Talk:Profit maximization/Archives/2012

marginal cost-revenue diagram
isn't the marginal cost revenue diagram for a firm in perfect competition, which is sort of unhelpful in this case as in the long run this nfirm will not make abnormal profit? Anyone got a better diagram?

Other methods of Profit Maximization
Anyone else think this article could benefit from discussing additional ways of maximizing profit, as well as the way methods change based on market power and available data? In particular, I was thinking along the lines of estimating optimal markup on marginal cost based on elasticity of demand. This is important because it allows firms with less data about their demand curve to profit-maximize. Thoughts?Edwardmking 18:31, 28 February 2007 (UTC) Edward if you are still around i took your suggestion and was beginning a discussion of pricing policies when i was black flagged. Since I am not a devote wiki i was at a loss as to what to do - so i did the impossible - nothing. well i did right this note - does that count?--Jgard5000 (talk) 21:08, 16 September 2009 (UTC)jgard5000

Marginal Cost-Marginal Revenue Method
Firms always maximze profits by producing where MR = MC. This profit maximization rule applies to all types of market structures. The implication that the rule only applies in perfectly competitive settings or that a different more complex rule applies in cases of imperfect competition is simply incorrect. More later.--Jgard5000 (talk) 01:57, 16 September 2009 (UTC)Jgard5000 In fact the perfectly competitive market structure is simply a special case of the ruls. In the PC structure the firm continues to produce where MR = MC. The only complexity is that in a PC market MR = AR = D = P.--Jgard5000 (talk) 21:03, 16 September 2009 (UTC)jgard5000

Behavioral Assumption
Profit maximization is the behavioral assumption that dictates how firms make output and pricing decisions. --Jgard5000 (talk) 02:00, 16 September 2009 (UTC)jgard5000

Calculating profit maximizing price and quantity
In neoclassical economics the assumption is that firms (producers of goods and providers of services) singular objective is to maximize profits. Profits are the difference between total revenue (TR = P x Q) and total costs (TC = FC + VC). The problem for the firm manager is to determine the qauntity of goods to be produced and sold and the price at which to sell the goods. Several methods are available to the manager to determine the profit maximizing quantity and price. First, the manager can use the profit function to determine the output level at which the marginal profit is zero. A numerical example illustrates how this is done. Assume that the firm's price function (inverse demand function) is $$ P = 120 - .5Q$$ and its cost function is$$C = 420 + 60Q + Q2 $$.

The first step is to create a profit function. Again profit is total revenue minus total costs. Total revenue equals price, P, times quantity, Q. We can use the price equation to derive the total revenue equation as follows: $$TR = P X Q = (120 - .5Q)Q = 120Q - .5Q2.$$ The second step is to incorporate the total revenue and total cost functions into the profit function. Thus: $$Pr = (120Q - .5Q2) - (420 + 60Q + Q2) = 60Q - 1.5Q2 - 420$$. Third, take the first derivative of the profit function to derive the marginal profit function: $$dPr/dQ = 60 - 3Q.$$Fourth, set the marginal profit equation equal to zero and solve for Q: $$0 = 60 - 3Q; -60 = -3Q; Q = 20.$$ Therefore, the profit maximizing quantity is 20. To determine the profit maximizing price you plug the Q-Max quantity, 20, into the price equation: $$P = 120 - .5Q; P = 120 - .5(20); P = 120 - 10 = 110$$. Note that this method requires that managers know their firm's demand and cost functions and have a rudimentary knowlege of differential calculus. Try to walk your typical CEO through this problem and see how far you get. All CEO's love word problems and the lower end of higher mathematics. Furthermore, the demand and cost functions for even a small business organization are infintely more complex that those in this example. Even if they were known to a manager it is extremely unlikely that the manager could arrive at any meaningful answer to the question of p-max price and quantity. The rule does not apply to situations where the firm's production capacity is reached at a point where MPr > 0. In this case the firm would continue to produce until capacity is reached.--Jgard5000 (talk) 15:14, 16 September 2009 (UTC)Jgard5000 See Samuelson & Marks, Managerial Economics, 4th ed. (Wiley 2003) at 57.

