‘2ra0/2020 Input - output Analysis - Definition, Formula, Slved Example Problems, Exercise | Mathematics Home (nw brink com) | Business Maths 11th st (httpiwww.brainkar.comisubjectBusiness-Maths-1th-std_8330 | put -oviput Analysis ‘Prev Page (tpuwonnrainkartcomiaricllinvereeote-mat 99868) Nex Page> (otpsewa brainkar comartlaPariaFractons_ 99874) (Chapter: ih Busnes Maha apd Sasten ENS) Mes an Determine Defnion, Farm, Save Exanple PrSlems,Exercie| Mathematics |Stly Mae, Lecarng Notes, Acsigamen Reference, Wik decrpon explain, be ti] Input - output Analysis ‘The foundation of npt- Output analysis inves input-output tables. Such tables include a seres of ows andcohimns of data that quantity the supply chaln for sectors ofthe economy. Input — output Analysis, Input ~Outpot analysis is @ technique which was invented by Prof, Wassily W.Leontef. Input Output analysis isa form of economic analysis based on the interdependencies between economic sectors, The method is most commonly used for estimating the impacts of Positive or negative economic shocks and analyzing the ripple effects throughout an economy. ‘The foundation of Input - Output analysis involves input ~ output tables. Such tables include a series of rows and columns of data that quantity the supply chin fr sectors ofthe economy. Industries are listed in the heads ofeach row and each column. The data in each column corresponds to the level of inputs used in that industry's production function, For example th column for auto manufacturing shows the resources required for building automobiles (je, requirement of stel, aluminum, plastic, electron et). Input ~ Output ‘models typically includes separate tables showing the amount of labour required per rupee unit of investment or production Consider a simple economic model consisting of two industries A, and A; where each produces only one type of product. Assume that «ach industry consumes part ofits own output and rest from the other industry for its operation. The industries are thus interdependent. Further assume that whatever is produced that is consumed. That is the total output of cach industry must be such as to mect its own demand, the demand of the other industry and the external demand (final demand), ‘Our aim is to determine the output levels of each of the two industries in order to meet a change in final demand, based on knowledge of the current outputs of the two industries, of course under the assumption thatthe structure ofthe economy does not change, Letay be the rupee value ofthe output of A, consumed by 4, i,j = 1,2 Leta, and xp be the rupee value ofthe current outputs of 4, and 4p respectively Let d and dz be the rupes value of the final demands for the outputs of 4, and 4p respectively. _wvw-brainkart.comiarticle/Input—outpul-Analysis_33870/ 18‘270072020 ‘The assumptions lead us to frame the two equations ail ‘The equations (1) take the form byt by + d,=s, bax bart dy ‘The above equations can be rearranged as, (ba =4, box + dabes =d; ‘The matrix form of the above equations is fe —bs | [| a, bl fs ore SE) = (-px=p where =| 2-9 x= [lone By solving we get XB ‘The matrix B is known as the Technology matrix: 1. The Hawkins — Simon conditions Tawkins ~ Simon conditions ensure the viability ofthe system, IB isthe technology matrix then Hawkins Simon conditions are i, the main diagonal elements in J B must be positive and fi, ~B|_ must be positive. Example 1.23 ‘The technology matrix of an economic system of two industries is & 02 ‘Test whether the system is viable as per Hawkins - Simon conditions. po aa: Tater P : _wvw-brainkart.comiarticle/Input—outpul-Analysis_33870/ Input - output Analysis - Definition, Formula, Slved Example Problems, Exercise | Mathematics 28Input - output Analysis - Definition, Formula, Slved Example Problems, Exercise | Mathematics ‘2072020 Solution los 02 5 fs 03] 1 0} [os 02 ra =[o t}-[5 oa] 02-02 Loo 03 2-02 WB I-09 03 = (0.2)(0.3)-(-0.2)(-0.9) = 006-018 12<0 Since |/~ Bis negative, Hawkins ~ Simon conditions are not satisfied. ‘Therefore, the given system is not viable. Example 1.24 ‘The following inter ~ industry transactions table was constructed for an economy of the year 2016, = agers 500 1,600 400 2,500 2 1,750 1,600 44650 8,000 Labours. 250 4,800 - = Construct technology co-efficient matrix showing direct requirements, Does @ solution exist for this system. Solution 500 4,,=500 a= 1600 x, = 1600 1000 hy bg= 2: _ww.brainkart.comvartclelinput—output-Analysis_33870/ 38Input - output Analysis - Definition, Formula, Slved Example Problems, Exercise | Mathematics 1600, oud , _ [02 02 The technology matrix is le at 3| 1 0} fo2 a2 ahaa 020 =[.05 33) tment of main cagonl are postive Nowa} =| 98-02 = (0.8)(0.8)-(-0-7)(-0.2) =0s4-o14 =03030 Since diagonal elements of are positive and |! ~ B| is positive, Hawkins ~ Simon conditions are satisfied Hence this system has a solution, Example 1.25 In an economy there are two industries P, and P, and the following table gives the supply and the demand position in crores of rupees. Determine the outputs when the final demand changes to 35 for P, and 42 for P, Solution a,=10 4,,=20 Ha 10. ag 8 bun BB _ww.brainkart.comvartclelinput—output-Analysis_33870/‘2ra0/2020 Input - output Analysis - Definition, Formula, Slved Example Probloms, Exercise | Mathematics ‘The technology matrix is B ~ [3 ¥ -(710 mew [| is 2 2 24 42} [204] 3} [is The output of industry P, should be 7150 crores and P, should be £204 crores. Example 1.26 ‘An economy produces only coal and steel, These two commodities serve as intermediate inputs in each other's production. 