Category: Marginal Cost

Marginal and Derivatives Analysis and Their Importance for Business and the Economy

In the early 1870s, three economists, William Stanley Jevons, Carl Meneger and Leon Walrus, made similar, though separate, observations in three different countries: England, Austria and Switzerland. They broke with classical economics in terms of the basic goods and services valuation principles. The classical economists based the value of a commodity on its cost of production, thus conferring on it a sort of intrinsic value, likewise from the point of view of the consumer, the value depended on the amount of commodity need or pleasure obtained from its consumption. Including the marginalists, as they came to be called, or neoclassical economists. The utility of a product or service is dependent on the cost of generating the last unit produced or the benefit of the last unit consumed, hence the marginal cost and marginal Benefit ideas. This way of thinking explained why a good for which there was no demand would be disposed of irrespective of its cast production and why air which is so vital to our survival is free. But the diamonds, without which we can exist, are too costly. The core principle of neoclassical economics was to optimize consumer utility and producer income. At the same time marginal costs and marginal utility had a ready-made equivalent in the form of a derivative calculus. A special case of optimization was to optimize utility or minimize costs. Therefore, the use of mathematics has increased in the economics. In 1892 Irving Fisher published his dissertation which used the mathematics extensively. Many economists used calculation tools and tackled various economic issues. It was Paul Samuelson who unified introduced the marginal in his foundations of economic analysis (1947). Today, marginal analysis and calculus usage are permeating every corner of the economy. Differentiation’s importance is not confined to microeconomics. Differentiation is the basis of the dynamic optimization and differentiation equation, which are the key methods of macroeconomics for dynamic analysis. Ultimately, in statistical and econometric estimation and inference, derivative and significant function.

The history of derivatives goes back to the origins of trade in Mesopotamia during the fourth millennium BC. Following the fall of the Roman Empire, contracts for the future production of goods continued to be used in the Byzantine Empire in the eastern Mediterranean and survived in Western Europe under canon law. Capital markets in Italy and Low Countries became more sophisticated during the Renaissance. For the first time in Antwerp, and then in Amsterdam in the sixteenth century, contracts for the future delivery of securities were used on a large scale. By the end of the seventeenth century, derivative trading on securities spread from Amsterdam to England and France. Financial practitioners created graphical devices to represent derivative contracts around 1870. Profit charts made derivatives available to young scientists, including Louis Bachelier and Vinzenz Bronzin, who had the technical skills required for rigorous derivative pricing analysis.

Marginal Analysis

To define marginal analysis is the evaluation of the costs and benefits of other activities outweighs costs, for example, if a business considers raising the amount of goods it produces, it would carry out a marginal analysis to ensure that the costs of manufacturing more items outweigh the potential costs that follow the decision. Examples include increased labor costs or additional materials you may need to manufacture the goods. Marginal analyzes are helpful in helping individuals and organizations determine how to distribute capital to optimize productivity and benefits and minimize objectives.

In economics, marginal analysis implies we look at the level of consumption or expense. it provides a clear image of the overall cost. For example, the net cost of running a plane from London to New York would be several thousand pounds. But, the cost of transporting an additional passenger is very small for a 50 per cent full aircraft. Therefore, the marginal cost of transporting 102nd passengers is also very low as compared to the overall cost.

Marginal cost (MC) is the cost of generating the final unit of product (the difference between Qn and Qn-1 in gross cost ‘TC’) since MC=∆TC/∆Q.

In business and economics, one important application of mathematics is marginal analysis. The word ‘marginal’ in economics refers to the rate of change, which is to a derivative. Therefore, if C(X) is the total cost of manufacturing X times, then C(X) is referred to as the marginal cost and reflects the instantaneous rate of change in the total cost proportional to the amount of products produced. Therefore, the marginal revenue is the product of the overall income function and the gross contribution function.

Marginal Benefit Vs Marginal Cost

The marginal benefit is the difference you’ll get when you make up a different choice. In business, this is usually the extra income that the company earns as it rises in production and/or selling additional products. Marginal cost is the additional cost you incur when manufacturing additional product units. Usually, marginal costs decrease if a business delivers a larger number of goods.

