Syllabus for B.A. (Hons.), Economics:2014-15

SEMESTER-II

ECB-201, Macro Economics –I

(For Both Main & Subsidiary)

Credits: 04

Objectives:

This is the first part in the two part course, and is designed to provide a sound knowledge in macroeconomic

theory. The goal of this course is to provide students with a thorough understanding of the fundamental

principles of macroeconomics that establishes the functional relationship between large aggregates. This course

looks at the determination of income and employment, consumption function ,theories of investment, multiplier

and accelerator

Unit-1

Introduction: Nature and scope of Macro Economics, difference between Micro and Macro Economics and

importance of Macro Economics.

National Income: Concepts, measurement and limitations of National Income Statistics, Circular flow of

income in two, three and four sector economy. National Income and Welfare.

Determination of Income and Employment: Classical Theory of Employment, Say’s Law of Market and its

implications, Keynesian objections to Classical Theory, Keynes Theory of Employment.

Unit-2

Consumption: The principle of effective demand; Consumption Function, Technical Attributes of

Consumption, Keynes Psychological Law of Consumption and Its Implications, Empirical evidence.

Income-Consumption Relationship: Absolute Income Hypothesis, Relative Income Hypothesis, Permanent

Income Hypothesis, Life Cycle Hypothesis.

Unit-3

Investment function: Types of Investment, Determination of Level of Investment. Classical, Keynesian and

Jorgenson's Neo-Classical Theory of Investment, Saving-Investment Equality.

Multiplier and Accelerator: Concept of Multiplier, Types of Multiplier, Investment Multiplier, Government

Expenditure Multiplier, Income determination involving government expenditure and tax Multiplier, Leakages

of Multiplier, Acceleration principle, Super Multiplier.

Readings:

1. Ackley, G (1978), :“Macroeconomics: Theory and Policy”, Macmillan, New York.

2.Andrew B. Abel and : “M acroeconomics”, Pearson Education, Inc.

Ben S. Bernanke (2011)

3.Branson, W. A. (1989), :“Macroeconomic Theory and Policy”, 3rd Ed., Harper & Row,

NewYork.

4.Hanson, A.H. (1953), : A Guide to Keynes, McGraw Hill, New York.

5.Errol D’Souza, 2009, : Macroeconomics, Pearson Education, New Delhi.

6.Heijdra, B.J. and : Foundations of Modern Macroeconomics, Oxford University Press, 7.

F.V. Ploeg (2001) Oxford.

7. Keynes, J.M. (1936), : The General Theory of Employment, Interest and Money,

Macmillan,London.

8. Lipsey R.G. and : “Principles of Economics”, 9th Ed., Oxford UniversityPress.

K.A. Chrystal (1999)

9. Soumen Sikdar(2014) : Principles of Macroeconomics. Oxford University Press.

10. Shapiro, E (1996), :“Macroeconomic Analysis” Galgotia Publication, New Delhi.

11. Stiglitz J. E. and : Principles of Macroeconomics, W.W. Norton & Company, New Carl

E. Walsh (2002) York.

12. Paul Samuelson and : “Economics” (18th Ed.) Tata Hill Publishing Company, New Dehli.

Nordhaus: (2005)

13. Mankiw N. Gregory: (2010) :“Macroeconomics”, Worth Publishers.

14. Lipsey R.G. and : “Economics”, Oxford University Press. Oxford.

K.A. Chrystal (2007)

Syllabus for B.A. (Hons.), Economics:2014-45

SEMESTER-IV

ECB-401, Micro Economics –II

(For Both Main & Subsidiary)

Credits: 04

Objectives:

This course is a sequel to Microeconomics-I. The emphasis will be to provide students with a thorough

understanding of the fundamental principles of different forms of market. To achieve this goal this course

covers the theory of perfect competition, theory of monopoly, monopolistic competition and oligopoly. This

course also deals with the theory of factor pricing.

Unit-1

Theory of perfect competition Perfect competition and pure competition—short run and long run equilibrium of a competitive firm- The short-

run supply curve of the firm. Long run equilibrium of the competitive industry- price determination in a

competitive industry–long run supply curves of the industry- effects of external economies and diseconomies.

Unit-2

Theory of Monopoly: Monopoly: Characteristics, Theory of monopoly: Characteristics- AR and MR curves

under monopoly-Relation among AR , MR and Elasticity of demand. Short run and Long run Equilibrium of

Firm, Discriminating Monopoly, degree of Monopoly power.

Monopolistic competition: Characteristics short run and Long run Equilibrium of Firm, Group Equilibrium,

Product differentiation and Selling Costs.

Oligopoly: Kinked demand model.

Unit-3

Theory of Factor pricing:

Demand for factors of production - Determinants of price elasticity of demand for a factor – marginal

productivity theory and its limitations.

Theory of wage - Choice between work and leisure – derivation of individual labour supply curve – total labour

supply curve – demand for labour – determination of equilibrium in a perfectly competitive labour market-

collective bargaining and wage rate.

Theories of rent and profit.

Readings:

1. Ahuja H.L. : Modern Micro Economics, S. Chand & Company Ltd New Delhi

2. G.Lipsey Richard : Micro Economics: An Introduction to Positive Economics

and Samuelson ,Paul A. Oxford University Press

3. Jain T.R. & Sandhu A.S. : Micro Economics, F K Publication.

4. Joshi,J.M. : Theory of Value, Distribution and Welfare Economics, Vikash

Publishing House

5. Koutsoyiannis A. : Modern Micro Economics, Macmillan London

6. Ray N.C. : An Introduction to Micro Economics, Macmillan Company

7. Sachdeva Amit : Micro Economics

8. Salvatore Dominick : Micro Economic Theory, Oxford University Press

9. Seth M.L. : Micro Economics, Lakshmi Narain Agrawal Publisher

10. Varian Hal R. : Micro Economic Analysis, W.W. Norton & Company

Syllabus for M.A. Economics:2014-15

SEMESTER-IV

ECM- X011, Mathematical Economics – II

(Optional)

Objectives:

This course is the second part of the two- part course. It is assumed that students have knowledge background

equivalent to material covered in Mathematical Economics-I and have ability to develop further mathematical

theory needed for important applications in micro and macro economics. More specifically the aim of this

course is to expose the students with optimisation techniques and familiarize with macroeconomic models

commonly used in economics. It also covers game theory and welfare economics.

