DEPARTMENT OF ECONOMICS



DEPARTMENT OF ECONOMICS

BAHAUDDIN ZAKARIYA UNIVERSITY, MULTAN

M.A ECONOMICS PART FIRST

Paper I: MICROECONOMIC THEORY

COURSE INSTRUCTOR: Muhammad Ramzan Sheikh

Part A

Topic: 1

Some Fundamentals of Micro Economics

Microeconomics: Comparison with other branches of economics. The uses and limitations of Microeconomic theories. The problem of Scarcity. The Concept of opportunity cost. Markets, Firms and Individuals. Demand and Supply: A Review. Relative and absolute Prices. Real and Nominal Prices. Cobweb Theorem. Slope and Elasticity of Demand. Short Run and Long Run Elasticity. Different Kinds of elasticities of demand. Price Controls. Consumer and Producer’s surpluses. Network Externalities.

Topic: 2

Theory of Consumer Choice

Cardinal measurement of utility: Consumer’s equilibrium one commodity and general case. Derivation of demand curve. Income and Substitution effects under Cardinal Approach. Diamond Water Paradox. Drawbacks of Cardinal Approach

Ordinal measurement of utility: Properties of preferences. The notion and examples of homothetic preferences and non-homothetic preferences. Axioms of consumer choice and their implications for preference ordering. Properties of indifference curves maps. The problem of bundles ranking and properties of consumption bundles. Types of utility functions.

Consumer’s choice: Interior and corner solution optimum of a consumer. Algebraic solution for the optimum of a consumer. Solution for the optimum in the case of perfect complements. Boundary optimum of a consumer.: choice with perfect substitutes, neutrals, mutually exclusive goods, “good /bad” cases.

Price Income and Substitution effects Under Hicksian and Slutsky Framework. Slutsky identity and Slutsky equation. Derivation of Slutsky equation and its economic interpretation. Indirect Utility Function and its derivation and properties. Application of Indifference curve analysis. Revealed Preference theory.

Topic: 3

Analysis of Demand

Determinants and properties of an individual demand function. Homogeneity of degree zero in prices and income. Deriving “income-consumption” and Engel curves. Engel expenditure curves. The difference between normal and inferior goods, .necessity and luxury goods in respect of marginal propensity to consume and income elasticity values. “Income-consumption” and Engel curves for homothetic preferences cases. Quasilinear preferences case. Deriving “price-consumption” and individual demand curves. The difference between ordinary and non-ordinary goods. The notion of a Giffen good. Gross substitutes and complements. The two notions of real income: in terms of Hicks and in terms of Slutsky. Substitution effect under Hicks and under Slutsky. Explanation of the sign of a substitution effect. Diagrams explaining price effect signs and derivations of individual demand curves for: a normal good, an inferior and ordinary good, a Giffen good.

Topic: 4

Theory of Production

The Concept of Production Function; Production with one variable and two variable inputs, Laws of Returns and Returns to scale. The substitution and Resource effects of change in input prices. Euler’s Theorem. The elasticity of substitution. Some special production functions: Cobb Douglas Production function. CES Production Function. Translog Production function. Homogenous Production Function.

Topic: 5

Cost of Production and Revenue

Definition and kinds of costs. Cost Functions. Traditional, Modern and Engineering costs theories. Economies of Scale and Scope. Learning Curve. Cost Minimization (A Mathematical Treatment). Revenue Analysis (Total, Marginal and Average Revenue)

Part B

Topic: 6

The Theory of Market Behaviour

6.1

Pure and Perfect competition: equilibrium of firm in Short run. The supply curve of the firm and the industry. Short run equilibrium of industry. equilibrium of firm and industry in Long run. Optimum Resource allocation. Dynamic changes and Industry Equilibrium: Shift in the Market demand, Predictions of the perfect competition model when costs change, Effects of Imposition of a Tax. Mathematically Price and Quantity Solution.

Evaluating the gains and loses from Govt polices--consumer and Producer surplus. The efficiency of a competitive market. Minimum Prices. Price Supports and Production Quotas. Import Quotas and Tariffs. The impact of Tax or subsidy. Mathematical Derivation of Price and Output Decision.

