Mathematics How Calculus used in International Business Homework

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Topic: How Calculus applies in International Business?

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Running head: APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

Application of Calculus in International Business
Student’s Name
Institutional Affiliation
Introduction

1

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

2

Application of Calculus in International Business
Calculus is one of the foremost branches of mathematics and it entails mathematical models
useful for solving real-life problems. The concept of calculus and its application was developed
by well-known scientists and mathematicians Isaac Newton and Gottfried Leibniz where they were
more concerned with understanding the rules governing the motion of the planets as well as the
moon. Other scientists and researchers have refined calculus basic ideas discovering easier
methods of calculations and found other areas to apply calculus besides the planetary and moon
motion. Perhaps most importantly, scientists and researchers have helped the world to use calculus
to describe physical, economic, biological and social phenomena by solving problems in those
areas to obtain the optimal solution. The power of calculus helps one to understand simple ideas,
describe then and solve problems from different fields. International enterprises compete in an
ever-challenging business economy. To encounter these challenges in the business economy,
business professionals with business and international skills are required. Understanding the
international and regional economics as well as the socio-political analysis of multiple regions is
of crucial importance for any organization venturing into international business. Calculus is
applied in different fields in the business such as computing marginal costs and marginal rates to
predict the maximum profits in a specific setting, decision making, determine cost minimization
and revenue maximization by economists, predicting the demand of certain goods, predict revenue
and manage expenses among others. Understanding the role of calculus in the international
business is of crucial importance to any individual or organization as it helps to understand how
different changes impact the business. This paper discusses how calculus applies to international
business.

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

3

Calculus is used in the international business to predict the profit that an organization or an
individual will generate from a certain production or any other business. One of the direct
applications of calculus in international business is marginal analysis. By computing the marginal
costs and marginal rates, a business can predict the maximum profit that is going to obtain after a
specific period after some transactions (Sato, Tan, & Tse, 2015). One can use calculus to maximize
the total profit equation thus predicting the possible profit to be obtained. Since calculus entails
changes of one variable with respect to another variable, it is possible to calculate the maximum
profit while minimizing the production cost. For instance, the concept of differential calculus is of
crucial importance for many manufacturers as it helps to solve problems of getting the maximum
profit that the company is likely to get after manufacturing a certain product at the minimum cost.
Also, Sato, Tan, & Tse (2015) articulates that an analyst in the operations research department is
able to increase the profits from a production process using the calculus knowledge where the
analyst considers different production processes then, using the different values of variables used
in the production, it becomes easy to improve the efficiency of the operation while increasing the
production thus maximizing the profits generated. Because calculus helps one to minimize the
production cost, it is also possible to maximize the profit that a business can make by the
knowledge of differential calculus. In the production industry calculus has a wide application. A
cost function is determined which facilitates the prediction of the expected profit from production.
For instance, if the total cost C of manufacturing and marketing x units of a certain product is
depended on different number of units (x), then the function relating the production cost C and the
x units is given as C = C(x) = F + V(x) where F is the fixed cost and V(x) is the variable cost
(Kamien & Schwartz, 2012). In this simple cost function, the fixed cost may include all the types
of cost which remain constant throughout the production and may include the taxes, premises rent

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

4

and insurance. On the other hand, the variable cost may be regarded as the total cost of all depended
variables where the cost varies with the level of production and may include labor cost and the
cost of production material used. From the profit function where the total cost of production and
revenue cost is known, then it is possible to predict the profit after selling x units of production.
Calculus is used in international business for decision making. In recent years, economic
and business decision making has become mathematically oriented where the calculus knowledge
is being applied to understand what is happening in the market and predict the future to make
informed decisions. Even if it means that one is not going to apply calculus directly to the business,
it helps one to think critically and solve complex and dynamic issues in the business thus being
able to make better decisions. According to Kochenderfer (2015), in the modern world, business
is ever adapting and fluctuating hence business analytics in the international business have
increasingly turned to mathematical models to use them for describing what is happening in the
market, predict the effects of different policy alternatives, and choose course of action from the
myriad possibilities. Understanding what is happening in the market helps one to plan and make
accurate predictions of how the business will be in the future hence being able to maximize the
profits (Kochenderfer, 2015). For instance, today calculus is used to determine the right time when
to buy and sell goods depending on the customers’ past buying behavior as well as how the current
market behaves. Precisely, calculus is used in international business to understand the demand of
products which helps to decide by the manufactures about the supply. Due to changes in customers'
buying behavior, differential calculus is used to determine the right time to increase the stock and
when to produce less stock hence making the best decisions. As a result, it becomes easy for
individuals and organizations to grow their businesses by making a well-informed decision about
consumer behavior (Kochenderfer, 2015). The international business today faces both fast and

