Economics
Cost Revenue and Profit Maximization
Cost, revenue, and profit maximization refers to the process by which a firm determines the level of output that will result in the highest possible profit. This involves analyzing the costs of production, the revenue generated from selling goods or services, and finding the output level that maximizes the difference between total revenue and total cost. It is a fundamental concept in business decision-making.
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10 Key excerpts on "Cost Revenue and Profit Maximization"
eBook - PDFEconomics for Investment Decision Makers
Micro, Macro, and International Economics
- Christopher D. Piros, Jerald E. Pinto(Authors)
- 2013(Publication Date)
- Wiley(Publisher)
Most economists believe that profit maximization pro- motes allocational efficiency—that resources flow into their highest-valued uses. Overall, the functions of profit are as follows: Rewards entrepreneurs for risk taking when pursuing business ventures to satisfy consumer demand. Allocates resources to their most efficient use; input factors flow from sectors with economic losses to sectors with economic profit, where profit reflects goods most desired by society. Spurs innovation and the development of new technology. Stimulates business investment and economic growth. There are three approaches to calculate the point of profit maximization. First, given that profit is the difference between total revenue and total costs, maximum profit occurs at the output level where this difference is the greatest. Second, maximum profit can also be cal- culated by comparing revenue and cost for each individual unit of output that is produced and sold. A business increases profit through greater sales as long as per-unit revenue exceeds per-unit cost on the next unit of output sold. Profit maximization takes place at the point where the last individual output unit breaks even. Beyond this point, total profit decreases because the per-unit cost is higher than the per-unit revenue from successive output units. A third approach compares the revenue generated by each resource unit with the cost of that unit. Profit contribution occurs when the revenue from an input unit exceeds its cost. The point of profit maximization is reached when resource units no longer contribute to profit. All three approaches yield the same profit-maximizing quantity of output. (These approaches will be explained in greater detail later.) Because profit is the difference between revenue and cost, an understanding of profit maximization requires that we examine both of those components.
eBook - PDF- Rhona C. Free(Author)
- 2010(Publication Date)
- SAGE Publications, Inc(Publisher)
Profit Maximization: The General Case Assumptions Because profit is the difference between the revenue and cost generated by factor inputs and outputs, the profit-maximizing model assumes given production, revenue, and cost functions. These, in turn, are defined only for given resource quality, technology, product prices, and factor prices. In addition to the assumptions that define production and cost functions, the simple profit-maximizing model assumes that individual firms have no effect on price (per-fect competition), that there is a predictable relationship between output and price (monopoly), or that the rival firms in imperfectly competitive markets react predictably to each other's actions in the market. It also generally ignores or assumes away risk and uncertainty, or at least that the firm's economic expectations are unchanged. Revenue, Cost, and Profit In its simplest form, the problem for the firm is to maximize profit (π), which is the difference between total revenue (77?) and total economic or opportunity cost (TO) —that is, to maximize π = 7 7 ? -TC. (1) The mathematical conditions for maximum profit apply to all profit-maximizing firms' choices in product and factor markets. Profit and Output The profit-maximizing firm will choose the output (q) that maximizes K(q) = TR(q)-TC(q), (2) where n(q), TR(q), and TC(q) are profit, revenue, and cost functions, respectively. Total revenue is simply the price of the product (P) multiplied by output (q), or TR(q) = Pq. (3) Output decisions are made in the short run, in which at least one of its factor inputs is fixed and does not vary with 111 112 . MICROECONOMICS output. The firm's short-run total cost is the sum of its fixed and variable cost, or TC(q) = FC + VC(q) (4) where TC(q) is the short-run total cost function, VC{q) is the variable cost function, and FC is fixed cost that does not vary with output. Substituting (4) and (3) into (2), the profit function becomes π (q) = TR(q) -TC(q) Pq-[FC+VC(q)].
