Dec 11, 2010 Stuart McClelland

Hat factory - *Ian Filmer*

I always like to start off my explanation of a theory by breaking down what the key words mean, so here we go:

**Definitions****1.** "Diminishing" = Falling or dropping (getting less)

**2.** "Marginal" = The next one, e,g. the next worker on the machine, the next good consumed, the next word in a sentence.

**3.** "Returns" = output you get for every piece of input. So if it takes 1 hour to make a cake, your return is 1 cake per hour. If it takes 2 hours to make a shoe, your return is 1 shoe per hour.

Overall then, it might be helpful to think of the theory of diminishing marginal returns simply as "the decreasing return you get every time you make one more item".

Next, I'd like to give you an easy example of how this theory works in practice, so you understand it fully, and are not just repeating words from a textbook. That might get you the marks, but it is risky. If you understand the theory fully, you'l be able to answer any related question that comes your way.

* An example of the theory in Action*Imagine a factory that makes hats. To make a single hat you need two types of inputs: fixed and variable.

Fixed inputs are things like your machines, your rent payments for the factory, the equipment you need to run everything - basically anything that does not increase in volume as you increase the number of hats you make. The cost of these fixed inputs is therefore also fixed. Even if you do not make a single hat, you still need to pay these fixed costs: your rent, depreciation on your machines, etc.

Variable inputs are those that increase as output increases. For example if one worker makes 10 hats for you in an hour, but you want to make 11 hats per hour, the only solution is to get another worker. The worker then is a variable input, because as you increase production of hats, you need to increase the number of workers you have too. Other examples of variable inputs include your raw materials (e.g. The fabric required to make hats), and the electricity needed to run your machines for longer.

So let's carry on with the example then. We are only going to focus on two of the factories inputs: The workers who help to make the hats (these are variable inputs), and a big hat-making machine they stand around (this is a fixed input).

When we only have one worker on the machine, he finds it hard to run it efficiently by himself. He must carry out all the tasks needed to run it and make the hats. He must check each hat for errors, add finishing touches to them, and move from through a range of different tools like sewing machines, scissors, and so on. Our output then is quite small. This worker is only able to make 5 hats in an hour.

If we add another worker to the process, productivity increases immensely. One worker is stationed permanently checking for errors and making sure the machine is running smoothly, and the other is responsible for touching up the hats. Between them, they can make 15 hats. Our marginal output then from adding one more worker is 10 hats. We can see that this is a much better situation then when we just had 1 worker.

If we add yet another worker, the 3 together can make 30 hats in an hour. The 3rd worker adds efficiency to the process by permanently being placed at the sewing machine, while the other two are responsible for the machine and cutting the fabric. Our marginal output has increased again with the added 3rd worker, this time to 15 hats per hour.

There is a point however where adding more workers to the machine area becomes less efficient. Let's say we add a fourth worker now, and we have a total output of 40 hats per hour. The marginal output of the new worker has now decreased to 10. We have reached "The point of diminishing marginal returns": From worker 3 onwards, each new worker is able to create less and less hats than the last.

*Why does this occur?*

Because there are too many variable inputs for the fixed input - The workers begin to get in each others' way dues to a lack of space in the work area, spend more and more time idle waiting to use tools that are already being used, and so on. Basically, the whole process gets more inefficient. We are now experiencing diminishing marginal returns - The cost of each additional hat we produce has begun to rise, as we still pay the same to get another worker, but every worker added produces less hats than the last.

**Extending the theory to explain why the supply curve slopes upwards**We have already established that beyond the point of diminishing returns, marginal cost increases as quantity produced increases (i.e. Each next hat becomes more expensive to make).

If you run a business, your goal is to make money. Therefore you will not sell something unless the price you receive for it is greater than it cost you to produce (P > or = MC). If each next hat we make is becoming more and more expensive, we are going to need to charge a higher and higher price for it in order to still make a profit. Another way to phrase this sentence is "As quantity supplied of a good increases, its price must increase". Somehow we have managed to reach the law of supply, and have been able to show why the supply curve slopes up.

**So let's Recap -** *How would you use all of this information to answer the question "Why does price increase as quantity supplied increases?"?*

There are only four points to remember:

**1.** The law of diminishing marginal returns states that, beyond the point of diminishing returns, as more and more variable inputs are added to a fixed input, marginal output falls and marginal cost rises.

**2.** To make a profit, Price must be greater than marginal cost.

**3.** If marginal cost is rising as supply increases, and the producer is rational, it will also increase the price it sells its goods for.

**4.** Therefore, the supply curve slopes upward, because price is positively related to quantity supplied.

Thank you for taking the time to read my article, and I hope that you found it useful. If you have any questions at all about this theory, just post them at the bottom of this page, and I will be happy to answer them for you free of charge.

Hat factory -

*Ian Filmer*

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