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# marginal benefit formula

From Wikipedia

Gross margin

Gross margin, gross profit margin or gross profit rate is the difference between the sales and the production costs excluding overhead, payroll, taxation, and interest payments. Gross margin can be defined as the amount of contribution to the business enterprise, after paying for direct-fixed and direct-variable unit costs, required to cover overheads (fixed commitments) and provide a buffer for unknown items. It expresses the relationship between gross profit and sales revenue. It is a measure of how well each dollar of a company's revenue is utilized to cover the costs of goods sold.

It can be expressed in absolute terms:

Gross margin = net sales - cost of goods sold + annual sales return

or as the ratio of gross profit to sales revenue, usually in the form of a percentage:

\text{Gross margin percentage} = \text{(revenue-cost of goods sold)/revenue}

Cost of sales (also known as cost of goods (CoGs)) includes variable costs and fixed costs directly linked to the sale, such as material costs, labor, supplier profit, shipping costs, etc. It does not include indirect fixed costs like office expenses, rent, administrative costs, etc.

Higher gross margins for a manufacturer reflect greater efficiency in turning raw materials into income. For a retailer it will be their markup over wholesale. Larger gross margins are generally good for companies, with the exception of discountretailers. They need to show that operations efficiency and financing allows them to operate with tiny margins.

## How gross margin is used in sales

Retailers can measure their profit by using two basic methods, markup and margin, both of which give a description of the gross profit of the sale. The markup expresses profit as a percentage of the retailer's cost for the product. The margin expresses profit as a percentage of the retailer's sales price for the product. These two methods give different percentages as results, but both percentages are valid descriptions of the retailer's profit. It is important to specify which method you are using when you refer to a retailer's profit as a percentage.

Some retailers use margins because you can easily calculate profits from a sales total. If your margin is 30%, then 30% of your sales total is profit. If your markup is 30%, the percentage of your daily sales that are profit will not be the same percentage.

Some retailers use markups because it is easier to calculate a sales price from a cost using markups. If your markup is 40%, then your sales price will be 40% above the item cost. If your margin is 40%, your sales price will not be equal to 40% over cost (indeed it will be 60% above the item cost).

## Markup

Markup can be expressed either as a decimal or as a percentage, but is used as a multiplier. Here is an example:

If a product costs the company $100 to make and they wish to make a 50% profit on the sale of the product (sale dollars) they would have to use a markup of 100%. To calculate the price to the customer, you simply take the product cost of$100 and multiply it by (1 + the markup), e.g.: 1+1=2, arriving at the selling price of $200. The equation for calculating gross margin is: gross margin = sales - cost of goods sold A simple way to keep markup and gross margin factors straight is to remember that: 1. Percent of markup is 100 times the price difference divided by the cost. 2. Percent of gross margin is 100 times the price difference divided by the selling price. ## Gross margin (as a percentage of sales) Most people find it easier to work with gross margin because it directly tells you how many of the sale dollars are profit. In reference to the two examples above: The$200 price that includes a 100% markup represents a 50% gross margin. Gross margin is just the percentage of the selling price that is profit. In this case 50% of the price is profit, or $100. \frac{$200 - $100}{$200} * 100% = 50%

In the more complex example of selling price $339, a markup of 66% represents approximately a 40% gross margin. This means that 40% of the$339 is profit. Again, gross margin is just the direct percentage of profit in the sale price.

In accounting, the gross margin refers to sales minus cost of goods sold. It is not necessarily profit as other expenses such as sales, administrative, and financial must be deducted.And it means company are reducing their cost of production or passing their cost to customers. the higher ratio is better

## Converting between gross margin and markup

The formula to convert a markup to gross margin is:

\text{Gross margin} = \frac{\text{markup}}{(1 + \text{markup})}

Examples:

• Markup = 100%; GM = [1 / (1 + 1)] = 0.5 = 50%
• Markup = 66%; GM = [0.66 / (1 + 0.66)] = 0.39759036 = 39.759036%

The formula to convert a gross margin to markup is:

\text{Markup} = \frac{\text{gross margin}}{(1 - \text{gross margin})}

Examples:

• Gross margin = 0.5 = 50%; markup = [0.5 / (1 - 0.5)] = 1 = 100%
• Gross margin = 0.39759036 = 39.759036%; markup = [0.39759036 / (1 - 0.39759036)] = 0.659999996 = 66%

## Using gross margin to calculate selling price

Given the cost of an item, one can compute the selling price required to achieve a specific gross margin. For example, if your product costs $100 and the required gross margin is 40%, then Selling price =$100 / (1 - 40%) = $100 / 0.60 =$166.67

## Differences between industries

In some industries, like clothing for example, profit margins are expected to be near the 40% mark, as the goods need to be bought from suppliers at a certain rate before they are resold. In other industries such as software product development, since the cost of duplication is negligible, the gross profit margin can be higher than 80% in many cases.

