# application of integration in economics and commerce

Economic theory. But it is uncertain that there is interaction between the common growth and the VAR model can be used to explain that. 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. 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. We find the total revenue function $$TR$$ by integrating the marginal revenue function $$MR:$$, \[{TR\left( Q \right) = \int {MR\left( Q \right)dQ} }={ \int {\left( {100 + 20Q + 3{Q^2}} \right)dQ} }={ 100Q + 10{Q^2} + {Q^3} + C.}$. 1. Economics and Commerce are closely related fields of study; both deal with production, the different forms of business enterprises, marketing, finance and banking, transport, insurance, and a wide range of other topics. The Gini coefficient is a relative measure of inequality. 2019 words (8 pages) Essay. Link to worksheets used in this section. Department of Economic Affairs, Commerce and Industry (DEACI) L.G. Copyright © 2018-2021 BrainKart.com; All Rights Reserved. Integration helps us to find out the total cost function and total revenue function from the marginal cost. Application of Integration in Economics and Commerce. Simply put, the term refers to electronic commerce in which products are being sold and bought over the Internet. much punditry, international economic integration remains remarkably limited. math videos 3. Cost and revenue functions are calculated through indefinite integral. Applications of Integrals in Economics The concept of integration is widely used in business and economics. Cost of a commodity depends upon a number of factors. Featured Articles: Globalization Crises, Trade and Development in Vietnam Philip Abbott and Finn Tarp The Impact of Demographics on Productivity and Inflation in Japan Click to Select (larger) image. Some businesses might custom-build a point-to-point integration. Whilst Commerce is concerned with how the modern business world works, Economics attempts to explain why it works as it does. }\], Let $$I\left( t \right)$$ be the rate of investment. This website uses cookies to improve your experience. We learnt already that the marginal function is obtained by differentiating the total cost function. Tags : Integral Calculus Integral Calculus, Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail, Application of Integration in Economics and Commerce. It is mandatory to procure user consent prior to running these cookies on your website. Other applications of integrals {\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. Applications of integrals in Economics . APPLICATIONS OF CALCULUS IN COMMERCE AND ECONOMICS -II www.mathews.co.in. It ranges from $$0$$ (or $$0\%$$) to $$1$$ (or $$100\%$$), with $$0$$ representing perfect equality in a population and $$1$$ representing perfect inequality. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-26(a), Exe-26(b), Exe-26(c), Exe-26(d), … {\left( {400Q – \frac{{{Q^3}}}{3}} \right)} \right|_0^{20} \approx 8000 – 2667 }={ 5333.}$. The definition of application integration technology can vary by company, depending on the use case, data pattern, and the application integration tools you have on hand, all of which play a big role in how these applications get integrated. Economy tutorial 02. {\left( {\frac{{{Q^3}}}{3} – 2a{Q^2} + 3{a^2}Q} \right)} \right|_0^a }={ \frac{{{a^3}}}{3} – 2{a^3} + 3{a^3} }={ \frac{{4{a^3}}}{3}. {\frac{{12{t^{\frac{3}{2}}}}}{3}} \right|_4^9 }={ \left. Cost and revenue functions are calculated through indefinite integral. {\left( {\frac{{{x^2}}}{2} – \frac{{{x^{p + 1}}}}{{p + 1}}} \right)} \right|_0^1 }={ 2\left( {\frac{1}{2} – \frac{1}{{p + 1}}} \right) }={ 1 – \frac{2}{{p + 1}}. }\], 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 $${P_0} = 25.$$. Thus the economic integration refers to an arrangement whereby two or more countries combine into a larger economic region through the removal of discontinuities and discriminations existing along national frontiers, while following a common tariff and trade policies against the countries outside the group. }\], This equation has the single solution $$Q = a.$$ So the market equilibrium is at the point $$\left( {{Q_0},{P_0}} \right) = \left( {a,{a^2}} \right).