Unit-I: Optimization Techniques

Linear programming – Primal and dual problem, Solution by Graphical Method and Simplex Method.

Input-output analysis – Open and closed systems, Hawkins-Simon conditions; Leontief’s dynamic system.

Differential and Difference Equations-First order linear differential equations- stability of market equilibrium.

First and second order difference equations.

Unit-II: Game Theory

Introduction: Some Useful Terminology and Key Concepts, strategic form games: dominant strategy, Pure

Strategies – Locating a Saddle Point .Mixed Strategies: Arithmetic Method and Graphic Method. Nash

Equilibrium (definition)- Nash Equilibrium-Games of incomplete information- Bayesian Nash Equilibrium-

proof of Existence-Extensive form games-Repeated and dynamic games-Games of perfect information and

backward induction strategies- Nash Equilibrium and backward induction.

Unit-III: General Equilibrium and Welfare Economics

Pareto Optimality and Competitive Equilibria; Partial Equilibrium Competitive Analysis; The Fundamental

Welfare Theorems in a Partial Equilibrium Context; Pure Exchange: Edge worth Box; One consumer one

producer Economy, 2x2 Production Model; General versus Partial Equilibrium Theory; Pareto Optimality with

Social Optima; Existence of Walrasian Equilibrium; Core and Equilibria in Competitive Economies

Readings List: 1.

Abel, A., B.S. Bernanke and B. Mcnabb (1988), Macroeconomics, Addison Wesley, Massachusetts.

2.

Allen, R.G.D. (1974), Mathematical Analysis for Economists, Macmillan Press and ELBS, London.

3.

Allen, R.G.D. (1974), Macro-Economic Theory: A Mathematical Treatment

4.

Arrow, K.J. and M. Intrilligator (Eds.) (1982), Handbook of Mathematical Economics, Volumes I, II and III, North Holland, Amsterdam.

5.

Arrow, K.J . (1974). ‘General Economic Equilibrium, Purpose, Analytic Techniques, Collective Choice’. American Economic Review, Vol. 64, pp. 253 - 273.

6.

Baumol, W. J. 1972. Economic theory and operation analysis. Prentice Hall,

7.

Black and J.F. Bradley (1973), Essential Mathematics for Economists, J. Wilay and Sons. London

8.

Chiang, A.C. (1986), Fundamental Methods of Mathematical Economics, McGraw hill, New York.

9.

Chung, J.W. (1993), Utility and Production: Theory and Approach, Basil Blackwell, London.

10.

Hadley, g. (1962), Linear Programming, Addison Wesley Publishing Co., Massachusetts.

11.

Henderson, J, M. and R.E. Quandt (1980), Microeconomic Theory: A Mathematical Approach, McGraw Hill, New Delhi.

12.

Intrilligator, M. Mathematical optimization and economic theory. Prentice Hall, 1971.

13.

Jean Soper (2003): Mathematics for Economics and Business: An Interactive Introduction, Blackwell Publishing Ltd.

14.

Jha, R. (1991), Contemporary Macroeconomic Theory and Policy, Wiley Eastern Ltd., New Delhi.

15.

Jones, H.G. (1976), An Introduction to the Modern Theory of Economic Growth, McGraw Hill- Kogakusha, Tokyo.

16.

Kapoor, V.K. (1995): Essentials of Mathematics for Business and Economics, Sultan Chand and Sons, New Delhi.

17.

Kothari, C.R. (1992), An Introduction to Operations Research, Vikas Publishing House, New Delhi.

18.

Kuhn, Harold W. (Ed.) (1997), Classics in Game theory, Princeton, University Press, Princeton.

19.

Martin Anthony & Norman Bigg (2000): Mathematics for Economics and Finance, Methods and Modeling, Cambridge University Press, U.K.

20.

Mas-Colell, Andreu, Michael D.Whinston and Jerry R. Green, (1995), Microeconomic Theory, OUP, New York

21.

Mehta, B.C. and G.M.K. Madnani, Mathematics for Economists, Sultan Chand and Sons, 1997.

22.

Metwally, M.M. (1995): Mathematical Macroeconomic Models, Academic Publishers, Calcutta.

23.

Quirk J.P., & Saposnik, R. (1968), Introduction to General Equilibrium Theory and Welfare Economics.

24.

Varian, Hall R., (1992), Microeconomic Analysis (Third Edition), W.W. Norton & Company, New York, London.

Sessional Test Marks B.A. (I

st SEMESTER) 2014-15: Paper: EC- 101 (Micro Economics-1) SECTION - A

40 14ECB-42 MOHD SHAMARUKH 08 08 16

41 14ECB-44 MOHD WAHAJ KHAN A A A

42 14ECB-45 SYED ABDUR RAHMAN J 08 08 16

43 14ECB-47 DANISH KHAN 07 07.5 15

44 14ECB-48 MOHD HASSAN A 06 06

45 14ECB-49 ALTAMESH MOHD FATEH 06 07.5 14

46 13ECB-21 ASJAD AHMAD A A A

S.N. Roll No.

