It is better to refer to this model as revenue maximisation model rather than sales maximisation model, since, here the objective of the firm is assumed to be maximisation of money value of sales and not total quantity of sales.
Revenue Maximisation Model without Profit Constraint:
Baumol’s model is based on total revenue curve. We know that for an oligopolistic, TR is inverted U-shaped (see section 4.9). We also need to draw total cost (TC) curve in order to show the difference between equilibrium price-quantity combination under revenue maximisation and profit maximisation, because the use of TR curve can only identify the revenue maximising point while identification of profit maximising point calls for both total revenue curve and total cost curve, since profit is determined by the difference between TR and TC.
The total cost curve of this model is of normal shape, because the shape of the TC curve does not depend on the structure of market where the firm operates in.
In panel (a) of diagram 12.4, TR represents total revenue curve and TC represents total cost curve of a firm. The profit of the firm is represented by n curve in panel (b). The ? curve is obtained by measuring the difference between TR and TC at all levels of output.
So, at each and every level of output, the gap between TR and TC is equal to the gap between ? curve and the horizontal axis of panel (b). For example, the difference between points’s’ and ‘q’ in panel (b) is exactly the same as the difference between points ‘a’ and ‘b’ in panel (a).
Similarly, the difference between points ‘e’ and ‘f in panel (b) is equal to the difference between points ‘c’ and ‘d’ in panel (a). At points’m’ and ‘n’, differences between TR and TC are zero and these are also reflected at points ‘p’ and ‘r’ respectively showing zero profit.
To identify the revenue maximising point, we need to look at the TR curve. The TR curve reaches its peak at point c, ensuring revenue maximising point. In figure 12.4, we find that the revenue maximising output level is Q3. From the diagram we cannot obtain the price corresponding to the revenue maximising output level.
To get revenue maximising price, we need to divide total revenue (TR) by output (Q), i.e., TR/Q = P.Q/Q =P. Thus, in our diagram the revenue maximising Price is TR1 /Q3.
Now, we would like to find out the profit maximising price and output of the oligopolist. The profit maximising point can be obtained by looking at the profit (?) curve. The profit curve reaches its peak at output level Q2, because the gap between TR and TC is maximum at that output level. Hence, the profit maximising output is Q2 Like revenue maximising price, we can find out profit maximising price,
Which is equal to TR2/Q2.
Revenue Maximisation Model with Profit Constraint:
Revenue maximisation alone cannot carry any significance unless it is backed by minimum profit constraint. In other words, firms need to maximise revenue but revenue maximising output must also ensure a pre-specified amount of profit.
In case, the revenue maximising output does not satisfy minimum profit constraint, firms are to search for the levels of output that fulfils minimum profit constraint and out of those levels it will select that one which generates maximum revenue. We illustrate this with the help of a diagram.
Let us introduce a profit constraint, say ? 0, in the previous framework (figure 12.5). It means that the firm has to earn O?0 amount of profit per unit of output. But we have observed that, the revenue maximising output, i.e. OQ3, generates per unit profit of ‘ef’, which is higher than O?0. So the revenue maximising output automatically generates more profit than what is required. So, the profit constraint is automatically satisfied.
Assume that profit constraint is increased from O?o to O?1 Since the revenue maximising output generates ‘ef’ amount of profit, and ‘ef’ equals O?1 maximisation of revenue and satisfying minimum profit constraint – both the conditions are satisfied at OQ3 level of output.
Problem arises when the revenue maximising output level does not satisfy the minimum profit constraint set by the firm. To illustrate this case, let us assume that the minimum profit constraint is further augmented to O?2.
The revenue maximising output OQ3 does not satisfy the profit constraint, since profit constraint O?2 (or ‘gh’) is higher than ‘ef. So the firm should first search for output levels which satisfy the profit constraint, and then among those levels, the firm needs to find out the level of output that maximises revenue of the firm.
In figure 12.5, we observe that if the firm produces any output between OQ6 and OQ5, profit constraint is satisfied. So the firm will choose OQ5, since it satisfies profit constraint and also generates maximum revenue among the other output levels lying between OQ6 and OQ5.