6.2

Monopoly its basis. The negatively sloping demand curve: Short run and Long Run equilibrium, Predictions in dynamic changes: Shift in the Market demand, An increase in the costs of monopolist. Imposition of a Tax. Comparison with perfect competition: Govt regulated Monopoly. Monopoly Power its sources and social cost. Monopsony and Monoply compared. Monopsony Power its sources and social cost. Bilateral Monopoly. Multi-plant Monopolist Firm, Mathematical Derivation of Price and Output Decision.

6.3

Monopolistic competitive conditions: The historical setting of the theory of monopolistic competition, Characteristics of Monopolistically competitive firms. The concepts of industry & group: The basic Chamberlin theory of Monopolistic competition:(Model No 1: Equilibrium with new firms entering the industry, Model No 2: Equilibrium with Price competition, Model No 3: Equilibrium with Price competition and free entry). Critique of Chamberlin Model. Comparison with pure competition. Mathematical Derivation of Price and Output Decision.

6.4

Oligopolistic conditions: A simple statement of the problem of oligopoly: Non-collusive Oligopoly: Models of Cournot, Bertrand, Chamberlain, Sweezy & Stackelberg Collusive Oligopoly: Model of cartels and Price Leadership. Mathematical Derivation of Price and Quantity Determination.

Topic: 7

Pricing With Market Power

Capturing Consumer Surplus. Price Discrimination (First, Second and Third degrees) Intertemporal Price Discrimination and Peak Load Pricing. The two part tariff. Advertising. A rule of thumb for advertising. Transfer pricing when there is no outside market, when there is competitive outside market, when there is noncompetitive outside market. (A numerical example).

Topic: 8

Pricing of Factors of Production and Income Distribution

Factor Pricing in perfectly competitive and imperfectly competitive Markets. Elasticity of Factor substitution, Technological progress and Income Distribution. The Price of fixed Factors: Rents & Quasi-rents. Non homogenous factors and Wage differentials. The adding up problem and product exhaustion theorems.

Topic: 9

General Equilibrium and Economic Efficiency

Partial and general Equilibrium Analysis. Two interdependent markets -moving to general equilibrium (an example). Efficiency in exchange. Equity and Efficiency. Efficiency in Production.

Topic: 10

Welfare Economics

Criteria of social welfare: Growth of GNP as a welfare criterion, Bentham’s criterion, A cardinalist criterion. The Pareto optimality criterion. The Kaldor-Hicks Compensation criterion. The Bergson criterion ‘social welfare function’. Maximization of social welfare. Determination of the welfare maximizing output mix, Commodity distribution and Resource Allocation. Welfare Maximization and Perfect Competition.

Recommended Books:

1. Bilas, Richard A, Microeconomic Theory*. McGraw-Hill Kogakusha,Ltd, (2nd Edition).

2. Koutsoyiannis, A., Modern Microeconomics*, London, Macmillan, (Latest Edition.

3. Pindyck, Robert. S, Daniel L. Rubinfeld and Prem L.Mehta, Microeconomics*. Pearson Education Inc, (Sixth Edition).

4. Henderson, J.M & Quandt, R.E., Microeconomic Theory*. N.Y Macmillan II A Book Co.

5. Varian Hal R., Micro Economics Analysis*, Norton & Company, New York, 1992.

6. Ferguson, C.E & Gould, J.P, Microeconomic Theory. Macmillan, (Latest Edition).

7. Layard and Walter A.A., Micro Economics, McGraw Hills, (Latest Edition).

8. Walter Nicholson, Microeconomic Theory: Basic Principles and Extensions (6th edition)

Additional Readings:

1. Baumol, W)., Economic Theory and Operations Analysis, Prentice Hall (Last Edition).

2. Hirshleifer Jack, Price Theory and Applications*, Prentice Hall (Latest Edition).

3. Kameischon: D.T. R., Readings in Microeconomics, Nevi York, The world publishing co (last Edition).

4. Stiglor, GT., The Theory of price, N.Y Macmillan, London. (Last Edition).

5. Silberberg E., The Structure of Economics, A Mathematical Analysis, McGraw Hill, (Latest edition).

6. Dwivedi, D.N. Microeconomics theory and applications. Pearson Education Inc, (Second Edition).

7. Salvatore, Dominick, Micro Economic Theory*, McGraw Hills, (Latest Edition).

(*Strongly Recommended).