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

5

slow changes which are better understood with calculus knowledge. For instance, when a new
technology emerges in the business, technology can drastically change the entire industries'
landscape. From the drastic changes brought by changes in technology, decisions can be made to
encourage slow and steady growth by adopting the new technology. According to Kochenderfer
(2015), in the current business world, investors and other business analysts have learned the
concept of dividend growth models which enable one to understand the intrinsic value of stock of
a certain company or business thus being able to make a decision on whether to buy or sell
depending on the intrinsic value of the stock. As such, the growth models derived from the concept
of calculus are used to make investment decisions.
Calculus is used in the international business for direct marketing. The concept of
mathematics, specifically calculus knowledge is essential for marketing purposes as it is used to
determine whether a certain advertisement method reaches the targeted customers and how the
advertisement should be sent to the customers (Jensen, Palangkaraya & Webster, 2015). Direct
marketing is used in many cases where mathematical models derived from calculus are used to
determine how often the advertisements reach the targeted audience. The marketer aims to send
ads that will reach a large number of targeted customers and reach them more often. To understand
how often the ads are working, equations are used. As a result, many firms are using ads in social
media to target a large number of potential customers for their products (Jensen, Palangkaraya &
Webster, 2015). Most of these ads have similar targeting criteria but varying budgets hence the
delivery system applies the calculus knowledge to decide on which ad to serve at a particular time
while ensuring that the budgets of different clients are spent evenly. Another application of
calculus in the marketing industry is marketing research and sales. Jensen, Palangkaraya &
Webster (2015) states that the concept of decision calculus is required when a business or an

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

6

organization in the international business wants to understand whether a certain trend means
selling or allocating their resources to another field. In other words, decision calculus is used to
make business models. For instance, in the production field, a firm with diversified production
might send its marketing team to find out about the lasted sales trend in the market for a specific
item in which the firm wants to produce more. In this case, the firm might ask its marketing team
to research the sales trend whether they may apply calculus knowledge to explain which item the
firm should produce more instead of focusing on other items that might be unprofitable during a
certain trend (Jensen, Palangkaraya & Webster, 2015). Equations of calculus are applied due to
different variable which is involved to explain why a certain decision was made. Decision models
are being developed by marketing executives and mathematicians to solve problems involving the
size of the sales force that can lead to maximum profits, new-product development as well as the
media selection for marketing a firm's products.
Calculus has a wide application in business economics. Business economics entails
analysis of business enterprises and the factors which lead to diversity in the structures of an
organization as well as the relationships of firms with the products, labor, and capital (Hoffmann,
Bradley & Rosen, 2007). Economics on the other entails the study of the utilization of the
economic resources scarcely in the market place. The business economic analysis applies
quantitative methods while analyzing the international economy. The analysis is facilitated by
mathematical concepts mainly from calculus which help economists to make sure that the
judgments which they make, inferences they make and theories which they develop are supported
by meaningful calculations. Thus, economists in many cases apply differential calculus to analyze
business economic information. One of the common economic models that use calculus concepts
in international business is the demand and supply graph (Kamien & Schwartz, 2012). To analyze