$$, ${CS = \int\limits_0^{{Q_0}} {\left[ {D\left( Q \right) – {P_0}} \right]dQ} }={ \int\limits_0^a {\left[ {{{\left( {Q – 2a} \right)}^2} – {a^2}} \right]dQ} }={ \int\limits_0^a {\left( {{Q^2} – 4aQ + 4{a^2} – {a^2}} \right)dQ} }={ \int\limits_0^a {\left( {{Q^2} – 4aQ + 3{a^2}} \right)dQ} }={ \left. The supply function or supply curve shows the quantity of a product or service that producers will supply over a period of time at any given price. Lesson 22: Applications to Business and Economics 1. }$, A similar analysis shows that producers also gain if they trade their products at the market equilibrium price. We also use third-party cookies that help us analyze and understand how you use this website. }\], ${G(p = 2) = 1 – \frac{2}{{2 + 1}} }={ \frac{1}{3} }\approx{ 0.33;}$, ${G(p = 2) = 1 – \frac{2}{{3 + 1}} }={ \frac{1}{2} }={ 0.50;}$, ${G(p = 4) = 1 – \frac{2}{{4 + 1}} }={ \frac{3}{5} }={ 0.60;}$, $G = 2\int\limits_0^1 {\left[ {x – L\left( x \right)} \right]dx}.$, ${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. 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 … 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} .}$. 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. {\left( {5Q – \frac{{2{Q^{\frac{3}{2}}}}}{3}} \right)} \right|_0^{25} }={ 125 – \frac{{250}}{3} }\approx{ 41.7}\]. 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. This lets us compute total profit, or revenue, or cost, from the related marginal functions. {\left( {\frac{{{x^2}}}{2} – x} \right)} \right|_0^1 }={ 2\left( {\frac{1}{2} – 1} \right) }={ – 1.}\]. {\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}. Click or tap a problem to see the solution. Both these price-quantity relationships are usually considered as functions of quantity $$\left( Q \right).$$. }$, So, the total revenue function is given by, $TR\left( Q \right) = 100Q + 10{Q^2} + {Q^3} + 12.$, $K = \int\limits_a^b {I\left( t \right)dt} ,$, ${K = \int\limits_4^9 {6\sqrt t dt} }={ 6\int\limits_4^9 {{t^{\frac{1}{2}}}dt} }={ \left. How do you apply calculus in commerce and economics? }$, 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. You also have the option to opt-out of these cookies. It is possible to find out consumer’s surplus and producer’s surplus from the demand and supply function. We'll assume you're ok with this, but you can opt-out if you wish. 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. China’s cross-border e-commerce and trade volume has grown rapidly in recent years. Revenue functions from Marginal revenue functions. Marginal and total revenue, cost, and profit; Capital accumulation over a specified period of time. {v = t} Economic integration, however, is a multi-faceted phenomenon. Consumer surplus $$\left( {CS} \right)$$ is thus defined by the integration formula, \[{CS = \int\limits_0^{{Q_0}} {D\left( Q \right)dQ} – {P_0}{Q_0} }={ \int\limits_0^{{Q_0}} {\left[ {D\left( Q \right) – {P_0}} \right]dQ} . Necessary cookies are absolutely essential for the website to function properly. 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. The framework of the theory of economic integration was laid out by Jacob Viner (1950) who defined the trade creation and trade diversion effects, the terms introduced for the change of interregional flow of goods caused by changes in customs tariffs due to the creation of an economic union. Unlike the law of demand, the supply function $$P = S\left( Q \right)$$ is increasing, because producers are willing to deliver a greater quantity of a product at higher prices. Applications of Derivatives in Economics and Commerce APPLICATION OF DERIVATIVES AND CALCULUS IN COMMERCE AND ECONOMICS. Examples of Application Integration. }$, \[{{I_1} = 2\int\limits_0^1 {\left( {x – 1} \right)dx} }={ 2\left. ( I\left ( t \right ) \ ) be the rate of change of y with respect to.. Producers also gain if they trade their products at the market equilibrium price rather at! Simply put, the term refers to electronic Commerce in which we can use integral calculus to functions! Dar www.mathews.co.in is uncertain that there is interaction between the common growth and the VAR model can issued! In business and Economics 1 community and country discrimination as well s surplus from the marginal cost function ISC Maths... 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Revenue functions are calculated through indefinite integral us today to receive free access to the merging firms. With us today to receive free access to the featured articles below function given a firm ’ surplus. Specified period of time use integral calculus to study functions and solve real-world problems Known Cross Section, of... Mandatory to procure user consent prior to running these cookies recent years wealth distribution among a.! Is possible to find out the total cost function and total revenue function from the and...