eBook - ePub- John H Hoag(Author)
- 2012(Publication Date)
- WSPC(Publisher)
So far we have looked at the firm’s costs, but costs are only half of the information that firms need to make decisions. Firms also need to know revenue. The revenue and cost together determine profit which, in our model, is the focus of the firm’s attention. We will assume that firms act to maximize profit. Is this an accurate description of how firms behave?At one level, it is clearly not a very descriptive assumption. We know firms that do things that raise their cost without discernable impacts on their revenue. You must have seen firms supporting charities and other worthwhile projects. These clearly cost something without discernable revenues attached. One could argue that these activities enhance the firm’s reputation, but reputation is not revenue. So why do economists stick with this assumption? While not a perfect reflection of reality, the assumption does seem to reflect quite a bit about how businesses make decisions. We have seen news stories of firms that break laws in the pursuit of profit. Tales of Wall Street greed abound. These are, to a large extent, behaviors that start with profit maximization. For the economist, the assumption of profit maximization is the simplest assumption we can make that captures a sizable part of the behavior of firms. While not perfect, it is also not a bad assumption.To make progress toward understanding how this assumption yields results, we need to move forward with our discussion of the general revenue concepts. We will then develop the revenue concepts for competitive firms, which we will then combine with the cost concepts of the previous chapter to obtain profit. Once we have profit, we can move to profit maximization, the shutdown condition, and the firm’s supply curve. Here we go!5.2 Revenue ConceptsIn this section, we will develop the revenue concepts that will be used for all firms. When we are done with the general concepts, we will turn to the particular case of the competitive firm and see what the revenue curves look like in this case. We begin with definitions.
eBook - PDFManagerial Economics
The Analysis of Business Decisions
- Stephen Hill(Author)
- 2016(Publication Date)
- Red Globe Press(Publisher)
Sales revenue can be used as a surrogate for the size of the firm, and the manager's income, prestige, and aspirations more closely identified with sales revenue than with profit. Moreover, by maximising sales revenue, managers Profits and objectives 55 avoid the risks inherent in the adoption of highly profitable but risky ventures. Steady performance is seen as a more comfortable alternative than the possibility of losses. However, Baumol includes within his model the notion of a profit constraint, being some minimum absolute amount of profit neces-sary to satisfy shareholders (who are unlikely to know what max-imum profit is possible anyway) , and to prevent the possibility of a shareholder revolt endangering the security of managers. By making some simplifying assumptions, the Sales Revenue model can be described in terms of a diagram. Assume a single period, with conventional cost and revenue functions . Figure 3.3 is then just a repeat of Figure 3.1. Given the cost and revenue functions, profit is maximised at the output level Qm. The point of maximum sales revenue is at the highest point on the total revenue curve, corresponding to output Qs. The profit constraint can be represented by a horizontal line, the height of which above the output axis is determined by the amount of profit necessary to satisfy shareholders. If the profit constraint is 1l't> the absolute maximum sales revenue produces enough profit to satisfy this, and output will be Qs. Note that output is higher, and price lower, than with the objective of maximising profit (hence sales revenue max-imisation is a substitute for profit maximisation) . TC TR ~t=========~~~~~=t=====~ 3 1-1-1-----------:~---t--t---t---* ; / Qm ~ Output Figure 3.3 Sales revenue maximisation 56 Managerial Economics However, if the profit constraint is above 1r 1 (say 1r 2 ) then output Qs does not produce enough profit to satisfy the constraint.
eBook - PDF- Paul Cashian(Author)
- 2017(Publication Date)
- Red Globe Press(Publisher)
Equation 2.3 shows the firm’s objective function, which is to maximise profits given the constraints discussed above. The firm needs to maximise the difference between revenue and costs – but can only do this by varying its output level Q as the price is fixed by the market. ...................................... The Economists’ Firm 27 Max = rP Q − cC Q w.r.t Q (2.3) From this, we thus arrive at the familiar profit maximisation condition that marginal revenue, the revenue from the last unit produced, should equal marginal cost, the cost incurred in producing the last unit. MAX P = rP Q − cC Q w.r.t Q ⇒ (2.4) ⇒ R/Q − C/Q = 0 ⇒ R/Q = C/Q MR = MC In effect, all firms pick a level of output Q that maximises Equation 2.4. This profit maximising condition can also be represented graphically as shown in Figure 2.4. The explanation for the shape of the various curves forms the central part of any introductory microeconomics course on production theory, and readers are referred to any of the numerous texts for an explanation (for example, Sloman and Sutcliffe, 2003). The profit maximising output of q * is shown as where the Quantity Revenue, cost C = c ( C , Q ) R = r ( P , Q ) q * δ C / δ Q δ R / δ Q Quantity Revenue, cost q * Figure 2.4 The production process (graphical representation) ........................................................
