The Demand for Labour

The labour market is another topic that is becoming very popular with examiners. Although many students find it more complicated than some of the previous macroeconomic topics, it is, as is so much in A level economics, simply an application of supply and demand.

Before we get going, it is important that you understand how the labour market differs from the product market. In the product market, the supply curve represents the firm's supply of the good in question and the demand curve represents the consumer's demand for the good. With labour markets the roles are reversed; the demand curve represents the firm's demand for labour and the supply curve represents the consumer's (or worker's) supply of labour.

As with the product market, we will start with demand and supply, and then combine the two to get the equilibrium price and quantity (in this case, price is the wage rate and quantity is the quantity of labour).

The first point to note is that the demand for labour is a derived demand. Labour is only demanded as an input into the production process. If the demand for the good in question changes then so will the demand for the labour that helps to make that product.

In the product market, the demand curve is downward sloping. As the price of a good falls, one would expect its demand to rise, ceteris paribus. One would expect this to be the case in the labour market too. If the price of labour falls (i.e. the wage rate falls) one would expect a firm's demand for labour to rise, ceteris paribus. If the price of labour were falling relative to, say, capital, then it would make sense for the firm to substitute labour for capital.

Of course, in the short run we assume that the amount of capital is fixed, but given the law of diminishing marginal returns (see the topic on 'Costs and revenues' for details), eventually, additional workers will be worth less to the firm than previous workers, and so their wage will be lower to reflect this fact. So looking at it from a different angle, one would expect lower wage rates at higher employment levels; again the demand curve for labour ought to be downward sloping.

We need to look at this in more detail. We can derive the demand curve for labour using something called Marginal revenue product theory.

Before we get going, we need to define some terms.

Marginal physical product (MPP): This is the extra physical output produced by one extra worker.

Marginal revenue product (MRP): This is the extra revenue gained by the firm as a result of employing one more worker. If an extra worker adds 10 units to total output (his MPP), and they are sold for £5 each, then the MRP will be £50.

Hopefully you can see, then, that the following formula follows:

MRP = MPP times marginal revenue (MR)

So for the example of the worker who produces 10 units, each sold for £5:

£50 = 10 times £5

In the analysis that follows, I will hopefully convince you that the marginal revenue product curve is the firm's demand curve for labour. But first, as usual, we need to make some assumptions. As with perfect competition in the product market, some of these assumptions are fairly unrealistic.

  1. Workers are homogenous. They have identical skills. This is a bit like the assumption of homogenous goods in the perfect competition model.
  2. Firms are operating in a perfectly competitive product market. The importance of this assumption is that, just as they have no control over the price they set, they also have no buying power when demanding labour. They are price takers in the product market and 'wage' takers in the labour market. Also, in perfectly competitive product markets, marginal revenue is constant and equal to price. So the formula above becomes: MRP = MPP times price (which is constant).
  3. For the time being, we assume that there are no trade unions. We are assuming that the labour market is competitive. Trade unions distort this competitive labour market just as powerful firms (in monopoly or oligopoly) would with their superior buying power (buying labour, that is).
Deriving the demand curve for labour

We mentioned the law of diminishing marginal returns earlier. Remember that this 'law' stated that, in the short run, "if a firm increases output by adding variable labour to fixed capital then eventually diminishing marginal returns (physical product of labour) will set in." In other words, at some point an extra worker will add less output to the grand total than the previous worker.

So I think it is fair to say that the marginal physical product curve will look exactly the same as the marginal returns curve that we used in the 'Costs and revenues' topic They are, basically, the same thing. We can now derive the MRP curve.

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Notice in the diagram above that the shape of the MRP curve is exactly the same as the shape of the MPP curve. The only difference is the scale on the y-axis. Every value for the output in the middle diagram has been multiplied by £5 (given in the diagram on the right) to give the values on the y-axis in the diagram on the left.

So, the MRP curve is derived from the MPP curve, which is derived from the law of diminishing marginal returns.