Name of Candidates Ist IInd Grand

Total 14ECB Test Test

1 14ECB-01 MOHD UL HAQ 06 06.5 13

2 14ECB-02 ABDULLAH DANISH A A A

3 14ECB-03 MOHD FADHLAM 05.5 06 12

4 14ECB-04 SHAHNAWAZ ANWAR 06.5 08 15

5 14ECB-05 MOHD AARISH KHAN A A A

6 14ECB-06 MOHD SARFARAZ ALAM 08 08 16

7 14ECB-07 RAYEES AHMAD 08 08 16

8 14ECB-08 AHAB RIZVI 07.5 07.5 15

9 14ECB-09 IQBAL HUSSIAN LASKAR 06.5 07 14

10 14ECB-10 UMMAR FAROOQ SHEIKH 06 07 13

11 14ECB-11 ZIA MALIK 07.5 08 16

12 14ECB-12 SHIFIN TK 07.5 06.5 14

13 14ECB-13 MD ARSHE ALAM 08.5 07.5 16

14 14ECB-14 FAIYAZ JULFIKAR 08 08 16

15 14ECB-16 SAIF ZAIDI 08 08 16

16 14ECB-17 RAMEEZ RAJA 08.5 07.5 16

17 14ECB-19 MOHD ABAD 08 07.5 16

18 14ECB-20 MOHD SHAHWAZ A A A

19 14ECB-21 MOHD INZAM HAQ 06.5 07 14

20 14ECB-22 AJAZ AHMAD 05.5 06 12

21 14ECB-23 MOHD ADIL 07.5 06 14

22 14ECB-24 MOHD TATHEER S KHAN 06 06.5 13

23 14ECB-25 MOHD UMAIR KHAN 06.5 07.5 14

24 14ECB-26 ABUZAR ALI A A A

25 14ECB-27 FARRUKH ADIL 06 07.5 14

26 14ECB-28 MOHD SHAHWEZ 08 08 16

27 14ECB-29 MD ADNANUDDIN 06.5 07 14

28 14ECB-30 MOHD SAQIB 07 07 14

29 14ECB-31 MD SAJID ALAM 07 06.5 14

30 14ECB-32 MD SALIK ALI 07 07.5 15

31 14ECB-33 ATHER HASSAN 07.5 08 16

32 14ECB-34 SADAB QADRI 07 06.5 14

33 14ECB-35 MOHD DANISH 07 05 12

34 14ECB-36 ZEESHAN AFZAL 07 0 07

35 14ECB-37 MOHD AQIL 07 06.5 14

36 14ECB-38 MD ABU TORAB 05.5 06 12

37 14ECB-39 ASHIQUE ALI 06.5 06.5 13

38 14ECB-40 SHAHZEB KHAN A 05 05

39 14ECB-41 SARTHAK KAPOOR 06.5 07 14

Sessional Test Marks

B.A. (III SEMESTER), 2014-15 Paper: ECB- 301: Mathematical Methods

S.No. Roll No. Name of Candidates Ist Test IIndTest GrandTotal

1. 13ECB-01 SAIF ALI 09 07.5 17

2. 13ECB-02 ASAD KALAM 09 08 17

3. 13ECB-03 MD QAMAR AZAM 09 08 17

4. 13ECB-04 ABDUL MUKHTADIR 8.5 08 17

5. 13ECB-05 BAHAUDIN M SHAHBAZ 08.5 08.5 17

6. 13ECB-07 BASHARAT RAMZAN 08 08.5 17

7. 13ECB-08 FARHAN AKRAM 08.5 08.5 17

8. 13ECB-09 MOHD UMAR KHAN 09 06 15

9. 13ECB-10 FAISAL GULZAR MIR 08.5 08.5 17

10. 13ECB-12 MOHD ROSHAN 07 07 14

11. 13ECB-13 PRABEESH V 08 08.5 17

12. 13ECB-14 ZAFAR A RAHMAN 08.5 07.5 16

13. 13ECB-15 GAUHAR RASOOL 07.5 08.5 16

14. 13ECB-16 AZAM NAWAZ 07.5 07.5 15

15. 13ECB-17 SHARIQUE MUMTAZ 08 09 17

16. 13ECB-18 MOHD BAHAUDDIN 05.5 08 14

17. 13ECB-19 CHINMAY SAXENA 04 06 10

18. 13ECB-20 MD ABRAR ALAM 08 09 17

19. 13ECB-22 AMANUL RAHMAN 08 07.5 16

20. 13ECB-25 ABU KASIM 08.5 08 17

21. 13ECB-26 TARIQ IQBAL 08 07.5 16

22. 13ECB-27 M RAHMAN MUNZIR A A A

23. 13ECB-28 S ANAS AHMAD 09 08 17

24. 13ECB-30 MOHD MOAZZAM 08.5 07 16

25. 13ECB-31 SOHAIL ALAM 08 08.5 17

26. 13ECB-32 SHAH MOHD A 09 08 17

27. 13ECB-33 RAMZAN SAMRAT A A A

28. 13ECB-34 MEHBOOB AHMAD 07.5 07.5 15

29. 13ECB-37 AKASH KUMAR VERMA 08 07 15

30. 13ECB-38 SHIVAM SHARMA 07 07 14

31. 13ECB-39 PRAKHAP PANDEY 08 08 16

32. 13ECB-40 MOHD MUZXAMMIL 07 08 15

33. 13ECB-41 ANSHUL AGARWAL 08.5 07.5 16

34. 13ECB-42 PRASHANT SINGH 08 06.5 15

35. 13ECB-43 MOHD IMRAN KHAN A 06 06

36. 13ECB-45 MD GHULAM S 08.5 07 16

37. 13ECB-46 SAJID JAMIL KHAN 08.5 08.5 17

38. 13ECB-47 ABDUL MOIZZ 08.5 08.5 17

39. 13ECB-48 GHULAM ALI HUSSAIN 09 08 17

40. 12ECB-28 MOHD ANAS JAVED A 08 08

M.A. III Semester (Economics) Session – 2014-15 Paper: ECM-9011: MATHEMATICAL ECONOMICS-I

S.No. Role No. Name of the Candidate First

Test

Second

Test Grand

Total 1 13ECM-02 AMIR WANI 08 10.5 19 2 13ECM-03 MD SHAHNAWAZ S 10.5 11 22 3 13ECM-05 SADAF FATIMA HUSAIN 10.5 10.5 21 4 13ECM-06 RANA AFREEN 11 11 22 5 13ECM-07 FARHAT BANO 10.5 11 22 s6 13ECM-08 SADAF 10 10 20 7 13ECM-09 HUMAIRA KHAN 11 10.5 22 8 13ECM-10 NEHA HAFEEZ 10 09.5 20 9 13ECM-11 SHABANA ANJUM 11.5 11.5 23 10 13ECM-12 JIGISHA SINGH 11 11.5 23 11 13ECM-13 MOHD FAISAL 11 11.5 23 12 13ECM-15 MOHD JAVED A A A 13 13ECM-17 FARAZ KHAN 08 11 19 14 13ECM-19 MOHD AQIB 10 10.5 21

15 13ECM-22 NAGHMA M 09 11 20

16 13ECM-23 FARHEEN FIROZ 10 10.5 21

17 13ECM-25 FAHAD ALAM 10 10.5 21

18 13ECM-26 RIYAZ ALAM 09.5 11 21

19 13ECM-27 SULTAN FAIZUDIN 08.5 10.5 19

20 13ECM-28 MOHD EQBAL 10 10 20

21 13ECM-29 BENAZIR AHMAD 11 11.5 23 22 13ECM-30 NUZHA IRFAN 10.5 10.5 21 23 13ECM-32 MOHD ASHIQ 09 07.5 17 24 13ECM-36 SAFEERA SIDDIQUI 10.5 10.5 21 25 13ECM-37 ARIFA KHAN 11 10 21 26 13ECM-40 WASEEM ALAM 08 09.5 18 27 13ECM-41 SHOWKAT AHAMD 10.5 10.5 21