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

7

the demand and supply graph, differential calculus is applied where the original demand and
supply models are used to show how different factors affect the shifting of the supply and demand
lines in the business market (Hoffmann, Bradley & Rosen, 2007). Additionally, economic models
play important roles in proving or disapproving theories and inferences which the economists
propose. In the international market, calculus is applied with economic information by business
firms and individuals to forecast the expected sales by considering the operations of the firm or
the business. Moreover, the economic analysis which uses mathematical models from calculus is
used as an important management tool which is crucial for making business decisions as well as
business plans (Kamien & Schwartz, 012). However, firms and individuals may not be required to
apply heavy differential calculus concepts to understand economic information (Hoffmann,
Bradley & Rosen, 2007). The owners of these businesses might use the information from the
economists to make predictions and decisions depending on the business operations from the
economic models derived from calculus.
Calculus is used to analyze the demand for a certain commodity and predict future demand.
Customer buying behavior is seasonal and there are times when the demand is high compared to
what is supplied. Other times, the demand changes and becomes little compared to huge supplies
(Montal et al., 2013). As a result, manufacturers use the demand and supply models that apply
differential calculus knowledge to predict the best times of production when the demand is high.
To predict the demand and supply patterns, both supply and demand functions are developed
(Varian, 2014). The demand function is used to explain and predict the quantity that will be
demanded by consumers in the future time at a given price from the available data (Montal et al.,
2013). On the other hand, the supply function predicts the quantity that producers or manufactures
need to supply at any particular price. To understand how demand and supply changes, different

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

8

factors are considered and in most cases, the changes in demand and supply curves can be
expressed as lines whose equations can be calculated using the changes in one variable with respect
to another variable (Varian, 2014). The use of calculus while drawing the curves is required since
the lines should follow a particular pattern. This is common in business economics where market
analysis is carried out to determine the viability of the economy. Also, the supply and demand at
a particular price can be determined easily by analyzing the demand and supply graph which are
drawn using the past data obtained from the market research (Varian, 2014). Once one predicts the
demand and supply of a certain commodity, the manufacturers and suppliers estimate the likely
sales that they are likely to make by selling at any particular price they set. Estimating the sales
volume helps the manufactures to plan and make the decision to venture in manufacturing the
goods which have a higher demand at any particular time and price (Montal et al., 2013). As a
result, we can say that business owners in the international business require the knowledge of
technical mathematics like calculus to ensure that they have concepts that they can use to break
down the business information thus making basic decisions regarding operations from the calculus
models (Varian, 2014). An example of such a decision is the production and supply of goods
depending on their demand in the market.
Calculus is used in the business to determine the marginal revenue from its sales. The
marginal analysis applies the concept of differential calculus and it is one of the important aspects
of business development as every business needs to understand its revenue generation from its
sales (Sato, Tan, & Tse, 2015). The concept of marginal analysis is used to calculate the profits,
revenue and cost in the market. Marginal revenue is the change in the total revenue over the change
in quantity when the change in quantity is equivalent to a single unit. Therefore, since marginal
revenue entails changes of one quantity with respect to another quantity, knowledge of differential

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

9

calculus is required to understand how it works (Hoffmann, Bradley & Rosen, 2007). As a result,
marginal revenue can be represented as a derivative with its equation written MR = d (TR)/d Q
where MR represents the marginal revenue, TR represents the total revenue, and Q is the number
of goods sold at a price P (Sato, Tan, & Tse, 2015). The concept of differential calculus is then
applied to marginal revenue since marginal revenue can be described as a change of the total
revenue divided by the change in the number of units sold by a company during a particular fiscal
year. Application of differential calculus and rates of change applies to differential calculus thus
calculus is used in the international business to calculate the marginal revenue (Kamien, &
Schwartz, 2012). Understanding the marginal revenue generation by the company enables the
owners to make decisions on expanding their businesses to increase their revenue generation
(Hoffmann, Bradley & Rosen, 2007). Additionally, being able to understand the marginal revenue
helps one to evaluate their businesses to determine whether the business is doing a loss the making
profit that can sustain it and facilitate development. According to Sato, Tan, & Tse (2015),
marginal analysis is also used to allocate the available resources appropriately by comparing the
marginal benefits of activity change with the change in the marginal costs. Therefore, differential
calculus is used to determine the marginal revenue which helps to allocate resources efficiently
and maximize the profits that a business can generate from its operations. According to Montal et
al. (2013), differential calculus can also be used for decision making depending on the marginal
revenues that the business makes. For instance, it can be used to indicate whether a company can
expand its operations or the company can be closed if no progress is revealed. Marginal analysis
can also be used to maximize problems. For instance, one may be interested to find the maximum
profits which require the knowledge of differential calculus.

