The basic goal of every firm—whether it is a competitive firm or a monopoly—is maximisation of profit. We have also seen that profit [π] represents the excess of total revenue [TR] over total cost [TC]:
π = TR — TC
For an economist, profit is ‘abnormal’ or ‘supernormal’, when π > 0, and it is normal when π = 0. When π = 0, it implies that all the costs, implicit as well as explicit, are recovered. For an accountant, the concept of profit means excess of TR over explicit costs only.
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Total Revenue represents the money value of the output sold. Thus,
TR = P × Q
Total cost represents the sum of explicit and implicit costs. Both of them could be partly fixed and partly variable. Thus, from the viewpoint of analysis, we can say that total cost is the sum of the total fixed cost and the total variable cost
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TC = TFC + TVC
From equations 7.1, 7.2 and 7.3, we have
π = P × Q – TFC – TVC
For obtaining the conditions for profit maximisation, we use equation 7.1. The necessary condition for the purpose is that the first order derivative of n with respect to Q must be zero while the sufficient condition is that the second order derivative of n with respect to Q must be negative at the point where the first order derivative is zero.
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Differentiating equation 7.1 with respect to Q, we have
dπ / dQ = d (TR) / dQ – d (TC) / dQ = MR – MC
This should be zero for maximisation of π. Thus, MR = MC
Equation 7.6 provides the necessary condition of profit maximisation. Differentiating equation 7.5 with respect to Q once again, we obtain
d2π / dQ2 = d (MR) / dQ – d (MC) / dQ
= Slope of MR – Slope of MC
This should be negative, for maximisation of π
Slope of MR – Slope of MC < 0
=> Slope of MR < Slope of MC
Inequality 7.7 provides the sufficient condition of profit maximisation. Both the conditions of profit maximisation remain unchanged irrespective of whether the firm is a monopoly or a competitive one. Figure 7.1 and 7.2 show the applicability of these conditions in respect of the two types of firms.
In both the figures, MC = MR at the points E1 and E2, but slope of MR is less than that of MC only at E2. Hence, E2 is the point in equilibrium in each case. At this point MC cuts MR from below, which in simple language states the necessary and sufficient condition of profit maximisation.
Profit per unit of output can be obtained by dividing both the sides of Equation 7.1 by Q.
π / Q = TR / Q – TC / Q
Profit per unit = AR – AC
Where AR and AC are average revenue and average cost respectively. From the discussions above, it is clear that the profit maximising output is determined at the point where MC cuts MR from below and the profit maximising price is determined at the point at which the vertical line through the profit maximising output cuts the AR curve.
Profit per unit of output is the excess of AR over AC at the profit maximising output and the total profit earned by each firm is given by the product of (AR – AC) and the output produced. Profit per unit for a competitive firm [Figure 7.1] is E2C2 and that for a monopoly [Figure 7.2] is P2C2 and total profits earned are the shaded regions in the respective figures.
In illustrations 7.1 and 7.2, it is just a coincidence that profit maximisation outputs, prices and profits work out the same for the competitive firm as well as the monopoly.