28 13ECM-45 AIYASH AARIF 11 10.5 22

29 13ECM-47 ABIDA TABASSUM 10.5 11 22

30 13ECM-53 SIDRA TARIQ 11 10.5 22

31 13ECM-55 NOOR FATIMA 10 11 21

32 13ECM-56 NIKITA DWAWASH S 10 11 21

33 13ECM-57 ARBIYA NASEEM A 10.5 11 22 34 13ECM-59 MOHD MOSTAGH FIRUL MULK 10.5 10 21 35 13ECM-64 SAMAN AZIZ 11 11 22 36 13ECM-66 ASIF AHMAD KHAN 07 10.5 18 37 13ECM-67 PUSHP KUMAR 10.5 11 22 38 13ECM-69 MD TAMIM HUSSIAN 10 10 20

Syllabus for M.A. Economics

2014-15: SEMESTER-III

ECM- 9011, Mathematical Economics – I

(Optional)

Objectives:

This is the first of a two-part course. The principal aim of this course is to: introduce students to the

Mathematical concepts and methods used to analyse consumer behaviours, producer behaviours and

determination of price in various markets; equip students with the necessary knowledge to express economic

ideas with formal mathematical concepts and develop students’ ability to derive logical implications of formal

economic models.

Unit-I: Theory of Consumer Bahaviour

Cardinal and ordinal utility; Ordinal utility maximization; Slutsky equation, compensated demand

functions, income, substitution, and price effects; Concept of elasticities – generalization to n variable

case; homogeneous and homothetic utility functions; Constant elasticity of substitution (CES) utility

function; indirect utility functions; Consumer’s surplus; Theory of revealed preference and index

numbers; Consumer behaviour under risk and uncertainty.

Unit-II: Theory of Production

Production function – homogeneous and non-homogeneous; Properties of Cobb-Douglas Production function;

CES; VES and trans-log production function; Simple derivation of short and long run cost functions; Modern

approach to theory of costs; Cost function; Producer’s equilibrium – Laws of return and return to scale;

Constrained optimization of a producer; Generalization to n variable case; Input demand functions; Adding up

theorem; Technical progress through production function; Production possibility curve; Empirical uses of

production function analysis.

Unit-III: Price Determination in Various Markets

Price determination in perfect competition, monopoly, monopolistic competition, duopoly, oligopoly;

Pricing of factors of production; bilateral monopoly. Single market equilibrium – Marshallian and Walrasian

equilibrium conditions; Lagged market equilibrium;

Readings List:

1. Allen, R. G. D. Mathematical analysis for economists. Macmillan, 1995.

2. Chiang, A. C. Fundamental methods of mathematical economics. McGraw-Hill, 1985.

3. Chung, J.W. (1993), Utility and Production: Theory and Approach, Basil Blackwell, London

4. Mehta, B.C. and G.M.K. Madnani, Mathematics for Economists, Sultan Chand and Sons, 1997.

5. Baumol, W. J. Economic theory and operation analysis. Prentice Hall, 1972.

6. Henderson, J, M. and R.E. Quandt (1980), Microeconomic Theory: A Mathematical Approach, McGraw Hill,

New Delhi.

7. Intrilligator, M. Mathematical optimization and economic theory. Prentice Hall, 1971.

8. Jean Soper (2003): Mathematics for Economics and Business: An Interactive Introduction, Blackwell

Publishing Ltd.

9. Kapoor, V.K. (1995): Essentials of Mathematics for Business and Economics, Sultan Chand and Sons, New

Delhi.

10. Ma ett, A.J. Mathematics for economists: work out, Macmillan Master Series, 1986.

11. Ostrosky, A.L. and J.V. Koch. Introduction to mathematical economics, Houghton Mifflin Co. Boston,

1979.

12. Roberts B. and D.L. Schultze, Modern Mathematics and Economic Analysis, W.W. Norton and Company,

1973.

13. Rosser, M. Basic Mathematics for Economists, Routledge, 1993. Department

Syllabus for M.A. Economics

2014-15: SEMESTER-IV

ECM- X011, Mathematical Economics – II

(Optional) Objectives:

This course is the second part of the two- part course. It is assumed that students have knowledge background

equivalent to material covered in Mathematical Economics-I and have ability to develop further mathematical

theory needed for important applications in micro and macro economics. More specifically the aim of this

course is to expose the students with optimisation techniques and familiarize with macroeconomic models

commonly used in economics. It also covers game theory and welfare economics.

Unit-I: Optimization Techniques

Linear programming – Primal and dual problem, Solution by Graphical Method and Simplex Method.

Input-output analysis – Open and closed systems, Hawkins-Simon conditions; Leontief’s dynamic system.

Differential and Difference Equations-First order linear differential equations- stability of market equilibrium.

First and second order difference equations.

Unit-II: Game Theory

Introduction: Some Useful Terminology and Key Concepts, strategic form games: dominant strategy, Pure

Strategies – Locating a Saddle Point .Mixed Strategies: Arithmetic Method and Graphic Method. Nash

Equilibrium (definition)- Nash Equilibrium-Games of incomplete information- Bayesian Nash Equilibrium-

proof of Existence-Extensive form games-Repeated and dynamic games-Games of perfect information and

backward induction strategies- Nash Equilibrium and backward induction.

Unit-III: General Equilibrium and Welfare Economics

Pareto Optimality and Competitive Equilibria; Partial Equilibrium Competitive Analysis; The Fundamental

Welfare Theorems in a Partial Equilibrium Context; Pure Exchange: Edge worth Box; One consumer one

producer Economy, 2x2 Production Model; General versus Partial Equilibrium Theory; Pareto Optimality with

Social Optima; Existence of Walrasian Equilibrium; Core and Equilibria in Competitive Economies

Readings List: 25.

Abel, A., B.S. Bernanke and B. Mcnabb (1988), Macroeconomics, Addison Wesley, Massachusetts.

26.

Allen, R.G.D. (1974), Mathematical Analysis for Economists, Macmillan Press and ELBS, London.

27.

Allen, R.G.D. (1974), Macro-Economic Theory: A Mathematical Treatment

28.

Arrow, K.J. and M. Intrilligator (Eds.) (1982), Handbook of Mathematical Economics, Volumes I, II and III, North Holland, Amsterdam.

