Monopolist Profit Maximization and Equilibrium
Total Revenue vs Total Cost Approach
A monopolist earns maximum profits when the gap between Total Revenue (TR) and Total Cost (TC) is maximum. The TR curve starts from the origin as there is no revenue if output is zero, and TR is inverse ‘U’ shaped because of the inverse relation between price and quantity. TC is inverse ‘S’ shaped because of the Law of Variable Proportions. Total profits are derived by subtracting TC from TR. Initially, with TC being greater than TR, the firm incurs losses. Points ‘A’ and ‘B’ are the breakeven points, where the firm experiences neither profits nor losses. Profit is maximum where the gap between TR and TC is highest; this corresponds to the equilibrium quantity.
Marginal Approach to Equilibrium
According to the marginal approach, a monopolist’s equilibrium can be analyzed based on the relationship between per-unit revenue and per-unit cost.
Conditions for Monopolist Equilibrium
The two conditions that must be satisfied to attain equilibrium are:
- MR = MC
- MC cuts MR from below (or slope of MR < slope of MC at the point of equilibrium)
Monopolist Equilibrium Time Periods
Equilibrium of a monopolist can be derived under two time periods:
Short Run Equilibrium
Short Run: It is a time period where certain costs are fixed, along with variable costs, and entry or exit of firms is not possible. In the short run, a monopolist may earn supernormal (or abnormal) profit, normal profit, or even incur a loss, depending on the position of the short-run average cost curve.
Short Run Supernormal Profit
Case 1: Supernormal Profit. This case shows downward-sloping Average Revenue (AR) and Marginal Revenue (MR) curves. Short-run Average Cost (SAC) and Short-run Marginal Cost (SMC) curves are also shown. Equilibrium is at point E where both conditions (MR = MC and MC cutting MR from below) are satisfied. The equilibrium quantity is OQ, which the monopolist would sell at a price of OP. Total profits can thus be calculated as follows:
Total Profit (TP) = Total Revenue (TR) – Total Cost (TC)
Short Run Normal Profit
Case 2: Normal Profit. Equilibrium is at point E where both conditions (MR = MC and MC cutting MR from below) are satisfied. The equilibrium quantity is OQ*, which the monopolist would sell at a price of OP*. Note that in this case, the SAC curve is tangent to the AR curve at point B, implying that both AR and SAC are equal to BQ* = OP*. Total profits can thus be calculated as follows:
TP = TR – TC = (Price * Quantity) – (Average Cost * Quantity)
Short Run Loss
Loss: Equilibrium is at point E where both conditions (MR = MC and MC cutting MR from below) are satisfied. The equilibrium quantity is OQ, which the monopolist would sell at a price of OP*. However, in this case, the SAC curve is positioned above the AR curve, implying that SAC (CQ) is more than AR (BQ or OP*). Total profits or losses can thus be calculated as follows:
TP = TR – TC = (Price * Quantity) – (Average Cost * Quantity)
Long Run Equilibrium
Long Run: It is a time period where all costs become variable, and entry or exit of firms is also possible. In the long run, a monopolist can change the level of output by changing any and/or all factors of production, as there are no fixed factors. Here, a monopolist usually earns supernormal profits due to barriers to entry for new firms.
Long Run Supernormal Profit
Equilibrium is attained where the Long-run Marginal Cost (LMC) curve equals Marginal Revenue (MR), and LMC cuts MR from below. (It is shown in Diagram 7). The figure shows downward-sloping Average Revenue (AR) and Marginal Revenue (MR) curves. Long-run Average Cost (LAC) and Long-run Marginal Cost (LMC) curves are also shown. Equilibrium is at point E where both conditions (MR = LMC and LMC cutting MR from below) are satisfied. The equilibrium quantity is OQ, which the monopolist would sell at a price of OP*. Total profits can thus be calculated as follows:
TP = TR – TC = (Price * Quantity) – (Average Cost * Quantity)