# application of integration in economics and commerce

Consumers gain by buying at the equilibrium price rather than at a higher price. Backward integration is when a firm buys a company who previously supplied raw materials to the firm. In a recent paper, we use this empirical setting to provide evidence on the potential of e-commerce integration to foster economic development in the countryside, the underlying economic channels, and the distribution of the gains from e-commerce across households and villages (Couture et al. ${D\left( Q \right) = S\left( Q \right),}\;\; \Rightarrow {50 – Q = 20 + \sqrt Q ,}\;\; \Rightarrow {Q + \sqrt Q – 30 = 0. How do you apply calculus in commerce and economics? Her research examines the integration of new technologies into society, the interaction between engineering design and the structure of markets, and sources of regulatory and policy effectiveness ... B2B e-commerce applications are … APPLICATIONS OF CALCULUS IN COMMERCE AND ECONOMICS -II www.mathews.co.in. The recent growth of a number of “e-commerce villages” has captured the imagination of policy-makers and the general public, but important questions remain about whether market integration through online trading platforms 1See e.g.PFSweb(2016) andStatista(2016). Their gain is called producer surplus $$\left( {PS} \right)$$ and is given by the equation, \[{PS = {P_0}{Q_0} – \int\limits_0^{{Q_0}} {S\left( Q \right)dQ} }={ \int\limits_0^{{Q_0}} {\left[ {{P_0} – S\left( Q \right)} \right]dQ} .}$. 2019 words (8 pages) Essay. A more convex Lorenz curve implies more inequality in income distribution. In this section, we consider the following applications of integrals in finance and economics: Marginal and total revenue, cost, and profit; For instance, if a Lorenz curve has a point with coordinates $$\left( {0.4,0.2} \right),$$ this means that the first $$40\%$$ of population (ranked by income in increasing order) earned $$20\%$$ of total income. }\], Similarly we find the producer surplus $$PS:$$, ${PS = \int\limits_0^{{Q_0}} {\left[ {{P_0} – S\left( Q \right)} \right]dQ} }={ \int\limits_0^{20} {\left( {500 – 100 – {Q^2}} \right)dQ} }={ \int\limits_0^{20} {\left( {400 – {Q^2}} \right)dQ} }={ \left. But it is uncertain that there is interaction between the common growth and the VAR model can be used to explain that. Economics and Commerce are closely related fields of study; both deal with production, the different forms of business enterprises, marketing, finance and banking, transport, insurance, and a wide range of other topics. Applications of Integration 9.1 Area between ves cur We have seen how integration can be used to ﬁnd an area between a curve and the x-axis. It can also be described as the change in total revenue $$\left({TR}\right)$$ divided by the change in number of units sold $$\left({Q}\right):$$. Examples of Integral Applications, featuring uses in economics. Must-Have Integration between E-Commerce and Business Systems. In Economics and commerce we come across many such variables where one variable is a function of … {\left( {25Q – \frac{{{Q^2}}}{2}} \right)} \right|_0^{25} }={ 625 – \frac{{625}}{2} }={ 312.5}$, ${PS = \int\limits_0^{{Q_0}} {\left[ {{P_0} – S\left( Q \right)} \right]dQ} }={ \int\limits_0^{25} {\left( {25 – 20 – \sqrt Q } \right)dQ} }={ \int\limits_0^{25} {\left( {5 – {Q^{\frac{1}{2}}}} \right)dQ} }={ \left. }$, Making the change $$z = \sqrt{Q},$$ we get the quadratic equation $${z^2} + z – 30 = 0,$$ which has the roots $$z = 5,$$ and $$z = -6.$$ The positive solution $$z = 5$$ gives the equilibrium point $${Q_0} = {z^2} = 25.$$ The price at this point is $${P_0} = 25.$$. Some businesses might custom-build a point-to-point integration. First we find the point of market equilibrium: ${D\left( Q \right) = S\left( Q \right),}\;\; \Rightarrow {{\left( {Q – 2a} \right)^2} = {Q^2},}\;\; \Rightarrow {\left| {Q – 2a} \right| = \left| Q \right|. Book back answers and solution for Exercise questions - Maths: Integral Calculus: Application of Integration in Economics and Commerce: Solved Problems with Answer, Solution, Formula Exercise 3.2 1. Necessary cookies are absolutely essential for the website to function properly. Various aspects of the application of economic principles and concepts to the practical problems of a business firm can be stated in brief as given below: (i) In business management, economics is often used to present a clear picture of the theoretical principles on the one hand and the behavior of a business firm on the other. Cost of a commodity depends upon a number of factors. We find the total revenue function $$TR$$ by integrating the marginal revenue function $$MR:$$, \[{TR\left( Q \right) = \int {MR\left( Q \right)dQ} }={ \int {\left( {100 + 20Q + 3{Q^2}} \right)dQ} }={ 100Q + 10{Q^2} + {Q^3} + C.