29.

Arrow, K.J . (1974). ‘General Economic Equilibrium, Purpose, Analytic Techniques, Collective Choice’. American Economic Review, Vol. 64, pp. 253 - 273.

30.

Baumol, W. J. 1972. Economic theory and operation analysis. Prentice Hall,

31.

Black and J.F. Bradley (1973), Essential Mathematics for Economists, J. Wilay and Sons. London

32.

Chiang, A.C. (1986), Fundamental Methods of Mathematical Economics, McGraw hill, New York.

33.

Chung, J.W. (1993), Utility and Production: Theory and Approach, Basil Blackwell, London.

34.

Hadley, g. (1962), Linear Programming, Addison Wesley Publishing Co., Massachusetts.

35.

Henderson, J, M. and R.E. Quandt (1980), Microeconomic Theory: A Mathematical Approach, McGraw Hill, New Delhi.

36.

Intrilligator, M. Mathematical optimization and economic theory. Prentice Hall, 1971.

37.

Jean Soper (2003): Mathematics for Economics and Business: An Interactive Introduction, Blackwell Publishing Ltd.

38.

Jha, R. (1991), Contemporary Macroeconomic Theory and Policy, Wiley Eastern Ltd., New Delhi.

39.

Jones, H.G. (1976), An Introduction to the Modern Theory of Economic Growth, McGraw Hill- Kogakusha, Tokyo.

40.

Kapoor, V.K. (1995): Essentials of Mathematics for Business and Economics, Sultan Chand and Sons, New Delhi.

41.

Kothari, C.R. (1992), An Introduction to Operations Research, Vikas Publishing House, New Delhi.

42.

Kuhn, Harold W. (Ed.) (1997), Classics in Game theory, Princeton, University Press, Princeton.

43.

Martin Anthony & Norman Bigg (2000): Mathematics for Economics and Finance, Methods and Modeling, Cambridge University Press, U.K.

44.

Mas-Colell, Andreu, Michael D.Whinston and Jerry R. Green, (1995), Microeconomic Theory, OUP, New York

45.

Mehta, B.C. and G.M.K. Madnani, Mathematics for Economists, Sultan Chand and Sons, 1997.

46.

Metwally, M.M. (1995): Mathematical Macroeconomic Models, Academic Publishers, Calcutta.

47.

Quirk J.P., & Saposnik, R. (1968), Introduction to General Equilibrium Theory and Welfare Economics.

48.

Varian, Hall R., (1992), Microeconomic Analysis (Third Edition), W.W. Norton & Company, New York, London.

Syllabus for B.A. (Hons.), Economics

2014-15: SEMESTER-I

ECB-101, Micro Economics –I

(For Both Main & Subsidiary)

Credits: 04

Objectives:

This is the first part of the two part course, and is designed to expose students to the basic principles of

economics. This course has the objective of equipping the students in a rigorous and comprehensive manner

with the various aspects of demand analysis, consumer behaviour, production theory, cost analysis and market

structure.

Unit-1 Consumer theory

Nature and Scope of Economics, Methodology of Economics, Demand and supply function; Law of demand,

Elasticity of demand – price, income and cross elasticities, and their measurements; Elasticity of supply; Price

determination.

Theory of consumer behaviour: Cardinal and ordinal Utility analysis and Consumer’s equilibrium. Indifference

curve and its properties, the consumer-– price consumption curve and income consumption curve, - price effect,

income effect and substitution effect (Hicks and Slutsky methods), inferior goods and giffen goods, derivation

of demand curve.

Unit-2 Production, Costs & Revenue

Production decisions; Production function; law of variable proportions; returns to scale; characteristics of

Isoquants, Factor substitution; Ridge lines; least cost combination of factors, Internal and external economies

and diseconomies.

Cost function: different concepts of costs, short run cost analysis and long run cost Analysis- relation between

the expansion path and cost function.

Concepts of revenue; total, average and marginal revenue and their relationships, Break-even-analysis & its

uses.

Unit-3 Market Structure

Perfect and imperfect markets, Pure competition, Equilibrium of the firm and industry under perfect

competition, Role of time element in the determination of value, supply curve under perfect competition,

Equilibrium of the firm under monopoly, Discriminating monopoly, Conditions of equilibrium under price

discrimination, Degree of monopoly power.

Readings: 1. Gauld, J.P. and Edward P. L. (1996), : Microeconomic Theory, Richard. Irwin, Homewood.

2. Gravelle and Rees- : Microeconomics; Pearson Education, 2nd Edition

3. G.S. Maddala and E. Miller. 1989. :Microeconomics. McGraw-Hill International Editions.

4. Henderson J. and R.E. Quandt (1980), : Microeconomic Theory:A Mathematical

Approach,McGraw Hill, New Delhi.

5. Heathfield and Wibe (1987), : An Introduction to Cost and Production Functions,

Macmillan,London.

6. Koutsoyiannis, A. (1990), : Modern Microeconomics, Macmillan.

7. Lipsey, R.G. and K.A. Chrystal (1999), : Principles of Economics, Oxford UniversityPress,

Oxford.

8. Mansfield, E. (1997), : Microeconomics (9th Edition), W.W. Norton and

Company, New York.

9. Ray, N.C. (1975), : An Introduction to Microeconomics, Macmillan

Company of India Ltd.,Delhi.

10. R S. Pindyck and D.L. Rubinfeld, (2000), : Microeconomics, 3rd edition, Prentice Hall, India.

11. R S. Pindyck, D.L. Rubinfeld and : Microeconomics, 7Th edition, Prentice Hall, India.

Mehta (2007)

12. Samuelson, P.A. and W.D. Nordhaus (1998), : Economics, Tata McGraw Hill, New Delhi.

13. Stonier, A.W. and D.C. Hague (1972), : A Textbook of Economic Theory, ELBS & Longman

Group, London.

14. Varian, H.R. (2000), : Intermediate Microeconomics : A Modern Approach,

East-West Press, New Delhi.

Syllabus for B.A. (Hons.), Economics

SEMESTER-III: 2014-15

ECB-301, Mathematical Methods

(For Main Only)

Credits: 04

Objectives:

The knowledge of Mathematics is now days almost essential to understand the subject matter of Economics.

The students in this direction are expected to have an elementary knowledge of the concept of functions, limits

and continuity, differential and integral calculus and matrices & determinants. This course has been designed

keeping in mind the aforesaid need of the students. It emphasises on the application of Mathematics in

Economics.