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

10

Calculus is widely applied in business for optimization purposes. The knowledge of
calculus especially differential calculus is used to find the minimum and maximum values of some
functions given by business equations (Klatte & Kummer, 2006). Additionally, optimization in
business is used to find the minimum cost of production, the maximum profits that a business can
generate, finding the optimal management that the company needs to successful development,
determine the optimal design and the minimum error. For instance, in the manufacturing industry,
a company may be interested in determining the minimum number of employees, material and
other inputs that will produce a product using the lowest cost as possible. To solve this problem,
optimization knowledge which is an application of calculus is required to help the company to
produce the product at the minimum cost possible. Additionally, calculus is used by companies
and other businesses to optimize their profits from the sales they make (Klatte & Kummer, 2006).
For instance, if a company selling its products realizes that its profit is reduced because of the
number of advertisements that the company carries or it is reduced by a large number of employees
that it has employed, then the company might decide to either reduce the number of its advertising
agent or the number of its employees. This helps the company to incur less cost in both advertising
and labor (Kamien & Schwartz, 2012). As a result, then the company can plan its operations
appropriately and while minimizing its production cost and maximizing its profits through
optimization, a concept of differential calculus which requires that optimal points be allocated for
cost minimization. According to Klatte & Kummer (2006), Lagrangian multiplier techniques are
used to solve constrained optimization problems as many organizations have constraints on their
decision variables thus applying calculus knowledge to solve the constrained problems which
require optimization concepts.

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

11

Differential calculus is used by credit card companies to compute the minimum payments
by a credit card. Since the minimum payment by credit card varies from time to time, one must
understand how the amount to be paid is calculated (Crack & Roberts, 2015). Calculus is applied
by the credit card companies to set the minimum payments that any holder is required to pay at the
exact time the credit card statements are processed. Understanding how the credit card companies
calculate the minimum payment, one can predict the amount that they are likely to pay each month.
Different variables such as a change in interest rates and fluctuation of the available balance
reconsidered while computing this minimum payment and it is calculated by the amount of money
as per the due date listed on the bill (Crack & Roberts, 2015). To provide the customer with the
accurate minimum balance, calculations are carried out simultaneously considering all the changes
happening, available balance and the interest rates. The calculations used an equation that requires
the knowledge of differential calculus since the amount is subject to change from month to month
depending on the available balance (Klatte & Kummer, 2006). Different factors that lead to
variation in minimum payment and are considered during a calculation are late payments, going
beyond the limit, changes in interest rates, change in percentage which card user uses to calculate
the minimum payment and fluctuations in balance (Crack & Roberts, 2015). Combining these
factors lead to a differential function which helps to calculate the minimum payment by the credit
card companies using the knowledge of differential calculus.

Calculus has wide applications in international business. Calculus can be used to predict the
profits that an organization or an individual can obtain from venturing into a certain business using
the concepts of marginal analysis. Businesses also apply the knowledge of calculus to make
decisions as well as calculating the marginal revenue of an investment. Additionally, calculus is

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

12

used in business economics to analyses the market using economics models such as demand and
supply graphs. Credit card companies are also using differential calculus to calculate the minimum
payments that a card user is supposed to pay. While finding optimal solutions, calculus is applied
to optimize the solutions.

Calculus
Sato, Y., Tan, K. H., & Tse, Y. K. (2015). An integrated marginal analysis approach for build-toorder products. International Journal of Production Economics, 170, 422-428.
Crack, T. F., & Roberts, H. (2015). Credit card balances and repayment under competing for
minimum payment regimes. Review of Quantitative Finance and Accounting, 45(4), 785-801.
Kochenderfer, M. J. (2015). Decision making under uncertainty: theory and application. MIT
press.
Jensen, P. H., Palangkaraya, A., & Webster, E. (2015). Trust and the market for
technology. Research Policy, 44(2), 340-356.
Montali, M., Maggi, F. M., Chesani, F., Mello, P., & van der Aalst, W. M. (2013). Monitoring
business constraints with the event calculus. ACM transactions on intelligent systems and
technology (TIST), 5(1), 17.
Klatte, D., & Kummer, B. (2006). Nonsmooth equations in optimization: regularity, calculus,
methods, and applications (Vol. 60). Springer Science & Business Media.

