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Profit maximisation

Combining revenue and cost curves

Now, some diagrammatical work. Let's combine the two examples developed in this section and the figures from the previous notes on costs. This gives us the data below.

Output (units) 0 1 2 3 4 5 6 7 8 9 10
Total cost ($ 000) 100 110 125 145 170 200 235 275 320 370 425
Total revenue ($ 000) 0 100 180 240 280 300 300 280 240 180 100
Profit ($ 000) -100 -10 55 90 110 100 65 15 -80 -190 -325
Marginal revenue ($ 000) 100 80 60 40 20 0 -20 -40 -60 -80
Marginal cost ($ 000) 10 15 20 25 30 35 40 45 50 55

Now let's plot yet another graph. From the table above plot the marginal cost, marginal revenue and profit figures. You should get a graph looking like the figure below.

There is also a static version of the graph available.

See clearly that the profit is maximised when MC = MR. You can see this from the graph, but can confirm from the data that this is the case as well.

Profit maximisation

The traditional model of the firm assumes that the objective of all firms is profit maximisation. This is particularly applied to private firms. Publicly owned firms are treated differently.

As we have seen above, profit maximisation occurs where marginal cost is equal to marginal revenue. So, the first condition that you need to commit to memory is:

Profit maximisation occurs when MC = MR (Marginal cost = marginal revenue)

Below in figures 1 and 2 are the usual diagrams that show firms maximising profits:

Figure 1 Small firm in perfect competition (price taker)

Figure 2 Large firm in imperfect market (price setter)

We'll come back to these diagrams and look at them in more detail later on in this module, but the key difference between the two diagrams is in the shape of the revenue curves. The firm in perfect competition is a 'price-taker' - they are too small to influence price and so they simply charge the price given by the market. The firm in imperfect competition on the other hand has a degree of market power. This makes them a 'price setter'. They can set their price (subject to the constraints of the demand curve) and find the profit maximising level of output.

Why does profit maximisation occur where MC = MR?

  1. Profit = revenue - cost
  2. As you sell more, profit will grow as long as the extra revenue obtained is greater than the extra cost incurred (extra revenue = MR, extra cost = MC).
  3. MR is constant or falls, and MC may fall initially but quickly rises.
  4. This means that they will soon cross if plotted on the same graph.
  5. Before they cross MR is greater than MC and each extra unit will increase total revenue. However, once they have crossed MC is greater than MR and then each unit will reduce total profit (as more is being added to cost than revenue).
  6. Therefore maximum profit is where MR and MC cross.

Therefore if MR is greater than MC, increasing output is worthwhile as it will add more to revenue than to cost. If the MC is greater than MR, however, increasing output will not be worthwhile as more will be added to cost than to revenue. Thus the best place to produce is where MC =MR.