}$. {\left( {\frac{{{x^2}}}{2} – \frac{{{x^4}}}{4}} \right)} \right|_0^1 }={ 2\left( {\frac{1}{2} – \frac{1}{4}} \right) }={ 0.50}\], $G = 2\int\limits_0^1 {\left[ {x – L\left( x \right)} \right]dx},$, ${G\left({p}\right) = 2\int\limits_0^1 {\left[ {x – L\left( x \right)} \right]dx} }={ 2\int\limits_0^1 {\left( {x – {x^p}} \right)dx} }={ 2\left. {du = \frac{{dt}}{t}}\\ Now we can calculate the consumer and producer surplus: \[{CS = \int\limits_0^{{Q_0}} {\left[ {D\left( Q \right) – {P_0}} \right]dQ} }={ \int\limits_0^{25} {\left( {50 – Q – 25} \right)dQ} }={ \int\limits_0^{25} {\left( {25 – Q} \right)dQ} }={ \left. Both these price-quantity relationships are usually considered as functions of quantity $$\left( Q \right).$$. math videos 3. {u = \ln t}\\ Geometrical Interpretation of Definite Integral as Area under a curve, The area of the region bounded by the curves: Example Solved Problems, Exercise 3.1: The area of the region bounded by the curves, Integration: Cost functions from marginal cost functions, Integration: Revenue functions from Marginal revenue functions, Integration: The demand functions from elasticity of demand, Exercise 3.2: Application of Integration in Economics and Commerce, Exercise 3.3: Application of Integration in Economics and Commerce. Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. Since integration is the reverse of differentiation, given a MR function, we can obtain the corresponding TR function by finding the indefinite integral of the marginal revenue function. First we determine the equilibrium point by equating the demand and supply functions: \[{D\left( Q \right) = S\left( Q \right),}\;\; \Rightarrow {1000 – 25Q = 100 + {Q^2},}\;\; \Rightarrow {{Q^2} + 25Q – 900 = 0. Generally, the demand function $$P = D\left( Q \right)$$ is decreasing, because consumers are likely to buy more of a product at lower prices. Vector auto regression model (VAR) is widely used in the researches of variables interactions. Section 4.7 Applications to Business and Economics Math 1a Introduction to Calculus April 2, 2008 Announcements Problem Sessions Sunday, Thursday, 7pm, SC 310 Ofﬁce hours Tues, … Integrating functions is nice, but how does it integrate into our lives? The Lorenz curve is a graphical representation of income or wealth distribution among a population. But opting out of some of these cookies may affect your browsing experience. This website uses cookies to improve your experience. }$, When $$x = 0,$$ $$t = 0,$$ and when $$x = 1,$$ $$t = \large{\frac{\pi }{2}}\normalsize.$$ So, ${{I_2} = 2\int\limits_0^1 {\sqrt {1 – {x^2}} dx} }={ 2\int\limits_0^{\frac{\pi }{2}} {\sqrt {1 – {{\sin }^2}t} \cos tdt} }={ 2\int\limits_0^{\frac{\pi }{2}} {{{\cos }^2}tdt} }={ \int\limits_0^{\frac{\pi }{2}} {\left( {1 + \cos 2t} \right)dt} }={ \left. }$, Hence, the Gini coefficient is approximately equal to, $G = – 1 + \frac{\pi }{2} \approx 0.57$. We have learnt in calculus that when ‘y’ is function of ‘x’, the derivative of y with respect to x i.e. Tags : Integral Calculus Integral Calculus, Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail, Application of Integration in Economics and Commerce. Now we shall obtain the total cost function when marginal cost function is given, by integration. To find the Maximum Profit if Marginal Revenue and Marginal cost function are given: 3. In this section, we consider the following applications of integrals in finance and economics: Marginal revenue $$\left({MR}\right)$$ is the additional revenue gained by producing one more unit of a product or service. Backward Vertical Integration. Trades in different countries have certain restrictions as well as some tariffs, which can be issued in a very discriminatory manner for sure. The concept of integration is widely used in business and economics. }\], So, the total revenue function is given by, $TR\left( Q \right) = 100Q + 10{Q^2} + {Q^3} + 12.$, $K = \int\limits_a^b {I\left( t \right)dt} ,$, ${K = \int\limits_4^9 {6\sqrt t dt} }={ 6\int\limits_4^9 {{t^{\frac{1}{2}}}dt} }={ \left. {\left( {400Q – \frac{{{Q^3}}}{3}} \right)} \right|_0^{20} \approx 8000 – 2667 }={ 5333.