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

13

Varian, H. R. (2014). Intermediate microeconomics with calculus: a modern approach. WW
Norton & Company.
Hoffmann, L. D., Bradley, G. L., & Rosen, K. H. (2007). Applied calculus for business, economics,
and the social and life sciences. McGraw-Hill higher education.
Kamien, M. I., & Schwartz, N. L. (2012). Dynamic optimization: the calculus of variations and
optimal control in economics and management. Courier Corporation.

find attached the final version of your assignment ahead of the deadline. Please review and accept the work.

Running head: APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

Application of Calculus in International Business
Student’s Name
Institutional Affiliation
Introduction

1

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

2

Application of Calculus in International Business
Calculus is one of the foremost branches of mathematics and it entails mathematical models
useful for solving real-life problems. The concept of calculus and its application was developed
by well-known scientists and mathematicians Isaac Newton and Gottfried Leibniz where they were
more concerned with understanding the rules governing the motion of the planets as well as the
moon. Other scientists and researchers have refined calculus basic ideas discovering easier
methods of calculations and found other areas to apply calculus besides the planetary and moon
motion. Perhaps most importantly, scientists and researchers have helped the world to use calculus
to describe physical, economic, biological and social phenomena by solving problems in those
areas to obtain the optimal solution. The power of calculus helps one to understand simple ideas,
describe then and solve problems from different fields. International enterprises compete in an
ever-challenging business economy. To encounter these challenges in the business economy,
business professionals with business and international skills are required. Understanding the
international and regional economics as well as the socio-political analysis of multiple regions is
of crucial importance for any organization venturing into international business. Calculus is
applied in different fields in the business such as computing marginal costs and marginal rates to
predict the maximum profits in a specific setting, decision making, determine cost minimization
and revenue maximization by economists, predicting the demand of certain goods, predict revenue
and manage expenses among others. Understanding the role of calculus in the international
business is of crucial importance to any individual or organization as it helps to understand how
different changes impact the business. This paper discusses how calculus applies to international
business.

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

3

Calculus is used in the international business to predict the profit that an organization or an
individual will generate from a certain production or any other business. One of the direct
applications of calculus in international business is marginal analysis. By computing the marginal
costs and marginal rates, a business can predict the maximum profit that is going to obtain after a
specific period after some transactions (Sato, Tan, & Tse, 2015). One can use calculus to maximize
the total profit equation thus predicting the possible profit to be obtained. Since calculus entails
changes of one variable with respect to another variable, it is possible to calculate the maximum
profit while minimizing the production cost. For instance, the concept of differential calculus is of
crucial importance for many manufacturers as it helps to solve problems of getting the maximum
profit that the company is likely to get after manufacturing a certain product at the minimum cost.
Also, Sato, Tan, & Tse (2015) articulates that an analyst in the operations research department is
able to increase the profits from a production process using the calculus knowledge where the
analyst considers different production processes then, using the different values of variables used
in the production, it becomes easy to improve the efficiency of the operation while increasing the
production thus maximizing the profits generated. Because calculus helps one to minimize the
production cost, it is also possible to maximize the profit that a business can make by the
knowledge of differential calculus. In the production industry calculus has a wide application. A
cost function is determined which facilitates the prediction of the expected profit from production.
For instance, if the total cost C of manufacturing and marketing x units of a certain product is
depended on different number of units (x), then the function relating the production cost C and the
x units is given as C = C(x) = F + V(x) where F is the fixed cost and V(x) is the variable cost
(Kamien & Schwartz, 2012). In this simple cost function, the fixed cost may include all the types
of cost which remain constant throughout the production and may include the taxes, premises rent

APPLICATION OF CALCULUS IN INTERNATIONAL BUSINESS

4

and insurance. On the other hand, the variable cost may be regarded as the total cost of all depended
variabl...


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