Now, why is the MRP curve the demand curve for labour for each of these perfectly competitive firms?

Earlier, we assumed that the labour market that we are dealing with is competitive. This means that the wage is constant. Firms can employ as many workers as they want at the given wage, just like they can sell as many goods as they want at the given price in perfectly competitive product markets. We can call the wage the marginal factor cost (MFC). Factor, meaning factor of production (in this case, labour). So the MFC is the extra cost to the firm of employing one more worker.

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Look at the diagram above. I've drawn an MRP curve and three MFC curves. Firms in product markets maximise profits at the level of output where marginal cost = marginal revenue (MC = MR). If you can't remember why this is the case, I seriously advise you to look at the 'Costs and revenues' topic. The same concept can be applied in the labour market. Firms will employ labour up to and including the point where the extra revenue gained from the last unit of labour is the same as the extra cost of employing it. In other words, where MRP = MFC.

So, when the given wage is W1, this occurs at point A, giving an employment level of L1. At wage rate W2, MRP = MFC occurs at point B, giving an employment level of L2, and at W3, for the same reason, L3 units of labour will be employed. At each given price (wage rate) the firm reads his demand (for labour) from the MRP curve. This is a pretty good definition of a demand curve! The MRP curve is the demand curve for labour.

What if the firm is not operating in a perfectly competitive goods market?

In the analysis above, we assumed that the firm was operating in a perfectly competitive goods market. This meant that its marginal revenue curve was constant and equal to its price. Hence, the formula MRP = MPP times MR became MRP = MPP times price.

But most firms operate in an imperfectly competitive goods market (particularly oligopoly and monopoly). This means that they face a downward sloping demand curve in the product market. Seeing as the marginal revenue curve must be below a falling demand curve (which is the average revenue curve, remember) and falling twice as fast, this will affect the MRP formula quite a lot. Luckily, it does not affect the fact that the MRP curve is downward sloping. In fact, it just means that the MRP curve is even steeper. MRP = MPP times MR. If MPP is falling (due to diminishing marginal returns) and MR is falling, then MRP must be falling too.

Hence, the firm's demand curve for labour will be downward sloping whatever type of goods market the firm happens to be involved with.

When we looked at the demand curve in the product market, its elasticity was important. In turn, it was important to assess what determined the value of the elasticity. We must do the same thing with the demand curve for labour. Remember that elastic demand curves are relatively flat, so for a given change in the wage rate the proportionate change in the demand for labour will be larger. Inelastic demand curves are relatively steep, so for a given change in the wage rate the proportionate change in the demand for labour will be much smaller.

Many of these determinants are similar in character to those for the demand in the product market. Check back in the 'Elasticity' topic to see if you agree.

  1. Availability of substitutes: In the product market, if a good had lots of substitutes then its demand was more elastic. This is true of labour too. The more substitutes there are, in terms of factor inputs (capital, in particular), then the more elastic the demand for labour will be.
  2. Labour costs as a proportion of total cost: In the product market, if a good was very cheap, and so made up a very small proportion of a consumer's income, then its demand was relatively inelastic. The same is true of labour costs. If labour costs are a small proportion of total costs (perhaps at a nuclear plant) then the demand curve for labour will be relatively inelastic.
  3. The derived demand factor: Remember that labour is a derived demand. It makes sense, therefore, that the elasticity of demand for labour will be greatly affected by the elasticity of demand for the good that the labour is producing. If the product in question has relatively inelastic demand (e.g. petrol) then the demand for those working in the industry will also be fairly inelastic (e.g. workers at an oil rig).
  4. The time factor: As with all elasticity's, the longer the time period in question, the higher the value of the elasticity. In this case, the longer the time period, the easier it is to substitute labour for capital. Also, in the short term, employers may be bound by contracts. It the short term, therefore, it is difficult for a firm to vary the number of workers regardless of the wage rate. Over the long run, though, the demand curve will be more elastic.

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