Unit-1Functions

Function; Types of Function; Equations: Linear and quadratic, Simultaneous; Graphs, slopes and intercepts;

Economic applications of graphs and equations; Calculation of growth rates, present value and annuities. Limits and Continuity

Introduction; Limit Theorems; Examples on Limits; Continuity of Functions ; BasicProperties Concerning Continuity.

Unit-2Differential Calculus

Average rate of change; The Derivative as a rate of change; Rules for Simple, Partial and Total differentiations; Higher-

Order Derivatives; Concavity and Convexity: A Graphical Exposition; Problems of maxima and minima in single and

multivariable functions. Constrained optimization with Lagrange multiplier.

Integral Calculus

Indefinite Integral; Basic Integration Formulas; Methods of Integration; Definite Integral; Properties of Definite

Integrals. Application of Integration in Economics: Finding out total functions (TR, TC, Consumption

Function, Saving function) when marginal functions are given – Consumer’s Surplus – Producer’s surplus

Unit-3Matrices and Determinants The Concept of a Matrix; Types of Matrices; Operations on Matrices; Determinants: Characterization, Properties

and Applications; Rank of a Matrix; Matrix Inversion; Solution of Simultaneous equations: Cramer’s rule and Matrix

Inversion method, Leontief Input- Output Models (closed).

Readings:

1. Allen, R.G.D. (1974), : Mathematical Analysis for Economists,

Macmillan Press and ELBS, London.

2. Carl P. Simon and Lawrence Blume (2007), : Mathematics for Economists, Viva Books Pvt.

Ltd. New Delhi.

3. Chiang, A.C. (1986), : Fundamental Methods of Mathematical

Economics (3rd Edition), McGraw Hill, New

Delhi.

4. Henderson, J. and R.E. Quandt (1980), : Microeconomic Theory: A Mathematical

Approach, McGRaw Hill, New Delhi.

5. K. Sydsaeter and P. Hammond (2005), : Mathematics for Economic Analysis, Pearson

Educational Asia, New Delhi

6. Monga, G.S. (1972), : Mathematics and Statistics for Economists,

Vikas Publishing House, New Delhi.

7. Mukherji, B. and V. Pandit (1982), : Mathematical Method of Economic Analysis,

Allied Publishers, New Delhi.

8. SALAM, MD. ABDUS (2012), : AN INTRODUCTION TO MATHEMATICAL ECONOMICS,

LAP LAMBERT ACADEMIC PUBLISHING GMBH

& CO. KG, GERMANY.

M.A. IV Semester (Economics) Session – 2013-14 Paper: ECM-X011: MATHEMATICAL ECONOMICS-II

