Marginal costs and marginal returns

A common aim in economics is to maximise the benefits of using a given set of resources. This maximisation may take the form of deciding what quantity of a given input to use in one production process, or it may take the form of deciding how to allocate a given input amongst a set of competing production processes.

Resource use in one production process

Consider the production process shown in the graph for the law of diminishing returns. Initial fertiliser applications provide large increases in production while incremental applications provide successively smaller increments in production.

We can convert these physical production parameters to dollar values by multiplying by their respective prices. Say each unit of output is worth $5 while each kg of fertiliser costs $2. How much fertiliser should be applied to maximise the profit?

We can deduce that each additional kg of fertiliser applied will increase the costs of the business by $2. So the marginal cost of applying more fertiliser is $2 per kilogram.

However, the value that is generated by applying more fertiliser is variable. If fertiliser is increased from 100 kgs to 200 kgs (marginal cost = $200), the output from the land goes up by 80 units (from 200 to 280) with a value of $400. Clearly it is worthwhile increasing the fertiliser usage to this level because the value of output generated exceeds the cost of the fertiliser.

Increasing fertiliser usage by another 100 kgs (to 300 kg) costs a further $200, while the value that is generated by the extra fertiliser is $300. Once again this is worthwhile.

Adding another 100 kgs of fertiliser costs a further $200, but the value this adds is also $200. Is this worthwhile? While the profit from using 400 kgs is no worse than that of using 300 kgs, it is unlikely that anyone would use 400 kg of fertiliser when they could use 300 kg for the same result. On this basis, it seems probable that we have gone past the point of maximum profit. A more detailed analysis of this production function reveals that the maximum profit point (at these prices) is reached at 350 kg of fertiliser input.

The underlying principle here is that it is worthwhile to continue adding an input to a production process only as long as the marginal revenue arising from adding that input exceeds the marginal cost of adding the input. Or more specifically, the point of maximum profit is reached when the marginal revenue equals the marginal cost.

Note also that the point of maximum profit occurs before the point of maximum production. While maximum production occurs between 500 and 600 kgs of fertiliser, maximum profit occurs at 350 kgs of fertiliser. At input levels above 350 kgs, while production is still increasing, the marginal value of that production is less than the marginal cost of the inputs used to produce it.

Allocating between production processes

What if there are multiple production processes available for a given input – say labour. How is labour allocated amongst these production processes?

Each production process will use labour as outlined in the preceding section – that is, each will employ more labour as long as they can acquire it for less than the marginal value of that labour unit’s output. Now, if each production process has a different marginal value of production, then the process with the highest marginal value of production will be in the best position to bid for labour – while other processes will not be able to compete for that labour resource until the marginal value of production of the first process drops to the level of the next best process. This allocation process will continue until all available labour is in use, or all production processes have employed all the labour they can profitably use at the prevailing price of labour.

Once again there are some important economic principles embodied in this seemingly simple example:

• Resources will flow to those areas where their marginal value is greatest, because those industries have the greatest capacity to bid for resources
• The marginal value of production for a given input will tend to equate across industries.

Implications

There are many interesting implications arising from these theories of resource allocation. Consider what happens if the price of an input increases. Possible responses for a firm include:

• Use less of the resource. If the resource has diminishing returns, then using less of the resource will increase the marginal productivity of the resource and its marginal value of production, allowing a new profit maximising point to be reached
• Low marginal value processes are stopped. If the new price of the resource is above the value that the process can sustain (marginal cost is greater than marginal revenue at all production points), then that activity will cease
• Increase the resource productivity. If the output from the resource can be increased for the same level of input, then the firm may be able to continue using the resource at its new higher price. For example, higher fuel prices encourage the development of more fuel-efficient cars.

Consider these implications with regard to the labour market and minimum wage levels. There is significant debate about the worth of minimum wage rates. Arguments include:

• Increased minimum wage rates actually reduce employment by raising the marginal cost of employing low skilled staff above their marginal value of production
• Workers with low marginal values of output are concentrated amongst the young and low educated, making these groups less likely to find work. Yet these are the very groups that minimum wage rates aim to assist
• Increases in minimum wages mostly assist those already in employment – not those trying to get employment
• Higher wages will force a change of employment focus away from low value opportunities towards higher value outputs

Most of the arguments listed above imply that raising minimum wage rates is not helpful to employment. Does this mean that economics itself says that raising minimum wage rates is a bad idea?

No. Economics can be used to analyse a situation, and will identify costs and benefits associated with that situation. But the judgement of the situation is ultimately made by people, rather than economics itself. Hopefully, their judgement will recognise the costs and benefits identified by the economic analysis.