Profit Maximization The simple definition of profit is revenue minus cost ( = R C). Profit is the primary economic objective of a business. As a working hypothesis, the firm maximizes profit that basically defines &quot;rational firm&quot; regardless of whether it operates in a competitive or monopolistic environment. Since our primary interest is in production, the models used to describe market structure are output-oriented. The general condition for profit maximization is to choose outputs so that &quot;<a href="/keyword/marginal-revenue/" >marginal revenue</a> &quot; (MR or mr) is equal to &quot;marginal cost&quot; (MC or mc). This is just a simple corollary of the general rule of equating marginal benefits to marginal cost. The key difference between competitive and monopolistic is that the competitive firm cannot influence price by manipulating output. The simple way of saying this is that the competitive firm acts as a price taker. In sharp contrast, monopolistic firms set prices by manipulating the demand curve. Since price is functionally related to quantity, its choice of output indirectly determines the price of the output. Except for this key difference, there is no reason to distinguish between competition and monopoly: both types of firm maximize profit by buying inputs (labor and capital) in factor markets to produce outputs for sale in product markets. Pure Competition: &quot;Atomistic Firms&quot; $/q . . . $/Q P* MR = p Firm acts as a &quot;price-taker&quot; q . . Q* S D Q Individual Firm Figure 1a MARKET Figure 1b This distinction bears repeating: the only difference (at least, in the model) between competitive firms and monopoly firms relates to control over the price (p) of their outputs. Whereas competitive firms act as price takers and treat p as a constant, a monopolist controls price and knows that raising or lowering price directly effects how much output (q) consumers are actually willing to buy (higher p, lower q, and vice-versa). This might disappoint you: competitive firms are not run by people who look like Robert Redford or Paul Newman and monopolists do not look like Lon Chaney or Bela Lugosi. A. Output Decision: Competitive Firm The competitive firm interacts with market forces. The price of its output is strictly determined by market forces (Figure 1b). The firm (Figure 1a) merely responds to that price by choosing its best output. The firm is very small (&quot;atomistic&quot;) relative to the market and, accordingly, any increase in its output (q) goes unnoticed in the market place. If that is true, the market absorbs additional output without a noticeable price reduction. This implies that each extra unit that is produced and sold increases the firm's revenue (don't confuse revenue with profit) by the market price (p). In other words, for the competitive firm (and only the competitive firm), MR and p are equivalent. To model the output choice, we now make use of the cost curves. That's why we went to the trouble of converting the accounting costs (wL + rK) in a function of output: c = c(q), which includes the fixed and variable components. By virtue of the law of diminishing returns, average cost (c/q) is u-shaped and marginal cost is upward sloping in its relevant range. In Figure 2, market price (p) is superimposed upon the average and marginal cost curves as a horizontal line. MAXIMUM PROFIT $/q = (p - c/q) q MC = P MC A p c/q Maximum Profit . . . ATC B NOT HERE !!! 0 Figure 2 We are going to use this graph a lot, so let's get familiar with it and focus on how it relates to profit. Start with a little algebra: = pq - c Total revenue minus total cost = (p c/q) q Profit per output (p c/q) multiplied by output In the graph, the latter formula relates to the area of a rectangle of dimensions p c/q (vertical) and corresponding q (horizontal). There are two points where p and c/q intersect (and the area shrinks to zero). Outside those two points, profit would be negative and the firm would operate at a loss (or shut down). In between the two points, there is one point (A) where the area is maximized. To locate that point, use marginal analysis: expand q as long as the last unit adds more to revenue (p) than it adds to cost (MC). Do not fight with the assumption that the firm cannot set price. In practice, nearly all firms get to post a price and do have some influence over it. However, the point is that a competitive environment greatly reduces pricing discretion. While a competitive firm can raise its price above &quot;market&quot; price, they rate to lose a lot of customers. The model just carries this to the extreme, whereby the firm loses all of its customers if it raises its price. In theory, price-taking behavior is a very useful abstraction, which captures the logic of &quot;perfect&quot; competition. It also provides a nice contrast to price-setting behavior (which is coming right up...). q* q B. Output Decision: Monopoly Note: This section may be postponed until we cover monopoly, but one reason to study it now is to clarify the difference between price-taking and price-setting. The most important feature of the monopoly model is that <a href="/keyword/marginal-revenue/" >marginal revenue</a> is less than price. By way of example, suppose the firm can sell either five units at a price of $10 apiece OR six units at a price of $9 each. It appears at the cash register that each sale adds $9 to total revenue. But the firm's real choice is between a total revenue of $50 or $54. Hence, <a href="/keyword/marginal-revenue/" >marginal revenue</a> is $4, not $9. The difference of $5 traces to those &quot;intramarginal units&quot; which get sold for $9 instead of $10 each. That reduction of $1 for each of 5 units captures the difference exactly. <a href="/keyword/marginal-revenue/" >marginal revenue</a> $/Q <a href="/keyword/marginal-revenue/" >marginal revenue</a> CURVE $/Q Generally lies below the Demand Curve Generally less than Price 10 9 .. 5 6 Extra unit adds price (P) to TR ... But price of &quot;intramarginal&quot; units has been reduced 10 9 .. A R = 50 R = 54 B 4 D Q 5 . D 6 MR Q Figure 2a Figure 2b Figure 2a illustrates the difference in terms of an ordinary market demand curve. In contrast to the competitive firm, the monopolist gets to set output for the whole market. For the increase in output from 5 to 6, the two rectangles measure the two components of <a href="/keyword/marginal-revenue/" >marginal revenue</a> . One area measures price (9 x 1) and the other measures the cumulative price reduction on intramarginal units (1 x 5). The distinction between price and <a href="/keyword/marginal-revenue/" >marginal revenue</a> generates a second curve (MR) in Figure 2b, in which <a href="/keyword/marginal-revenue/" >marginal revenue</a> is a function of quantity. To plot this curve accurately from discrete numbers, it is best to plot MR at midpoints at 5.5 for the increase from 5 to 6. The easy way is to use a little algebra. The equation for the example demand curve is p = 15 q. To get total revenue as a function of q, multiply by q: R(q) = 15 q q2. Then differentiate to get <a href="/keyword/marginal-revenue/" >marginal revenue</a> : R (q) = 15 2q. Note that R (q) = 4 if q = 5.5. To save steps, you can always go from a linear demand function to its <a href="/keyword/marginal-revenue/" >marginal revenue</a> function by merely doubling the slope coefficient. The monopolist's profit-maximizing position is illustrated in Figure 3, under the simplifying assumption that marginal cost is constant (instead of the usual upward-sloping curve). The point of profit maximization (M in Figure 3 is the monopoly equilibrium, representing both price and quantity. Equilibrium quantity (q* = 5) is determined from the intersection of MR and MC. At that quantity, the market determines a price of $10/unit. The profit of 25 is determined by multiplying the profit per unit (10-5) by the number of units produced (q* = 5), not counting fixed costs. Maximum Profit $/q 15 p* = 10 Maximum Profit = $25 5 . . M Set MR = MC MR = 15 2q* = 5 Solve for q* = 5 p* = 15 q* = 10 MC D q* = 5 MR q Figure 3