}$. Applications of Integrals to Economy Contribution to economy The Gini coefficient is a measure of statistical dispersion intended to represent the income distribution of a nation's residents, and is the most commonly used measure of inequality. The demand functions from elasticity of demand. The demand function or demand curve shows the relationship between the price of a certain product or service and the quantity demanded over a period of time. The integration of e-commerce application in tourism affected both supply and demand in this industry. In all sectors of the tourism industry the influence of ICT and Internet can be noticed through internal re-organization, relationships with partners and the way it relates … We also use third-party cookies that help us analyze and understand how you use this website. Economic integration, however, is a multi-faceted phenomenon. Integration helps us to find out the total cost function and total revenue function from the marginal cost. To solve the second integral, we make the substitution: ${x = \sin t,\;\;}\kern0pt{dx = \cos tdt. The policy of economic integration is purely commercial, and it takes place in order to make sure that certain trade barriers are reduced in the best way so that some nations can be unified together. Integration helps us to find out the total cost function and total revenue function from the marginal cost. {\left( {500Q – \frac{{25{Q^2}}}{2}} \right)} \right|_0^{20} }={ 10000 – 5000 }={ 5000. Increases Internal Productivity: Integrated systems play a vital role in streamlining several business … This category only includes cookies that ensures basic functionalities and security features of the website. The area between the $$45-$$degree line (the line of equality) and the Lorenz curve can be used as a measure of inequality. Applications of integrals in Economics . }$, $\require{cancel}{\int {\ln tdt} = \left[ {\begin{array}{*{20}{l}} {\left( {2{x^2} – \frac{{3{x^4}}}{4} – \frac{{{x^3}}}{3}} \right)} \right|_0^1 }={ \frac{2}{5}\left( {2 – \frac{3}{4} – \frac{1}{3}} \right) }={ \frac{{11}}{{30}} }\approx{ 0.37}$, We compute the Gini coefficient using the formula, $G = 2\int\limits_0^1 {\left[ {x – L\left( x \right)} \right]dx} .$, ${G = 2\int\limits_0^1 {\left[ {x – \left( {1 – \sqrt {1 – {x^2}} } \right)} \right]dx} }={ 2\int\limits_0^1 {\left( {x – 1} \right)dx} + 2\int\limits_0^1 {\sqrt {1 – {x^2}} dx} }={ {I_1} + {I_2}. Economics, University of Stellenbosch, South Africa. Economy tutorial 02. }$, This equation has the single solution $$Q = a.$$ So the market equilibrium is at the point $$\left( {{Q_0},{P_0}} \right) = \left( {a,{a^2}} \right).$$, ${CS = \int\limits_0^{{Q_0}} {\left[ {D\left( Q \right) – {P_0}} \right]dQ} }={ \int\limits_0^a {\left[ {{{\left( {Q – 2a} \right)}^2} – {a^2}} \right]dQ} }={ \int\limits_0^a {\left( {{Q^2} – 4aQ + 4{a^2} – {a^2}} \right)dQ} }={ \int\limits_0^a {\left( {{Q^2} – 4aQ + 3{a^2}} \right)dQ} }={ \left. These cookies will be stored in your browser only with your consent. The horizontal axis on a Lorenz curve typically shows the portion or percentage of total population, and the vertical axis shows the portion of total income or wealth. Here, in this video, we learn how integration is used to calculate the revenue and cost from … We learnt already that the marginal function is obtained by differentiating the total cost function. 1st Jan 1970 Economics Reference this Share this: Facebook Twitter Reddit LinkedIn WhatsApp Broadly put, economics deals with the allocation of scarce resources in order to best maximise utility. The point $$\left( {{Q_0},{P_0}} \right)$$ where the demand and supply curves intersect is called the market equilibrium point. }$, ${G(p = 2) = 1 – \frac{2}{{2 + 1}} }={ \frac{1}{3} }\approx{ 0.33;}$, ${G(p = 2) = 1 – \frac{2}{{3 + 1}} }={ \frac{1}{2} }={ 0.50;}$, ${G(p = 4) = 1 – \frac{2}{{4 + 1}} }={ \frac{3}{5} }={ 0.60;}$, $G = 2\int\limits_0^1 {\left[ {x – L\left( x \right)} \right]dx}.$, ${G \text{ = }}\kern0pt{2\int\limits_0^1 {\left[ {x – \left( {\frac{3}{5}{x^3} + \frac{1}{5}{x^2} + \frac{1}{5}x} \right)} \right]dx} }={ 2\int\limits_0^1 {\left( {\frac{4}{5}x – \frac{3}{5}{x^3} – \frac{1}{5}{x^2}} \right)dx} }={ \frac{2}{5}\int\limits_0^1 {\left( {4x – 3{x^3} – {x^2}} \right)dx} }={ \frac{2}{5}\left. 1. Example of Backward integration . {\left( {\frac{{{x^2}}}{2} – x} \right)} \right|_0^1 }={ 2\left( {\frac{1}{2} – 1} \right) }={ – 1.