Price, Quantity and Total Revenue
Suppose that a firm finds its elfin possession of a complete monopoly in its industry. The firm might be the fortunate owner of a patent for a new anticancer drug, or it might own the operating code to a valuable computer program. H the monopolist wishes to maximize its profits, what price should it charge and what output level should it produce? To answer these questions, we need a new concept. marginal or MR). From the firm’s demand curve, we know the relationship between price (P) and quantity sold (q). These are shown in columns (1) and (2) of Table 9-3 and as the black demand curve (dd) for the monopolist in Figure 9-3(a). We next calculate the total revenue at each sales level by multiplying price times quantity. Column (3) of Table 9-3 shows how to calculate the total revenue (TR), which is simply P X q. Thus 0 units bring in TR of 0; 1 unit brings in TR = $180.X 1 =$180; 2 units bring in $160 X 2 = $320; and so forth.
I~ this example of a straight-line or linear demand curve, total revenue at first rises with output, since the reduction in P needed to sell the extra q is moderate in this upper. elastic range of the demand curve. But when we reach the midpoint of the straight-line demand curve, TR reaches its maximum. This comes at q = 5, P = $100. ‘with TR = $500. Increasing q beyond (his point brings the firm into the inelastic demand region. For inelastic demand. reducing price increases sales less than proportionally, so total revenue falls. Figure 9-3(b) shows TR to dome-shaped; rising from zero’ at a very high price to a maximum of $500 and then falling to zero as price approaches zero.
How could you find the price at which revenues are maximized? You would see in Table 9-3 that TR is ‘maximized when q = 5 and P = 100. This is the point where the demand elasticity is’exactly 1. Note that the price per unit-can be called aver revenue (AR) to distinguish it from total revenue. Hence, we get P = AR by dividing TR by q (just as we earlier got AC by dividing TC by q). Verify that if column (3) had been written down before column (2). we could have filled in column (2) by division.
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