A second method is the marginal revenue - marginal cost method. As noted in the discussion section firm's will maximize profits by producing where marginal revenue, MR, equals marginal cost, MC. This rule applies to all market structures. The first step in this method is to derive the MR function. To accomplish this simply take the first derivative of the total revenue function. Using the equations above: $$TR = 120Q - .5Q2$$ take the first derivative of the TR function to give the MR function: $$MR = 120 - Q$$Next derive the MC function from the total cost function in the same fashion: $$C = 420 + 60Q + Q2; MC = 60 + 2Q$$Finally equate MR and MC and solve for Q: $$120 - Q = 60 + 2Q; Q = 20$$Again determine the P=max price by plugging 20 into price equation.

There are certain strategies that will not work under most circumstances. For example, maximizing revenue rather than profit. This strategy has intuitive appeal but simply does not work. Using the same information our firm would maximize revenue by setting the MR function equal to zero and solving for Q: MR = 120 - Q; 0 = 120 - Q; Q = 120. Solving the profit equation using the revenue maximizing quantity will yield a loss. Pr = 60Q - 1.5Q2 - 420 using the profit max quantity yields 60(20) - 1.5(20)(20) - 420 or 1200 - 600 -420 or 180. --75.251.25.118 (talk) 10:33, 17 September 2009 (UTC)jgard5000

The primary reason that revenue maximization does not generally work as a profit maximizing strategy is that it fails to take into consideration variable cost. In situations where VC is nominal or zero revenue maximization is an appropriate strategy. For example, a promoter books an 18,000 seat coliseum for a rock concert. Once the venue is booked the variable costs associated with having the concert are small. The promoter would be justified in simply ignoring any VC and setting a price that would maximize revenue.--75.251.25.118 (talk) 10:32, 17 September 2009 (UTC)jgard5000

Airlines are another firm that can safely use revenue maximizing strategies. Once a flight is scheduled the variable costs associated with additional passengers is low. Software developers can use revenue maximizing pricing plans since a far greater proportion of the costs are fixed cost involved in the development of the software programs than variable costs associated with the production, marketing and distribution of the product. Tobacco companies also benefit from negligable variable costs.--75.251.25.118 (talk) 10:32, 17 September 2009 (UTC)jgard5000 —Preceding unsigned comment added by Jgard5000 (talk • contribs) 15:08, 16 September 2009 (UTC) The majr costs associated with cigarette production were advertising and distribution costs. With the tobacco settlement the major tobacco companies essentially locked in their market share and eliminated many of their major costs. Big MO no longer had to introduce and promote new brands - it just keeps pumpong out billions of marlboro lights. I wonder why some T companies did not oppose FDA regulation of tobacco - barrier to entry??? --Jgard5000 (talk) 15:01, 17 September 2009 (UTC)jgard5000

There are of course other pricing strategies used in an effort to maximize.optimize profits. Two exampes are optimal markup pricing and price discriminatio. Under optimal markup pricimg the firm's price is determined using the following formula: P = (Ep/1+Ep)MC where MC is marginal cost and Ep is the price elasticity of demand. The formula is called the markup rule and provides a means by which firms will know the proper amount of markup of price over marginal costs.Samuelson & Marks, Managerial Economics 4th ed. (Wiley 2003) at 102-05. Price discrimination is another pricing strategy that use elasticity. As Samuelson and Marks note price discrimination involves "selling the same good ... to different buyers at different prices." Price discrimination is a common business pratice. Airlines use price discrimination extensively. Airlines charge business travelers full fares while offering steep discounts to leisure travelers. At least two conditions must be present for price discrimination pricing plans to be successful. First you must be able to separate customers by their price elasticity of demand - identify those with high PED from those with low PED. Second you must be able to prevent arbitrage - a high PED customer form buying at a low price then reselling at a profit to a low PED customer.--75.203.69.26 (talk) 18:19, 17 September 2009 (UTC)Jgard5000

lecture / textbook style
This edit looks like something which would be a helpful part of a microeconomics lecture, but it's inappropriate for Wikipedia. See Wikipedia is not a textbook. C RETOG 8(t/c) 18:01, 14 September 2010 (UTC)

Planned edits
I plan to make revisions to the article based on the following points (some of which are anticipated earlier on this discussion page) -- if anyone objects, please let me know on an item-by-item basis. Thanks.