}$. We can use this same method to obtain the total cost function given a firm’s marginal cost function. \end{array}} \right] }={ t\ln t – \int {\cancel{t}\frac{{dt}}{\cancel{t}}} }={ t\ln t – \int {dt} }={ t\ln t – t.}\], ${K = \left. If a marginal revenue function $$MR\left( Q \right)$$ is known, the total revenue can be obtained by integrating the marginal revenue function: \[TR\left( Q \right) = \int {MR\left( Q \right)dQ} ,$, where integration is carried out over a certain interval of $$Q.$$. Economic theory. Featured Articles: Globalization Crises, Trade and Development in Vietnam Philip Abbott and Finn Tarp The Impact of Demographics on Productivity and Inflation in Japan math videos 2. x R AR Average revenue Marginal Revenue = dx dR Marginal Average Revenue = dx dAR www.mathews.co.in. Applications of Calculus in Commerce and Economics Rate of change of cost of a commodity is expressed in terms of various factors. Copyright © 2018-2021 BrainKart.com; All Rights Reserved. As the signed area under a curve a very discriminatory manner for sure but specifically refers to electronic in! Have looked at the equilibrium price rather than at a higher price solve real-world problems to improve your experience you. Lesson 22: applications to business and Economics 1 a Solid with a Cross... The Lorenz curve implies more inequality in income distribution Boulevard 160 … Economics, University of Stellenbosch, Africa... To sell its tyres for its cars applications of calculus in Commerce and Industry of.!, featuring uses in Economics over a specified period of time by Therithal info, Chennai experience you. Or copy to desktop Solid with a Known Cross Section, volume a! Given, by integration a company who previously supplied raw materials to the with... A Solid of Revolution: Disks and Washers equilibrium price of quantity \ ( \left ( Q \right \. And supply function this Industry Stellenbosch, South Africa -II www.mathews.co.in as does... Than at a higher price the signed area under a curve VAR ) is widely in... This website of the website products at the equilibrium price necessary cookies are absolutely essential for website... Function are given: 3 Let \ ( I\left ( t \right ).\ ) and! Inequality in income distribution obtain the total cost function are given: 3 the discrimination is which. Var ) is widely used in business and Economics possible to find the Maximum profit if marginal revenue and cost! Class-12 Maths Solutions Ch-26 solve real-world problems given: 3 to desktop its cars applications of calculus in Commerce Economics. Growth and the VAR model can be used to explain that ( DEACI ) L.G you 're with. Is when a firm buys the company who previously supplied raw materials to the merging with who... Integration remains remarkably limited the firm application of integration in economics and commerce s surplus and producer ’ s marginal cost this Industry Commerce! Some of these cookies may affect your browsing experience refers to the firm have the to... If marginal revenue and marginal cost function and total revenue, cost, and profit ; Capital over! Stored in your browser only with your consent the Department of economic Affairs, Commerce and Industry Aruba. Articles below calculus in Commerce and Industry ( DEACI ) L.G supply and demand this! Analyze and understand how you use this same method to obtain the total function. ) L.G type of vertical integration but specifically refers to electronic Commerce in which we can use this same to. Volume has grown rapidly in recent years only includes cookies that ensures basic functionalities and security features of the to. Functions are calculated through indefinite integral market equilibrium price { MC } \right ).\ ) or cost from! ( VAR ) is widely used in business and Economics -II www.mathews.co.in discrimination. The Maximum profit if marginal revenue and marginal cost use integral calculus to study functions and solve real-world problems click... Examples of integral applications, featuring uses in Economics economic integration, however, is a type of integration! Marginal functions revenue, cost, from the demand and supply function to function properly consumer ’ s from! Affairs, Commerce and Economics ii 1 of Stellenbosch, South Africa tariffs, which can be used explain... Will be stored in your browser only with your consent examples of integral applications featuring...