Conditional probability

Conditional probability is the probability of some eventA, given the occurrence of some other event B. Conditional probability is written P(A|B), and is read "the (conditional) probability of A, given B" or "the probability of A under the condition B". When in a random experiment the event B is known to have occurred, the possible outcomes of the experiment are reduced to B, and hence the probability of the occurrence of A is changed from the unconditional probability into the conditional probability given B.

Joint probabilityis the probability of two events in conjunction. That is, it is the probability of both events together. The joint probability of A and B is written \scriptstyle P(A \cap B), P(AB) or \scriptstyle P(A, B)

Marginal probabilityis then the unconditional probability P(A) of the event A; that is, the probability of A, regardless of whether event B did or did not occur. If B can be thought of as the event of arandom variableX having a given outcome, the marginal probability of A can be obtained by summing (or integrating, more generally) the joint probabilities over all outcomes for X. For example, if there are two possible outcomes for X with corresponding events B and B', this means that \scriptstyle P(A) = P(A \cap B) + P(A \cap B^'). This is called marginalization.

In these definitions, note that there need not be a causal or temporal relation between A and B. A may precede B or vice versa or they may happen at the same time. A may causeB or vice versa or they may have no causal relation at all. Notice, however, that causal and temporal relations are informal notions, not belonging to the probabilistic framework. They may apply in some examples, depending on the interpretation given to events.

Conditioning of probabilities, i.e. updating them to take account of (possibly new) information, may be achieved through Bayes' theorem. In such conditioning, the probability of A given only initial information I, P(A|I), is known as the prior probability. The updated conditional probability of A, given I and the outcome of the event B, is known as the posterior probability, P(A|B,I).

## Introduction

Consider the simple scenario of rolling two fair six-sided dice, labelled die 1 and die 2. Define the following three events (not assumed to occur simultaneously):

A: Die 1 lands on 3.
B: Die 2 lands on 1.
C: The dice sum to 8.

The prior probability of each event describes how likely the outcome is before the dice are rolled, without any knowledge of the roll's outcome. For example, die 1 is equally likely to fall on each of its 6 sides, so P(A)&nbsp;=&nbsp;1/6. Similarly P(B) = 1/6. Likewise, of the 6&nbsp;&times;&nbsp;6 = 36 possible ways that a pair of dice can land, just 5 result in a sum of 8 (namely 2 and 6, 3 and 5, 4 and 4, 5 and 3, 6 and 2), so P(C) = 5/36.

Some of these events can both occur at the same time; for example events A and C can happen at the same time, in the case where die 1 lands on 3 and die 2 lands on 5. This is the only one of the 36 outcomes where both A and C occur, so its probability is 1/36. The probability of both A and C occurring is called the joint probabilityof A and C and is written P(A \cap C), so P(A \cap C) = 1/36. On the other hand, if die 2 lands on 1, the dice cannot sum to 8, so P(B \cap C) = 0.

Now suppose we roll the dice and cover up die 2, so we can only see die 1, and observe that die 1 landed on 3. Given this partial information, the probability that the dice sum to 8 is no longer 5/36; instead it is 1/6, since die 2 must land on 5 to achieve this result. This is called the conditional probability, because it is the probability of C under the condition that A is observed, and is written P(C&nbsp;|&nbsp;A), which is read "the probability of C given A." Similarly, P(C&nbsp;|&nbsp;B) = 0, since if we observe die 2 landed on 1, we already know the dice can't sum to 8, regardless of what the other die landed on.

On the other hand, if we roll the dice and cover up die 2, and observe die 1, this has no impact on the probability of event B, which only depends on die 2. We say events A and B are statistically independentor just independent and in this case

P(B \mid A) = P(B) \, .

In other words, the probability of B occurring after observing that die 1 landed on 3 is the same as before we observed die 1.