0.4 tonne of steel and 0.7 tonne of coal are needed to produce a tonne of steel. Similarly 0.1 tonne of steel and 0.6 tonne of coal ate required to produce a tonne of coal. No capital inputs are needed. Do you think that the system is viable? 2 and 5 labour days are requited to produce a tonne s of coal and steel respectively. If economy needs 100 tonnes of coal and 50 tonnes of steel, caleulate the gross output of the two commodities and the total labour days required. _wvw-brainkart.comiarticle/Input—outpul-Analysis_33870/ 58‘2ra02020 Input - output Analysis - Definition, Formula, Slved Example Problems, Exercise | Mathematics Solution Here the technology matrix is given under Steel of Ol 50 Coal 07 06 100 Labour days 5 ei e sem pa(4°! thetechnlogy avis B=[34 92] [os] 105s] =[-03 “cl 06 -0.1 -0.7 oa = (0.6)(0.4)-(-0.7)(-0.1) =0.24- 0.07 =0.17 Since the diagonal elements of I~ B are positive and value of|/~ Bl is positive, the system is viable, fos o.1 0.7 06 adj (1-8) | 8) = ph age 1 _foa o1 707 06, = -'D, where a x-1-0.xbeeo- [3] fo 0/50 0.7 06] [100] Steel output = 176.5 tonnes Coal output = 558.8 tonnes Total labour days required = 5(steel output) + 2( coal output) = 5(176.5) + 2(558.8) = 882.5 + 1176 2000.1 = 2000 labour days. _ww.brainkart.comvartclelinput—output-Analysis_33870/‘2ra0/2020 Input - output Analysis - Definition, Formula, Slved Example Prabloms, Exercise | Mathematics Qa - 1, The technology matrix of an economic system of two industries is i ar 033 ‘Test whether the system is viable as per Hawkins Simon conditions, whether the system is viable as per Hawkins-Simon conditions. 4. Two commodities A and Bare produced such that 04 tonne of A and 07 tonne of B are required to produce a tonne of 4. Similarly 0.1 tonne of A and 0.7 tonne of Bare needed to produce a tonne of B. Write down the technology matrix. If6.8 tonnes of A and 10.2 tonnes of B are required, find the gross production of both of them. 5. Suppose the inter-industry flow of the product of two industries are given as under, Production sector| CO™UMHION | Domestic demand | Total output ar 30 40 0 120 z 20 10 30 0 Determine the technology matrix and test Hawkin’s -Simon conditions for the viability of the system. If the domestic demand changes to 80 and 40 units respectively, what should be the gross output of each sector in order to meet the new demands. You are given the following transaction matrix for a two sector economy. (i) Write the technology matrix (ii) Determine the output when the final demand for the output sector 1 alone increases to 23 units. 7. Suppose the inter-industry flow of the product of two sectors X and Y are given as under. eduction | Consumption | Domestic eee pod feet! eri 1s 10 0 35 y 20 30 1s 6s Find the gross output when the domestic demand changes to 12 for X and 18 for Y. ‘4 Prev Page hto:won.rainkar.comariclliverse-ote-mat_ 90809) Nex Page (np:ewacrainkart comarlaParilFractons_2987%) _ww.brainkart.comvartclelinput—output-Analysis_33870/ 78‘2ra0/2020 Input - output Analysis - Definition, Formula, Slved Example Problems, Exercise | Mathematics SPONSORED SEARCHES o plastic manufacturing a cone input two output audio a ‘manufacturing industry a solve math problems a ‘Tags :Defintion, Formule, Sobed Example Problems, erie | Mathematics Defstion, Formula Solved Example Problens, Fert | Mathematics ‘Stusy Matera, Lecturing Notes, Assignment, Reference, Wk deaeroton explanation, bit deta ‘4 Prov Page (htp:twenbrankartcomfariclliverse-a-mat_ 398587) Nox Page> (np:ewacrainkart comarlPari-Fractons_2987%) Related Topics ‘Need fo eld wrk (pwn brink comiarickiNeadorld-wor 33865) Feld work rooees (hin brankar. comaricleFek-worcsooese_ 33868) Fels Report (hp ww brinkar. comvarcleFiet Repo. 39867), Determinants (ntpwwav erie conVarilelDeterninenls_S3868) Tree of rath (pa rainkartconvarlvereeotatin 38687) Porta Fractons (up. uwavorainkart converelelParil Fractions, 9587) Perulatons (Npiewscbaikar comarelelPermutaons_ 39972) “Combination (ip: brane comaria/Garsbinations 198730) Mathai induction (tp saw rankartconvartclaMatiematialnucton 33874) Binomial teorom (www braikar. comartle@inomial theorem, 33875) “arateal Geometry’ hvoducton (to siwww baka comiarcl/Rralyica- Gooneiynvoducion 5367S) Loous (htowawrareart.con/aricer.ous, 38877) o ve Big On Bloomberg.com Tverse Trigonometrc. 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