Marginal Analysis and Opportunity Cost

To consider the risk and profit of such practices, you do need to consider the risk of opportunity. Cost of opportunity is the valuable benefit you miss when choosing one option over another. For example, if an organization has place for another worker in its budget and is considering recruiting another worker to work in a warehouse, then a marginal analysis indicates that recruiting another worker has a net marginal

Profit

In other words, the capacity to produce more products outweighs the labor cost increase. However, hiring that person may not yet be the company’s best decision. For example, if the company knows that recruiting an extra sales agent will have a better net marginal profit, then the correct decision is to employ someone else for distribution rather than someone else to work at the plant. The extra productivity the company should have gained by recruiting someone to work in the warehouse is the cost of opportunity.

Marginal analysis and Observed Change

In certain cases, making minor organizational changes that make sense for an organization, and then doing a marginal review afterwards to identify improvements in costs and benefits that resulted as a result of such improvements. A business that makes children’s toys, for example, may prefer to raise production by 1 percent to see if improvements are happening in demand and how they affect capital. If the managers find that the advantages of an increase in output outweigh the increased costs incurred by the company, they may opt to retain the higher rate of production or even boost production again by 1 percent to monitor the improvements taking place. Companies may define optimum production levels through minor adjustments and observable improvements.

Marginal Analysis and Variables

When using marginal analysis for decision-making, you need to take into account cost and production variables. The amounts of the products you produce is evaluated by the most frequent variable companies. Others, however, such as shipping fees, are increasing as you produce and distribute a higher number or weight of products. You can select from a variety of production levels with differing degrees of productivity by making small improvements in output and tracking the gains and costs that follow those improvements.

Derivative Analysis

Derivative analysis is a powerful diagnostic tool which improves data understanding from pumping tests. The derivative used to measure the pumping test is given by the drawdown data plotted on a graph with semi log axes (linear drawdown and logarithmic time) throughout real-life; we make use of derivatives to measure market income and loss by using illustrations. They also use them to calculate the velocity or distance that they travel in miles per hour or kilometers an hour, and more. Similarly, they are also used to derive calculations of Physics. Differentiation is the method by which to find a derivative. A function’s derivative represents the exit value transition rate with respect to its input value. In contrast, differential means the actual function change.

We are going to show the relation between the marginal concepts and derivative of a function in an economics as marginal cost, marginal utility, and marginal revenue through an exampleю Let’s say the company’s cost function is illustrated as:

C=C (Q) =a+bQ

Where: (C) is the total cost, (Q) is the Output, and (a) and (b) are constants. If the company produces 350 units of output, then the total cost will be:

C1=a+350b

If the company exceeds its output to 40, then the cost will be:

C2=a+400b

The extra 50 units are:

∆C=C2-C1=a+400b-a+350b=50b

Therefore, the total additional cost is 50b and since we have extra 50 units of output, b will be illustrated as the additional cost of each unit.

∆C/∆Q=(C2-C1)/(Q2-Q1)=50b/50=b

The ratio of the additional cost to the additional output is therefore constant, making life easier because whether we add 50, 100 or 1 or even one-tenth of the output unit, the ratio of the additional cost to the additional output will be constant and equivalent to b. let’s suppose the cost function is:

C=C(Q)=a+bQ+cQ^2

So, if we move from 350b units to 400b units, the ratio of additional costs to additional output will be:

∆C/∆Q=(a+400b+160,000c-a-350b-122500c)/(400-350)=(50b+37500c)/50=b+75c

This ratio is not constant, and depends on the additional units produced. But if the outout increased from 350 to 36, and then we will get:

∆C/∆Q=b+710c

The concept of marginal cost is to calculate the extra infinitesimal cost. Let us consider the general case of enhanced production and see how this works, from Q to Q+∆Q we get:

∆C/∆Q=(a+b(Q+∆Q)^2-a-bQ-cQ^2)/∆Q

(b∆Q+2cQ∆Q+c(∆Q)^2)/∆Q

The principle of the marginal cost is to make ∆Q as small as possible, to let it go to zero and determine the factor afterwards. You could say at this point, something divided by zero equal infinity. So, to ease the ratio, we are getting:

∆C/∆Q=b+2cQ+c∆Q

Now if we let delta Q approach zero, the marginal cost of this formula is:

MC=b+2cQ

Make sure that the marginal cost (MC) relies on the output level, so as quickly as we recognize the output level, we can evaluate an infinitesimal quantity of the additional cost of the increased output. The limit of the ratio ∆C⁄∆Q, when ∆Q reaches zero is the derivative of the cost function with respect to output.