Intersection events and conditional events are related by the formula:

P(C \mid A) = \frac{P(A \cap C)}{P(A)}.

In this example, we have:

1/6 = \frac{1/36}{1/6}

As noted above, P(B \mid A) = P(B), so by this formula:

P(B) = P(B \mid A) = \frac{P(A \cap B)}{P(A)} .

On multiplying across by P(A),

P(A)P(B) = P(A \cap B). \,

In other words, if two events are independent, their joint probability is the product of the prior probabilities of each event occurring by itself.

## Definition

Given a probability space (&Omega;,&nbsp;F,&nbsp;P) and two eventsA,&nbsp;B&nbsp;&isin;&nbsp;F with P(B)&nbsp;>&nbsp;0, the conditional probability of A given B is defined by

P(A \mid B) = \frac{P(A \cap B)}{P(B)}.\,

If P(B)&nbsp;=&nbsp;0 then P(A&nbsp;|&nbsp;B) is undefined (see Borelâ€“Kolmogorov paradox for an explanation). However it is possible to define a conditional probability with respect to a &sigma;-algebra of such events (such as

2007 Formula One season

The 2007 Formula One season was the 58th season of FIAFormula One motor racing. It featured the 2007 FIA Formula One World Championship, which began on 18 March and ended on 21 October after seventeen events. The Drivers' Championship was won by Ferrari driver Kimi RÃ¤ikkÃ¶nen by one point at the final race of the season, making RÃ¤ikkÃ¶nen the third Finnish driver to take the title. An appeal by McLaren regarding the legality of some cars in the final race could have altered the championship standings, but on 16 November, the appeal was reportedly rejected by the International Court of Appeal, confirming the championship results. RÃ¤ikkÃ¶nen entered the final race in third position in the drivers' standings, but emerged as champion after the chequered flag, a feat that had been accomplished only by Giuseppe Farina in 1950. It has since been accomplished again, by Sebastian Vettel, in 2010.

A major talking point of the season had been an espionage controversy involving Ferrari and McLaren, which led to McLaren being excluded from the Constructors' Championship. As a result, Ferrari clinched the championship at the Belgian Grand Prix.

The 2007 season was significant in that it heralded the end of the existing Concorde Agreement between the existing Formula One constructors and Bernie Ecclestone. In particular, Mercedes-Benz, BMW, and Honda (collectively the Grand Prix Manufacturers' Association) had a number of outstanding disagreements with the FIA and Ecclestone on financial and technical grounds. They had threatened to boycott Formula One from the 2008 season onwards and instead stage their own rival series, before signing a memorandum of understanding (MoU) at the 2006 Spanish Grand Prix.

The 2007 Australian Grand Prix was the first time since the 1986 Spanish Grand Prix that there was a Formula One field without a Cosworth engine.

This was the last season for all the race cars to use traction control since 2001.

Honda F1 ran with an "Earth livery" on their RA107 car, the first time since 1968, when sponsorship in the sport became widespread, that a team ran sponsor-free for an entire season.

## Pre-season testing

Pre-season testing began in November 2006 at the Circuit de Catalunya, with ten of the eleven teams participating in the test sessions. The most notable absentees were Fernando Alonso and Kimi RÃ¤ikkÃ¶nen, who were still under contract at Renault and McLaren respectively. Jenson Button was also absent as he had suffered a hairline fracture on his ribs after a go-karting accident in preparations for the November tests. Lewis Hamilton made his first appearance in a McLaren since being confirmed as Alonso's team-mate for 2007.

Felipe Massa topped the times on the first two days of testing. Massa's testing partner, Luca Badoer, took the fastest time on the third day, although interest was on the fact that double World Champion Mika HÃ¤kkinen joined Hamilton and de la Rosa at McLaren for a one off test, although the Finnish driver was over three seconds slower than Badoer's time, completing 79 laps of the Spanish circuit.

The other big story of 2007 was the return to a single tyre formula (Bridgestone). It was perceived that this accounted for some of the reason why Ferrari led the early tests, although it was claimed by Bridgestone that the 2007 tyre is of a completely new build, thus minimising any real benefit for the 2006 Bridgestone teams (Ferrari, Toyota, Williams, Midland/Spyker and Super Aguri).

