One of the major motivations for growth is the pursuit of economies of scale – this becuase costs directly affect the level of output a firm can produce.
It is assumed that a firm under consideration produces a singe product as analysis of conglomerates more complex. It is also assumed that a firm only utilises two factors of production – labour (L) and capital (K). This is a strong assumption, but one that is used for simplicity.
These two factors are representative in a very particular way. In the short run, the firm faces limited flexibility. Varying the quantity of labour input the firm utilises may be relatively straightforward – a firm can increase the use of overtime, or hire more workers fairly quickly. However, varying the amount of capital a firm has at its disposal may take longer. For example, it takes time to commission a new piece of machinery, or to build a new factory – or a Channel Tunnel! Hence labour is regarded as a flexible factor, and capital as a fixed factor in the short run, whereas both are flexible in the long run. Of course, this may not always be accurate: for example it may be easier to bring in new computers than to train new staff to use them.
The production function
As the firm changes its volume of production, it needs to vary its inputs of its factors of production. Thus, the total amount of output produced in a given period depends upon the inputs of labour and capital. Of course, there are many different ways of combining labour and capital, some combinations being more efficient than others. The production function summarises the most efficient combinations for any given output level.
The nature of technology in an industry will determine the way in which output varies with the quantity of input. However, one thing is certain: if the firm increases the amount of inputs of the variable factor (labour) without increasing the amount of the constant factor (capital), it will gradually derive less and less additional output per unit of labour for each further increase. This is known as the law of diminishing returns, and is one of the few ‘law’s in economics. It is a short-run concept, as it relies on the assumption that capital is fixed.
It can readily be seen why this is the case. Suppose that a firm has 10 computer programmers working in an office, utilising 10 computers. The 11th worker may add some extra output, as the workers may be able to ‘hot-desk’. The 12th worker may be able to add some extra output, perhaps by keeping the printer stocked or making coffee. However, if the firm keeps expanding without increasing the number of computers, then each extra worker will be adding less and less output.
The production function can be graphed as a function with labour against output, with intial exponential growth, slowing with a decreasing gradient to zero, as diminishing returns sets in. A rise in capital shifts the graph up.
The production function thus carries information about the physical relationship between the inputs of the factors of production and the physical quantity of output. With this information and knowledge of the prices the firm mush pay for its inputs of the factors of production, it is possible to map the way in which costs will change in the short run.
Costs in the short run
Because the firm cannot vary some of its inputs in the short run, some costs may be regarded as fixed, and others as variable. Fixed costs do not vary with output, while variable costs do. In the short run some fixed costs are sunk costs: costs that the firm cannot avoid paying even if it chooses to produce no output. Total costs are the sum of fixed and variable costs:
total costs = total fixed costs + total variable costs
Total costs will increase as the firm increases the volume of production, because more of the variable input is needed to increase output. The way in which the costs will vary depends on the nature of the production function, and on how the prices of labour or capital alter as output increases (economies of scale).
A common assumption by economists is that in the short run, at very low levels of output, total costs will rise more slowly that output, but as diminishing returns set in, total costs will accelerate.
Total, marginal, and average costs
An important relationship exists between total, marginal and average costs. Marginal cost is the additional cost of producing one more unit.
Short-run average costs is calculated as short-run total cost divided by output. To calculate short run marginal cost, you need to work out the additional cost of producing an extra unit at each output level. Average variable costs and average fixed costs can be calculated by dividing total variable costs and total fixed costs respectively by output.
The relationships between these values are plotted below.
First, notice how short-run average total costs (ATC) takes on a U shape. This is the form often assumed in economic analysis. ATC is the sum of average fixed and average variable costs (AFC and AVC respectively). Average fixed costs slope downwards throughout – this is because fixed costs do no vary with output, so as output increases AFC must always get smaller, as the fixed costs are spread over more and more output. However, AVC follows a U shape, which gives ATC its U shape.
A very important of that diagram is that the short run marginal costs (MC) cuts both AVC and ATC at their minimum points. This is always the case. This is because if you are adding something which is greater than the average, then the average will always increase. For a firm, when the marginal cost of producing a good is higher than the previous average cost of doing so, the average must increase. If the marginal cost is the same, the average will not change, and if it is below it will fall. It is quite simply and arithmetic property.
So, when you draw the average and marginal curves of the firm, the marginal cost curve will always cut AVC and ATC at their minimum points. Another way of viewing MC is the derivative of ATC and AVC.
Remember that short-run cost curves show the relationship between the volume of output and costs under the assumption that capital is fixed, so that in order to change output, the firm has to vary the amount of labour. Again, this is called the law of diminishing returns and is why AVC and ATC have their shape. The position of these cost curves, however, depends on the quantity of capital. There is a short-run curve for each given level of capital.