Conclusion

Marginal and derivative analysis are very important in our everyday life especially in business and economics, as it gives a big support for the companies to know their current state to determine whether there is a profit and loss and make them able to predict their state in the future. So, marginal and derivative analysis should be put into more consideration to help stating the financial states in companies and in the markets.

Evolving, But Not Changing

I agree with Shapiro and Varian’s statement of technology changes, economic laws do not. I would say economic principles do not change but evolve as technological advances take place and have a significant influence on shaping our modern-day economy. As the technology that surrounds us and is immersed in our daily life advances, it changes the efficiency and level of production for the most part, in a beneficial form for the consumer and the producer, but at the cost of previous economic functionality. Although there are many improvements and growth in economics, the basic principles are still heavily prominent in our modern society. I am going to focus on the following economic principles stated by Shapiro and Varian: supply and demand, and marginal cost that have evolved due to technological advancements.

The economic principle of marginal cost is continuously evolving as our world is changing with technological advances, but the primary function does not, which is, “the rate of the increased expense depends on the production” (Muir 2). In other words, marginal cost is the cost added by producing an additional unit of product or service. I decided to touch on ‘marginal cost’ first because I feel like it has been the most influenced by technological advances such as information goods. Information goods are commonly defined as “products that can be digitized, such as books, software, videos, music, telecommunications services, and more” (Choudhary 3). The scholarly articles I used that support my idea in this paragraph are, Use of Pricing Schemes for Differentiating Information Goods by Vidyanand Choudhary, and Marginal Cost by Andrew Muir. Muir’s article defines the term ‘marginal cost’, explains a method of estimating these costs, and gives an example of its use (Muir 96). Information goods that have the most considerable effect on marginal cost are streaming devices such as Netflix and free to low-cost E-books.

Before the technological advances that massively decreased marginal costs, people would go to theaters and libraries for all their desires of movies and books. The movie theaters were ‘expensive’ because it costs the producer to build the theater, hire an electrician to make sure the movie’s function properly, have food and drinks available, customer service, and more, which are all additional costs that will be added to the service and therefore increase the price. The use of theaters slowly shifted to watching television at home as cable companies and television shows started to emerge. This means that all the consumers basically had to do is purchase a television, cable company, and technician. By doing this, it cuts the marginal costs by a significant amount in the long run, which meant it was is more affordable and the option of choice for most consumers. Today, many people use their computers to watch television and movies thanks to popular streaming devices such as Netflix and Hulu. Computers are often bought for work and school, and therefore is a two in one by having the consumers already owning their device and being able to watch films. This cuts near all marginal costs, which makes it affordable and efficient for the majority of consumers making this their option of choice. This equation can also be seen with E-books. In the past, consumers would go to libraries and bookstores for any reading material such as books, textbooks, articles, and more. The marginal cost for this was a labor of making the books, the distributor, the service of librarians, customer service, and more. Now, free to very affordable forms of these products are available online, which cut almost the entirety of marginal costs. As you can see these technological advances are beneficial for the consumers and the marginal cost principle has heavily evolved in some cases but it still does not change as it takes place with other products in our economy.

Supply and demand have been around for as long as we can remember, and it is still an essential principle of how our economy functions, even in modern times. Before technological advances, the supply and demand theory was relatively simple, “when the price goes down, demand should be stimulated, and when it goes up, there would be a slowing of demand. Price and demand have the ability to go in the same direction, if actual consumption is exceeding earlier demand predictions, there can be a firming of prices, or conversely, lower consumption statistics may depress prices” (Bartholomew 190). Things have slightly altered since then. In 1987 the USDA had an interesting supply and demand ratio which was often overlooked by many traders and analysts. “Domestic use predictions changed slightly, yet the price went up substantially. Export predictions rose early in the season by 1.5 million tons, then dropped by half that amount. Despite these factors, average prices advanced by 40% and held to the end of the season even though consumption did not total the amounts predicted earlier when the prices were lower. Low prices may have little influence on stimulating demand, but high prices may do little toward retarding demand. Many other factors are even more crucial than the price in changing demand, at least for periods of 12 to 18 months in the case of soybean meal. This includes animal price, cost of other feeds, interest rates, production in other countries, and foreign exchange relationships. Thus, it must be concluded that it can be misleading to attempt a simplistic analysis of USDA supply and demand projections in relation to average season prices provided” (Bartholomew 190).

