Monthly Archives: January 2015

277 – Perfection isn’t best

In whatever work we do, a common challenge is deciding how much effort to devote to a particular task. Additional effort will usually generate more output or better-quality output, but at what point does the cost of extra effort outweigh the benefits? It might be a lower point than you think.

A standard model from production economics provides some useful insights into this issue. The model represents a firm’s decision making about a production input. A classic example from agriculture is a farmer’s decision about how much fertiliser to apply to a wheat crop. I’ll go through this example and explain the insights it gives us. Later on, I’ll show how the same insights are often relevant to completely different types of work, such as writing a report or studying for an exam.

Looking at the fertiliser example for now, the question is, how much fertiliser should a farmer apply in order to get the outcome that is best overall?

The higher the rate of fertiliser applied, the higher the level of wheat production. However, the relationship between the input (fertiliser) and the output (wheat grain) is unlikely to be a straight line. It’s more likely to be shaped like Figure 1: as the level of input increases, the level of output increases but it tends to flatten out. Whatever its shape, economists call the relationship between an input and an output a “production function”.

pd277f1

Figure 1. A production function for fertiliser applied to a wheat crop.

 

Suppose the planned level of fertiliser in Figure 1 is low – say 20 kg/ha. As the graph shows, if the farmer increased the rate from 20 to 40 kg/ha, there would be quite a large increase in wheat yield. On the other hand, if the planned fertiliser rate was 120 kg/ha, increasing it by another 20 kg/ha would increase yield by only a small amount. At 200 kg/ha, a further increase in fertiliser would make no difference to yield (in this example).

There have been countless thousands of fertiliser trials conducted around the world, and the great majority show a shape like Figure 1 – steep at low fertiliser rates, flat at high rates.

One possible answer to the question, “what is the best rate of fertiliser?” would be, “the rate that gives the highest yield”. In Figure 1, the yield is maximised at 200 kg/ha.

The problem with this answer is that it ignores the cost of the input. Clearly, fertiliser is not costless.

Figure 2 shows the farmer’s revenue from the harvested wheat crop and the cost of the fertiliser that has been applied (all calculated per hectare). The revenue curve is the crop’s yield (from Figure 1) multiplied by its sale price (which I’ve assumed is $250 per tonne in this example). The cost curve is the cost of fertiliser ($1.90 per kg) times the rate of fertiliser applied.

pd277f2

Figure 2. Revenue and cost from wheat production at different fertiliser rates.

 

At any fertiliser rate, the benefit to the farmer (the profit) is the revenue received minus the cost of fertiliser. On the graph, the profit at a particular fertiliser rate is the vertical distance between the revenue and cost line at that fertiliser rate. You can see that if no fertiliser was applied, the benefit would be $300 per ha (the distance between the red and blue lines at the points where they hit the vertical axis, where fertiliser rate is zero). If the fertiliser rate was 80 (where the dashed line is), the vertical distance between the red and blue lines is a bit over $500, so 80 is clearly a better option than zero. At rates above 80, the revenue and cost lines get closer together, meaning that the overall benefit is less than at 80. In fact, 80 is the best possible input level in this example. It gives the highest profit to the farmer.

Figure 3 shows the farmer’s profit at different fertiliser rates. It is the difference between the two lines in Figure 2. In this graph it’s easy to see that the maximum profit is generated at 80 kg per ha of fertiliser.

pd277f3

Figure 3. Profit from wheat production at different fertiliser rates.

 

It’s also easy to see that the fertiliser rate that maximises crop yield (200 kg/ha) is not the rate that maximises profit. The reason for this is that, at rates above 80 kg/ha, the revenue from the additional grain isn’t enough to cover the cost of the additional fertiliser. In fact, at 190 kg/ha, increasing the fertiliser rate up to 200 kg/ha gives basically no additional yield at all, only additional costs (see Figure 1).

Figure 3 also shows that the profit function is quite flat in the vicinity of the optimum (80 kg/ha). Any rate between say 60 and 100 kg/ha gives very nearly as much profit as does 80 kg/ha. (See PD#88)

As promised earlier, let’s look at other types of outputs and inputs and see how this model is relevant. Economists have found that the shape of Figure 1 (or something like it) is relevant to many types of physical production processes. Just Google “production function” and you’ll see that this is the default assumption in the absence of evidence to the contrary. In all these cases, the optimal input level is less than the level that maximises output, and there is a range of input levels that are almost as good as the optimum.

What about work that doesn’t create physical products? In most developed countries, the service sector constitutes 70 to 80% of the economy. How relevant are the above conclusions to activities in that sector, like analysing some data, writing a report, marketing a product, or designing a building?

My proposition is that the shape of the production function in Figure 1 is very often relevant to these sorts of activities as well as to physical production processes. Consider the process of writing a report. It’s a common experience to find that one can prepare a report to a reasonable standard with a moderate amount of work, but further improvements in the standard of work take increasing amounts of work. As the report approaches perfection, there is a risk of continuing to work on it almost indefinitely without any real improvement in its quality. Clearly, this is just like the fertiliser example, with the main difference being that I’m focusing on the quality of the output rather than its quantity.

If that’s so, then it must also be true that the ideal level of effort to put into this type of work is less than the amount needed to produce a perfect report. Aiming for a 98% or even 95% perfect job (rather than 100%) will produce an output that is good enough in the majority of cases, and will allow you to move on more quickly to other work. For some people, adopting this as a conscious strategy can greatly increase their efficiency at work, especially people with strong perfectionist tendencies.

Of course, sometimes 95% really isn’t good enough. If a report is particularly important and will be carefully scrutinised, you might decide to aim for 99.9%, but even in these special cases, it is unlikely to be optimal to aim for 100%.

Further reading

Pannell, D.J. (2006). Flat-earth economics: The far-reaching consequences of flat payoff functions in economic decision making, Review of Agricultural Economics 28(4), 553-566. Prepublication version here (44K). IDEAS page here.