- Linda Low(Author)
- 2000(Publication Date)
- WSPC(Publisher)
Profit after tax may be distinguished from gross profit, since tax is paid to the government. Profit maximisation (ie, to make the largest profit possible) is the conventional goal of a firm, although other goals such as sales maximisation (a strategy of high volume sales to generate profitability) may be pursued. Profit maximisation is synonymous with cost minimisation. The economist's concept of profit is different from that of the accountant, as accounting profit is measured in actual dollars based on the firm's earnings and expenditures. Economists also consider the opportunity cost of allocating resources to produce a particular good in lieu of the next best alternative. As such, normal or zero profit (see chapter 3) is the minimum level of profit needed to encourage a firm to continue operations. Excess or supernormal profit, such as that enjoyed by monopolies, implies a sustained rate of return (before taxes on sales or invested capital) exceeding that of similar products or industries operating under similar conditions in terms of production, 40—ECONOMICS OF IT AND THE MEDIA distribution and risks. In the long run, excess profits hold for approximately five to ten years. The decision to stay in the industry while earning normal profits, or to fix the rate of return for excess profits, depends on the market structure and can be rather arbitrary. There is a need to distinguish between the concepts of average and marginal cost and revenue at the firm or industry levels. An industry is made up of all the firms that produce the same product (eg, the electronic industry). An individual firm can be privately owned (eg, a sole proprietorship incorporated but unlisted, or a private limited if listed on the stock market), or state-owned and formed to organise the factors of production in order to produce goods and services for the market. A distinction must be made between the long run and the short run.
eBook - PDF- David M. Kreps(Author)
- 2019(Publication Date)
- Princeton University Press(Publisher)
As for economic concepts and insights: • Thinking like an economist in many cases means thinking about the marginal impact of decisions being made. Think margins, not averages! • The pieces of the basic model of a single-product firm with market power are (a) the demand function the firm faces, typically denoted D ( p ) , (b) the total-cost function TC ( x ) , and (c) the assumption that the firm will select the price it charges/quantity it produces and sells to maximize its profit, or revenue less total cost. (And, despite its flaws as a realistic model of what firms do, it is a model that will generate a lot of insight into the actions of real firms.) • To find the profit-maximizing price–quantity pair: (a) If necessary, invert the demand function to find the inverse demand function P ( x ) . (b) Construct the total revenue function TR ( x ) = xP ( x ) and find its derivative, the marginal cost function MR ( x ) . (c) Find the derivative of the total cost function, the marginal cost function MC ( x ) . (d) Find the level of production at which marginal cost equals marginal revenue. And, as needed, (e) plug this level of production into inverse demand to find the profit-maximizing price to set. • For a firm with market power, MR ( x ) = P ( x ) + xP 0 ( x ) which, if P is downward sloping, is less than P ( x ) . The difference between MR ( x ) and P ( x ) reflects the loss in revenue that occurs because the price-per-unit must be lowered to sell the extra unit. • When you deal with multiproduct firms, profit maximization is where the marginal revenue from each good equals the marginal cost of the same good. But be careful : Marginal cost and marginal revenue of any good are the marginal impact of increasing production of that good on the the firm’s total revenue and total cost, not simply the impact on the total revenue or total cost of that specific good.
eBook - PDFMicroeconomic Theory
Basic Principles and Extensions
- Walter Nicholson, Christopher Snyder(Authors)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 368 Part 4: Production and Supply This result can be easily demonstrated. As before, total revenue ( R ) is the product of the quantity sold ( q ) times the price at which it is sold ( p ), which may also depend on q . Using the product rule to compute the derivative, marginal revenue is MR 1 q 2 5 dR dq 5 d 3 p 1 q 2 # q 4 dq 5 p 1 q # dp dq . (11.8) Notice that the marginal revenue is a function of output. In general, MR will be different for different levels of q . From Equation 11.8 it is easy to see that if price does not change Profits, defined as revenues ( R ) minus costs ( C ), reach a maximum when the slope of the revenue func-tion (marginal revenue) is equal to the slope of the cost function (marginal cost). This equality is only a necessary condition for a maximum, as may be seen by comparing points q * (a true maximum ) and q ** (a local minimum ), points at which marginal revenue equals marginal cost. Revenues, costs Profits Losses Output per period Output per period (a) (b) q ** q * q * C R 0 FIGURE 11.1 Marginal Revenue Must Equal Marginal Cost for Profit Maximization Copyright 2017 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-300 Chapter 11: Profit Maximization 369 as quantity increases 1 dp / dq 5 0 2 , marginal revenue will be equal to price. In this case we say that the firm is a price-taker because its output decisions do not influence the price it receives. On the other hand, if price decreases as quantity increases 1 dp / dq , 0 2 , marginal revenue will be less than price. A profit-maximizing manager must know how increases in output will affect the price received before making an optimal output decision. If increases in q cause market price to decrease, this must be taken into account.