1. The opening sentence says profit maximization is a short run concept. Actually there is short run profit maximization and there is long run profit maximization.

2. The lede says there are several approaches to the problem -- actually there is only one, which can be described in several ways: maximizing rev minus cost is the same as equating MR to MC, unless there is a binding external constraint on output.

3. The lede says "total profit in a perfectly competitive market reaches its maximum point where marginal revenue equals marginal cost." This is true whether the market is competitive or not.

4. The Basic definition section says that wages are a fixed cost. That's true in the very short run if hiring and firing is sticky for some reason, but in the conventional short run, and in the long run this is not true.

5. The Basic definition section says that equipment maintenance and rent are fixed costs. That's true in the short run but not in the long run.

6. The Basic definition section says


 * Marginal cost and revenue, depending on whether the calculus approach is taken or not, are defined as either the change in cost or revenue as each additional unit is produced, or the derivative of cost or revenue with respect to quantity output. It may also be defined as the addition to total cost or revenue as output increase by a single unit.

The second sentence is redundant, and its use of the word "also" is misleading.

7. The Basic definition section says


 * For instance, taking the first definition, if it costs a firm 400 USD to produce 5 units and 480 USD to produce 6, the marginal cost of the sixth unit is approximately 80 dollars, although this is more accurately stated as the marginal cost of the 5.5th unit due to linear interpolation.

Here "approximately" is wrong. As for calling it the MC of the 5.5th unit, I've never heard that before, and it doesn't make any sense. Maybe its author was thinking of taking the midpoint when computing arc elasticities of demand.

8. The Basic definition section says


 * Calculus is capable of providing more accurate answers if regression equations can be provided.

I have no idea what that's supposed to mean here.

9. The sections "Total revenue total cost method" and "Marginal revenue-marginal cost method" describe these as "alternative approach[es]". Not true, and the relation between them needs to be explained.

10. Some notation in the second graph needs to be defined, and the material in the middle of "Marginal revenue-marginal cost method" needs more explanation.

11. The section "Maximizing revenue method" says


 * In some cases a firm's demand and cost conditions are such that marginal profits are greater than zero for all levels of production.[2] In this case the Mπ = 0 rule has to be modified and the firm should maximize revenue.[2] In other words the profit maximizing quantity and price can be determined by setting marginal revenue equal to zero.

Doesn't make sense -- if marginal profit is always greater than zero, there is no level of output at which marginal revenue equals zero, because marginal profit is marginal revenue minus marginal cost, the latter being always positive. And accordingly, the airplane flight example needs to be reinterpreted, either as a case of marginal profit (and marginal revenue) being everywhere positive and profit maximization being subject to a quantity constraint, or as the marginal revenue curve suddenly plunging to zero at the (n+1)st seat so that marginal revenue equals marginal cost between seat n and seat n+1.

12. The section "Markup pricing" doesn't explain that less than perfect competition is assumed (until belatedly near the end). Also, it says


 * Firm managers are unlikely to have complete information concerning their marginal revenue function or their marginal costs.

Then it goes on to assume that marginal cost and the price elasticity of demand are known.

13. The section "Markup pricing" uses notation PED without defining it; presumably it means the same thing as Ep --notational consistency is needed. Duoduoduo (talk) 21:42, 25 March 2012 (UTC)


 * Sounds good. For 7, I'd suggest that the original author was trying to suggest that there is a different between computing MC(n) (on a calculus basis) and TC(n)-TC(n - 1), and that actually, TC(n + 0.5) - TC(n-0.5) is a better approximation of MC(n). But I'm only guessing. Again, to guess at 8, I assume it means "if the function is differentiable [at...]". I think I disagree with 9 - "alternative approaches" is perfectly fine, although maybe you'd prefer "methods"? I mean, they appear differently on the page, so they are different in a key respect. Agree though the mathematical similarity could be explained better. - Jarry1250 [Deliberation needed] 22:26, 25 March 2012 (UTC)


 * Thanks for the helpful comments! As for #9, I see your point that they appear different on the page. How about if I change it to "alternative perspectives"? Duoduoduo (talk) 14:56, 26 March 2012 (UTC)

Does profit maximization apply to entities that aren't firms?
The definition of this article mentions firms only. EIN (talk) 06:40, 2 November 2012 (UTC)