S.No. ROLL No. Name of the Candidate First

Test

Second

Test

Grand

Total

1. 11ECM-68 FURQAN ALI 11.5 11.5 23

2. 12ECM-01 RASHI SINGH 11 10.5 22

3. 12ECM-02 SARAH KAREEM 11 11.5 23

4. 12ECM-04 MOHINI AGARWAL 12 12 24

5. 12ECM-05 MOHINI GUPTA 12 12 24

6. 12ECM-06 SEHARISH J. ANSARI 11 11.5 23

7. 12ECM-07 NADA Z AYUBI 11.5 11 23

8. 12ECM-11 MOHD SHAHID ZAMAN 11 11.5 23

9. 12ECM-13 NADEEM AHMAD 10 11 21

10. 12ECM-14 YASIR HUSSAIN 8 11.5 20

11. 12ECM-16 IMRANA PARVEEN 11.5 12 24

12. 12ECM-17 SHOJAUDDIN 11 11.5 23

13. 12ECM-18 FARHANA KULSUM 10.5 11.5 22

14. 12ECM-20 RAFIQ HUSSAIN 11 11.5 23

15. 12ECM-23 MEHZABEEN SULTANA 11.5 11.5 23

16. 12ECM-24 SHAHNAZ KHAN 10.5 10.5 21

17. 12ECM-25 GULSHAN BANO 12 11 23

18. 12ECM-29 HAROON RASOOL 11 10.5 22

19. 12ECM-30 MASUDUL HASAN 11 12 23

20. 12ECM-31 ALI SAEED 10.5 10 21

21. 12ECM-32 MD SHARIQUE ANWAR 9 11.5 21

22. 12ECM-33 UMME HANI 10 11 21

23. 12ECM-38 ZAREEN ZAHIDI 11 11.5 23

24. 12ECM-39 BUSHRA HASEEB 10 11 21

25. 12ECM-40 MUNAWAR PT 9 11 20

26. 12ECM-45 VISHAL SHARMA 10.5 11.5 22

27. 12ECM-46 MOHD DANISH 11.5 11.5 23

28. 12ECM-47 NOSHEEN HAROON 11.5 11.5 23

29. 12ECM-54 LARAIB AFTAB 11 11.5 23

30. 12ECM-58 REHAN MUSTAFA KHAN 9 11 20

31. 12ECM-63 AAMIR REHMAINI 10.5 11.5 22

32. 12ECM-64 NEHA MOHAN 11.5 11.5 23

33. 12ECM-65 MEHVISH MEHMOOD 11.5 11.5 23

34. 12ECM-66 SADAF SHAKEEL 11 10.5 22

35. 12ECM-67 MOHD FAISAL 10.5 11.5 22

36. 12ECM-68 HAYA NAJAMUDIN 11 11.5 23

37. 12ECM-71 SADICHHA 11 11 22

B.A. (Ist Yr.) 2013-14:Paper: EC- 112 (Macro Economics) SECTION - B

S.N. ROLL NO. NAME OF CANDIDATES First Test Second Test Total Marks

1 12ECB-124 NAJARUDIN 08 07 15

2 12ECB-114 MOHD UMAIR HUSSAIN 5.5 6.5 12

3 12ECB-108 MOHD. IMRAN HAMID A 7.5 08

4 12ECB-104 MOHD ATIF 06 05 11

5 12ECB-101 NAVEED ANWAR A A A

6 12ECB-99 IRFAN KHAN A A A

7 12ECB-87 AFSAR AHMAD 6.5 6.5 13

8 12ECB-71 AASIM ANWAR 5.5 06 12

9 12ECB-69 ABDUL BASIT 5.5 6.5 12

10 13ECB-51 TALHA SHERWANI 5.5 07 13

11 13ECB-52 IFHAM AHMAD 06 07 13

12 13ECB-54 MOHD YASIR 08 07 15

13 13ECB-55 AMIR KHAN 06 5.5 12

14 13ECB-56 AQIB AKHTAR 06 6.5 13

15 13ECB-58 ADIL 5.5 6.5 12

16 13ECB-59 SYED SAIF HUSSAIN A A A

17 13ECB-60 SHARIQ KHAN 06 07 13

18 13ECB-61 MOHD SHEERAZ ANSARI 07 06 13

19 13ECB-62 RAHAT ANJUM 06 06 12

20 13ECB-63 ARSAL JAVED 06 07 13

21 13ECB-65 FARAZ ALI 6.5 6.5 13

22 13ECB-66 SHADAB 7 4.5 12

23 13ECB-67 FIROZ HASSAN A 7.5 8

24 13ECB-68 MOHD ASLAM 6.5 06 13

25 13ECB-69 USMAN CHOUDHARY 07 07 14

26 13ECB-71 ZEESHAN ABDULLAH 6.5 6.5 13

27 13ECB-72 MOHD REHAN 5.5 07 13

28 13ECB-73 MOHD ARIF 08 07 15

29 13ECB-74 ABDUL ADIL 6.5 6.5 13

30 13ECB-75 MOHD SALMAN 7.5 7.5 15

31 13ECB-78 FARMAN ZIA 6.5 06 13

32 13ECB-79 REHAN AKHLAQ 08 07 15

33 13ECB-80 MUDASSIR HUSAIN 6.5 06 13

34 13ECB-82 WASIM KHAN 02 05 07

35 13ECB-83 NOORUDIN AHMAD 6.5 06 13

36 13ECB-84 IMRAN KHAN 00 09 09

37 13ECB-85 MUSAB ZIA 5.5 06 12

38 13ECB-86 KR. WAQAR AHMAD 6.5 06 13

39 13ECB-87 MOHD ZOHID 08 07 15

40 13ECB-90 MOHD ZAIN KHAN A A A

41 13ECB-91 ZUBAIR QAMAR 6.5 5.5 12

42 13ECB-92 MOHD YASIR MAIRAJ 6.5 07 14

43 13ECB-94 MOHD ISHAQ 06 5.5 12

44 13ECB-95 MOHD RAZA 6.5 07 14

45 13ECB-96 FAIZ KHAN 08 07 15

46 13ECB-99 MD. MURSALIM 08 07 15

47 13ECB-100 MOHD AMAAN 6.5 5.5 12

48 13ECB-101 MOHD BILAL 06 06 12

49 13ECB-102 MOHSIN JAVED 6.5 07 14

50 13ECB-103 AMWARUL HODA 08 07 15

51 13ECB-104 MOHD HARIS 08 07 15

52 13ECB-105 NABEEL HASSAN 06 06 12

53 13ECB-106 MOHD AHSAN 06 07 13

54 13ECB-107 MD NAUSHAD ALAM 5.5 6.5 12

55 13ECB-108 DILIP KUMAR 08 07 15

56 13ECB-109 SARFARAZ ALAM 08 07 15

57 13ECB-110 MUNAZZAM AHMAD 6.5 07 14

58 13ECB-112 MOHD SUFIYAN 08 07 15

59 13ECB-113 AZHAN ZUBERI 08 07 15

60 13ECB-114 AREEB HUSSAIN 5.5 06 12

61 13ECB-116 ABBAS HAIDER 08 07 15

62 13ECB-117 MOHD. SADIQ USMAN 08 07 15

63 13ECB-118 MOHD. SAIF 5.5 07 13

64 13ECB-119 MOHD.TARIQUE 08 07 15

65 13ECB-120 MOHD.DANISH 08 07 15

66 13ECB-121 AMIR SUHAIL 06 5.5 12

67 13ECB-122 MOHD. SHUAIB 5.5 6.5 12

68 13ECB-123 CHADCHAI KHANTASAK 5.5 5.5 11

69 13ECB-124 SONGYOT KHANTASAK 08 07 15

70 13ECB-125 Mohd Akram Shamim 08 A 08

71 13ECB-126 SUDARWAN BOANG MANA 08 07 15

72 13ECB-127 MUHAMMAD ARIF RIDHO 08 07 15

Sessional Test Marks

B.A. (FINAL), 2013-14 Paper: EC- 317: Mathematical Economics

S.No. Roll No. Name of Candidates Marks Obtd

1 09ECB-105 AREEB SHAHID 12 2 10ECB-80 MD. SARFARAZ ALAM 14 3 10ECB-91 SHAN MOHD 14 4 10ECB-98 MOHD AFAQUE 14 5 11ECB-01 ISHFAQ ALI A 6 11ECB-04 GHULAM MOHD LONE 14 7 11ECB-09 SYED MOHD SHAHZEB 13 8 11ECB-13 HAIDER HUSSAIN ITOO 13 9 11ECB-17 HARES JAVED KHAN 13 10 11ECB-22 IRSHAD AHMAD MALIK 14 11 11ECB-23 MD SHOIB KHAN 14 12 11ECB-24 MUDASIR RAJAB 14 13 11ECB-28 ABDUL MALIK KHAN A 14 11 ECB-35 MUDASSIR IQBAL 14 15 11ECB-41 IMRAN ALI BAIG 14 16 11ECB-46 MUNEEM FAROOQ ITOO 13 17 11ECB-49 ZIAUL ISLAM ANSARI 11 18 11ECB-60 IMRAN 14 19 11ECB-71 ADNAN AZIZ 13 20 11ECB-78 MD YASIR ARFI 14 21 11ECB-82 SADAM HUSSAIN BHAT 13 22 11ECB-94 RAZIK MAHMOOD 14 23 11ECB-101 MOHD AARIF TAUHEED 15 24 11ECB-105 MD SHAMSHER ALAM 14 25 11ECB-114 NAZAR ALI 14 26 11ECB-117 SIRAJUL ISLAM YAZIDA 14 27 11ECB-118 MD JAVED 14 28 11ECB-119 SHAH HUSSAIN 14 29 11ECB-121 MOHD AARIF 14 30 11ECB-123 BILAL KHAN 14 31 11ECB-124 MOHD AZEEM KHAN 13 32 11ECB-125 TAHIR HUSSAIN ANSARI 14 33 11ECB-127 SHOAIB ANSARI 14 34 11ECB-128 SHAFKAT SHAFI DAR 14 35 11ECB-130 MUZAMMIL JAMEEL 14 36 11ECB-131 MOHD ABAD 13

First Sessional Test M.A. (III Semester), 2014-15 EC-9011: Mathematical Economics-I

Attempt all questions

Q1. From the Utility Function ),( 21 qqfU = subject to M = p1q1 + p2q2

Derive Slutsky equation and write it in the elasticity form.