Toyota was the only team out for the fourth day of testing at Barcelona, as the Japanese works team chose to miss the first day of testing. Both Ralf Schumacher and From Yahoo Answers

Question:What are the formulas for finding the Margin of Error? I remember one, but it doesn't seem to be finding the right answer. o.O And how do you find the boundaries of the confidence interval? Specific formulas or steps in SPSS would be great! THANKS EXAMPLE QUESTION: A random sample of 25 jack pines in a forest reserve showed an average of 2 mistletoe infections. It is known from previous data that the standard deviation of all mistletoe infections is 0.5 infections. It is also known that the number of infections in the population are normally distributed. A researcher wants to make a 99% confidence interval based on this information. What is the margin of error? (A) 1.288 (B) .1645 (C) 1.960 (D) .2576 What is the lower boundary of the confidence interval? (A) 2.2576 (B) 1.8355 (C) 1.7424 (D) 1.8040

Answers:To find the margin of error= Critical value x standard error Standard error: Standard Deviation/Square root (Sample size) Standard error: 0.5/sqr 25 : 0.5/5 : 0.1 Critical value: 99% confidence= 2.576 Margin of Error: 0.1 x 2.576 = .2576 answer is d Hope this helps

Question:Land is directly related to agriculture. If there is an increase in land does this lead to an increase or a decrease in the MPL in agriculture? Why?

Answers:In economics, the marginal product or marginal physical product is the extra output produced by one more unit of an input (for instance, the difference in output when a firm's labor is increased from five to six units). Assuming that no other inputs to production change, the marginal product of a given input (X) can be expressed as: Y = Y/ X = (the change of Y)/(the change of X). In neoclassical economics, this is the mathematical derivative of the production function.... Note that the "product" (Y) is typically defined ignoring external costs and benefits. In the "law" of diminishing marginal returns, the marginal product of one input is assumed to fall as long as some other input to production does not change. In the neoclassical theory of competitive markets, the marginal product of labor equals the real wage. In aggregate models of perfect competition, in which a single good is produced and that good is used both in consumption and as a capital good, the marginal product of capital equals its rate of return. As was shown in the Cambridge capital controversy, this proposition about the marginal product of capital cannot generally be sustained in multi commodity models in which capital and consumption goods are distinguished. Marginal product is the slope of the total product curve and is given by: MP = Total product Quantity of labor units In agriculture, land has a crucial importance in production process. If there is an increase in land it leads to an increase in production level. The same amount of labor is used in more land it will lead to increase the marginal production of a labor.

Question:two cold drawn bars (AISl steel)bolted together as a lap joint.The bolts are (ISO 5.8)200mm from one end and 450mm from the other and are 50mm apart.Centre of beam is 350 mm from end

Answers:Please visit: http://www.efunda.com/formulae/solid_mechanics/columns/calc_column_structural_steel.cfm The factor of safety (FS) is equal to the input cohesion (C) plus the effective normal stress acting on a plane (sigma prime sub n) times the tangent of the angle of internal friction (Phi), all divided by the reduced cohesion (C sub r) plus the effective normal stress acting on a plane (sigma prime sub n) times the tangent of the reduced angle of cohesion (Phi sub r). http://www.answers.com/topic/factor-of-safety-1

Question:OK so here is the question: 335 visitors were questioned as part of a survey done by the McDowell Group, 78 percent were "very satisfied" with their time in the town they were visiting. This is what they wanted to know: The reported margin of error was 5.5 percent. Does this agree with your calculation? Construct a 95% confidence interval for the true proportion of visitors who are "very satisfied" with their visit. ( I came up with 3.1% - 6.1% am I wrong?) Does it appear that the 'rule for sample proportions was used' to calculate the margin of error or the formula using the sample proportions? I came up with a margin of error 2.68% am I wrong? I don't understand how they came up with 5.5%! Assuming the sample is representative of all multiday visitors to, can you reasonably conclude that more than 50% of all such visitors are "very satisfied" with their visit? Can you reasonably conclude that more than 75% of all such visitors are "very satisfied"?

Answers:5.5% sounds reasonable for an n=335 sample size. The 95% confidence interval is probably 72.5%-83.5% of visitors very satisfied with their time. (Margin of error is the radius of a confidence interval for a particular statistic from a survey.) It'd be impossible to get a margin of error of 2.86% on a sample size that small. So, you could reasonably conclude that more than 50% of all the visitors were "very satisfied", but you couldn't say for sure that more than 75% of the visitors were "very satisfied".