This is an early observation that affected the basic knowledge of supply and demand, but with the many technological advances that are occurring every day, supply and demand continue to evolve. One of the modern technological advances that got my attention is GMOs – Genetically Modified Organisms. I decided to talk about this because it is something huge and controversial where I am from, Hawaii. Monsanto is a company that has an extensive influence on GMOs in Hawaii. It affects local farmers who have been in Hawaii since then 1800’s because it is more affordable for consumers, and uses pesticides that often kill locally grown produce on the local farmland. Before GMOs, we had seasonal fruits and vegetables that were almost entirely originating from Hawaii. This includes seasonal mangoes, pineapples, guavas, lychees, and more. The supply and demand for these products were steady, with very few fluctuations. Now, with GMOs, there are tons of fruits and vegetables for sale in Hawaii that originate from other parts of the world, and there are only a few seasonal locally grown fruits and vegetables that are higher in price. This altered our supply and demand status in Hawaii and had a drastic effect on our economy but still not changing the economic principle.

I chose these two economic terms as stated by Shapiro and Varian because I feel they have been the most affected and influenced by technology advances yet they still taking place in the world. My idea of change is changing entirely and therefore having a new economic principle arising which is not the case. We all grow as individuals and natural alterations are always taking place in the world so it is only right that the economic principles do as well.

Analysis of the Relationship Between Marginal Product and Marginal Cost

As we discuss the difference between ‘marginal product’ and ‘marginal cost’ in this write-up lets quickly look at the definition of these two words. According to “the marginal product of labor refers to the number of products a company can manufacture if it hires more workers or assigns its current workers additional hours. The marginal cost refers to the number of amount it costs a company to produce each additional item”. Let’s check an example for better understanding.

Marginal product

Let’s take for example Amsam restaurant, with two workers the restaurant can produce 13 cakes per day which can be considered as the total daily production. There was a time the number of cakes ordered always exceed their production. They decided to hire another two workers and their new daily production is 24. Here we can see that with four workers 11 extra cakes were produced as compared to two workers. This saws us how an increase in a unit of input can contribute to the total output. An increase in marginal product be considered an increase in production.

Marginal cost

Let’s take Bilal’s dental lab for example, assuming the production of one unit of denture is D500 and the total cost of producing to units of denture is D700. Here we can see that D200 is the marginal cost of producing the second unit. Also, if a company bought a new machine in order to produce more goods, the cost of that machine will be considered the marginal cost.

Factors Which Give Rise to Economics of Scale

Before directly moving to the factors that which gives rise to economic of scales, lets first throw light to the actual meaning of economics of scale for easy understanding. Economic of scale referred to as the ability of a company to produce goods and services on larger scales with low cost of production. The economic scale of a business is mainly determined by its size. The smaller the business the less cost saved. This can relate to the theory of economic which states that as companies grows in size and production capacity, costs decrease from the expanded operations. When unit production increases during a given period of time, the percentage increase in total cost is less than the percentage increase in total units. Some of the factors that give rise to economic of scale include:

1. Efficient Capital. Capital is the financial recourses that give companies the ability to improve and expand their operations. Economics of scale may be achieved through effectively using a mix of depth and equity financing. Positively creating cash flow through profitable operation is another important factor of economics of scale. Companies with good amount of cash can operate better when they focus more on using available to improve and less on generating cash.
2. Technology. Modern technology gives companies the access to automatically produce errors cause by human labor. Companies use technological terms such as business software, production robots and computes to develop their economy their economy of scale. Companies also use technological developments specify production technique than can give competitive advantages over other companies. Company gets more cash to spend on expanding operations whenever there is a reduce in expenses.
3. Specialization. Firms with large scale of production attracts large number of employees to work efficiently. This brings the idea of specialization to films by splitting jobs into smaller tasks. Each of these individual tasks are assigned to separate workers. In this way workers are given work based on their professional skills leading to proper and time sawing production. Overall result of this is that an average unit is produce at a lower cost.
4. Learning. Firms learn from both research and experience as they grow. At early stages firm are growing and have inefficient structure and processes. Firms with high level of research can get access to better process and new formulas pushing their cost per unit even lower.

Conclusion

It is the aim of all companies to make profit that is why determining amount of output and the price per unit of a product is very important in business. After going through marginal product and marginal cost we can realize, that there is a relationship between them. Just like stated “marginal product means the extra quantity of product that is produced. And marginal cost is the cost of producing that extra product”. Marginal cost depends upon quantity of marginal product. Due to the competitive gain that can be achieved, economies of scale are immensely beneficial to a growing business.