' the short run, however the business-by-business subjectivity of the short run and its (debatably) conjectural definition means it is hard to monitor.

This theory supports and justifies many business activities when at face value they may seem confusing. The distinction between the short and long run is essential to economics and how firms and individuals operate. Although as proven it sometimes may be beneficial for a firm to continue production in a loss making state in the short run, this is not sustainable and the length of time a firm can trade in this state depends on many internal and external factors.

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