eBook - PDF- Martha L. Olney(Author)
- 2015(Publication Date)
- Wiley(Publisher)
So profit increases if rev- enue increases more than costs. The notebook company is currently producing 6,000 notebooks per day. Should the company produce another 100 notebooks per day? The answer depends on the additional revenue (marginal revenue) from producing and selling the 100 notebooks and the additional cost (marginal cost) of producing the 100 notebooks. If the additional revenue exceeds the additional cost, the company should produce the 100 notebooks. Doing so would increase their profit. But if the additional revenue from producing and selling the 100 notebooks is less than the additional cost, the company should not produce that 100 notebooks. Doing so would decrease their profit. TRY Answers to all “Try” questions are at the back of the book. 1. A firm receives $4,000 in revenue per week and incurs costs of $3,000 per week. What is its weekly profit? 2. Pepper’s Pizza is currently producing 400 pizzas per week. Producing and selling an additional 40 pizzas per week would increase revenue by $400 and increase costs by $500. Will producing an additional 40 pizzas per week increase, decrease, or have no effect on Pepper’s Pizza’s profit? PRODUCT CURVES, COST CURVES, AND PROFIT MAXIMIZATION Now let’s take this profit-maximization story, break it out, and add in the graphs. Production refers to combining inputs—labor, machines, materials, and so on—into output. Economists define the short run as a period of time when some inputs are fixed in quantity. Easy examples are the square footage of the business and the number of machines. Capital refers to buildings and machines. So economists often say: In the short run, the amount of capital is fixed. The long run is defined as a period of time long enough that the quantities of all inputs can be changed. A business can sell its building or get out of its lease. Machinery can be sold or purchased.
eBook - PDF- Lee S. Friedman(Author)
- 2017(Publication Date)
- Princeton University Press(Publisher)
However, perhaps the sales maximizer may produce too much output, that is, a quantity greater than Q E . With constant-returns-to-scale tech-nology, this is not possible: Profits are down to zero at Q E , so the profit constraint keeps output less than Q E . But in Figure 10-8b, another case is illustrated 37 : The sales maximizer Private Profit-Making Organizations 399 36 This is demonstrated shortly. A common phrase that is also a logical impossibility is “getting the maximum output for the minimum cost.” You can produce a given output at minimum cost or you can maximize output for a given cost, but you cannot maximize and minimize simultaneously. It is always possible, for example, to reduce costs by reducing output. 37 A necessary condition for this case is that MC > AC at the point where MC intersects the demand curve, which in turn implies that the firm is producing on the rising portion of its average cost curve (usually associated 400 Chapter Ten Figure 10-8. Revenue maximization with a minimum profit constraint: (a) The quantity is in-efficiently low ( Q R Π < Q E ). (b) The quantity is inefficiently high ( Q E < Q R Π ). (a) (b) O O with diseconomies of scale). Monopolies can still be “natural” in this situation as long as the subadditive condi-tion is met by the (least total) cost function: C ( Q ) < C ( Q 1 ) + C ( Q 2 ), where Q is the monopoly quantity and Q 1 and Q 2 are production amounts of two separate firms with Q 1 + Q 2 = Q. This case arises when economies of scale char-acterize lower production levels and when they more than offset the diseconomies that set in at the higher level. 38 Patrick Bolton and David S. Scharfstein, “Corporate Finance, the Theory of the Firm, and Organizations,” Journal of Economic Perspectives, 12, No. 4, Fall 1998, pp. 95–114. 39 F. M. Scherer, “Corporate Takeovers: The Efficiency Arguments, ” Journal of Economic Perspectives, 2, No.
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