Q2. Given the Utility Function 2/1

2

4/1

121 ),( qqqqfU ==

and budget constraint M = p1q1 + p2q2

i. Find the Marshallian demand functions for q1 and q2.

ii. Estimate the demand function for q1 and q2 when M=60, P1=2 and P2=4.

iii. Find the indirect utility function.

Q3.The Utility Function of a Consumer is

XZZYXXYU 252

594

2

1

2

52 222

++−+−−= & the Budget Constraint is 25= X+2Y+3Z.

Derive the first and second order conditions for the Consumer’s equilibrium assuming him to be a

rational consumer.

Q 4. Find the optimum commodity purchases for a consumer whose Utility function and Budget constraint are:

U = q16 q2

4 + 1.5 ln q1 + ln q2 and 3q1 + 4q2 = 100 respectively.

First Sessional Test, 2013-14 ECM—X011, Mathematical Economics-II

Attempt All Questions

Q1. Solve the following differential equations:

(i) Y”+2Y’-3Y=0

(ii) Y”+3Y’-10Y=0

(iii) Y”+14Y’+49Y=0 with the initial conditions Y (-4) = -1 and Y’ (-4) = 5

(iv) 16 Y”-40Y’+25Y=0 with the initial conditions Y (0) =3 and Y’ (0) = -9/4

Q.2The following is the input-output table for three industries X1, X2, X3. To

From

Users Total Output

X1 X2 X3 d

Produ X1 2 4 3 7 16

cers X2 5 7 5 7 24

X3 3 2 4 11 20

(a) Find the technology matrix A.

(b) If the final demand for the outputs of industries X1, X2, X3 becomes 10, 10, 10 respectively, find the new outputs

produced by the industries.

Q.3. For the following primal problem (i) formulate the dual and (ii) solve the dual graphically/simplex

method: Minimize P = 36Y1 + 30Y2+ 40Y3

Subject to

2Y1 + 5Y2 + 8Y3≥ 40

6Y1 + 3Y2 + 2Y3 ≥ 50

and Y1 ≥ 0, Y2≥ 0, Y3 ≥ 0.

Second Sessional Test M.A. (III Semester), 2014-15 EC-9011: Mathematical Economics-I Attempt all questions

Q 1. (a) When Q (L, K) = αα −1KAL with A>0 & 0<α <1, show that σ=1.

(b) When Q (L, K) = A ρρραα

1

])1([−

−−−+ KL show that MRTSL for K =

)1(

1

ρ

α

α+

− L

K

Q 2. Verify that CES production function: Q = f (L, K) = A ρρραα

1

])1([−

−−−+ LK displays constant returns

to scale, qualifies for the Euler’s Theorem and marginal products of factors are homogeneous of degree

zero.

Q 3. A producer desires to maximize his output of production: Q=30L+162K-L2+LK-K

2 subject to the given

cost function: 260=10L+4K. Find the optimum combination of factor inputs (L&k) and the maximum

output (Q).

Second Sessional Test, 2013-14 ECM—X011, Mathematical Economics-II Attempt All Questions

Q1: What is the difference between contractionary and expansionary fiscal policy? Which do you think is more

appropriate today? Explain how monetary and fiscal policy can be used to eliminate a deflationary gap. Q2: Explain how macroeconomic equilibrium is determined within the classical and Keynesian models of the

economy? Q3: Consider the following model of the economy?

C=200+0.25 (Y-T) ; I=150 + 0.25Y - 1000r ; G=250 ; T=200; (M/P)d

= 2Y - 8000r ; (M/P)s

=1600 (a) Derive the equations for the IS curve and LM curve.

(b) Find the equilibrium level of income Y* and interest rate r*.

(c) If Govt. expenditure increases from 250 to 400 find the impact of this on the equilibrium level of income and

interest rate.

(d) How large is the crowding out?

Q4: Consider the Following model of the economy:

C=200+0.75 (Y-T) ; I= 200 - 25r; G=100; T=100; (M/P)d

= Y - 100r; P=2; (M)

s =1000

(1) Find the equilibrium level of income Y* and interest rate r*.

(2) If Govt.-expenditure increases from 100 to 150. Find the impact of this on the equilibrium level of income

and interest rate.

(3) How large is the crowding out?

Q5: Consider the following model of the economy

C = 89+0.6Y; I = 120 – 150 r; Ms = 275; M

d = Mt + Mz; Mt = 0.1 Y; Mz = 240 – 250 r

(a) Find the equilibrium level of income Y* and interest rate r*.

(b) Find the levels of C, I, Mt and Mz, when the economy is in equilibrium.

First Sessional Test B.A.(Final), Economics2013-14 EC-317:Mathematical Economics

Attempt all questions:

Q1. Differentiate the following w.r.t. x,

c. - b

ax Y )(

2 3x

1 Y )(

x 1

x- 1 Y )(

6

+=

+=

+=

xcba

Q2. Evaluate the following integrals:

(a) dx x

4 x )(dx

x2x

12x )(dx x )(

5

1

2 4

3 3

∫∫∫

+

+

+cba

Q3: Solve the following differential equations:

(i) Y”+2Y’-3Y=0

(ii) Y”-4Y’+4Y=0

(iii) Y”+Y’-2y=0 with the initial conditions Y (0) = 2 and Y’ (0) = 0

(iv) Y”+14Y’+49Y=0 with the initial conditions Y (-4) = -1 and Y’ (-4) = 5

Third Sessional Test B.A. (Final), Economics (2013-14) EC-317: Mathematical Economics

Attempt all questions: Q1. What is Production function? Explain how a producer achieves an optimum or a least cost combination of factors

of production.

Q 2. By explaining the Cobb-Douglas and C.E.S. production function describe that C.E.S. function is comparatively

superior to the Cobb-Douglas production function.

Q 3. The production function of a firm is given by: Q = 12 – (L+K)/LK

The price of Labour, Capital and Output are given as Rs. 1, 4 and 9 respectively. Find the maximum profit

combination of Labour and Capital as well as Output.