NOTE: Assignment No. 1 will be formulated from Part A and Assignment No. 2 will be based on Part B.

BAHAUDDIN ZAKARIYA UNIVERSITY, MULTAN

DEPARTMENT OF ECONOMICS

Note: Attempt all questions. Answers should be brief and relevant.

MICRO ECONOMIC THEORY: ASSIGNMENT NO: 1

Q1: What is price consumption curve (PCC)? Can you prepare a demand schedule on this basis of data provided by the PCC? Illustrate the derivation of demand curve for a normal good and a Giffen good.

Q2: How will you distinguish between production with one variable input and production with two variable inputs? Does the difference between the two techniques of production make any difference in the laws of production?

Q3: A consumer’s preferences are given in the form of following direct utility function:

Drive the Indirect Utility function and prove Roy’s Identity. Compare the results.

Q4: What is meant by the ‘envelope curve? Show graphically the derivation of the long run average cost curve (LAC). How can you find the minimum LAC?

Q5: How are the revenue and cost curves under monopoly different from those under perfect competition? How are AR and MR curves related to one another?

BAHAUDDIN ZAKARIYA UNIVERSITY, MULTAN

DEPARTMENT OF ECONOMICS

Note: Attempt all questions. Answers should be brief and relevant.

MICRO ECONOMIC THEORY: ASSIGNMENT NO: 2

Q1: Show graphically long run supply a curve of an industry is drawn under perfect competition? Also illustrate graphically the derivation of the long run supply curve of a firm under perfect competition.

Q2: Why does price leadership sometimes evolve in oligopolistic markets? Explain how the price leader determines a profit maximization price.

Q3: Monopolistic competition is the middle ground between perfect competition and monopoly. Explain this statement.

Q4: What is MRP? What roles does it play in the derivation of demand curve for a factor or production?

Q5: What is marginal rates of transformation (MRT)? Explain why the MRT of one good for another is equal to the ratio of the marginal costs of producing the two goods.

Paper II: MACROECONOMIC THEORY

COURSE INSTRUCTOR: Muhammad Zahir Faridi

Part A

Topic: 1

Introduction to Macro Economics and National Income

The development of Macro Economics. Introduction, main objectives, scope and subject matter of Macroeconomics. Circular flow of national income, national income aggregates, measurement of GNP, expenditure approach, income approach, product approach, GNP as a measure of welfare. Outlays and components of demand, some important identities, rules for computing GDP, real GDP VS nominal GDP, actual GDP VS potential GDP, prices indices. GDP deflator, CPI, PPI, Measuring job less-ness. The unemployment rate, unemployment, GDP, and Okun’s Law. Inflation and Inflation rate, GDP growth rate.

Topic: 2

Classical Theory of Output and Employment

a) The classical revolution, production function and employment, demand for and supply of labor, labor market equilibrium, the determinants of output and employment, derivation of classical aggregate supply curve.

b) What is money? Functions of money and types of money, how quantity of money is measured? The quantity theory of money, the money demand function and the quantity equation, relationship between money, prices and inflation, Seigniorage, real vs nominal interest rates, the fisher effect. The classical aggregate demand curve. The classical theory of the interest rate. Say’s Law of markets, pricing implications of the classical equilibrium model.

Topic: 3

Keynesian Theory of Income and Output Determination

a) Simple Keynesian model, conditions for equilibrium output. The components of aggregate demand. Consumption function, saving function (relationship between APC, MPC, APS, MPS, investment function) Govt. expenditure and net exports, aggregate demand equals aggregate output. Theory of multiplier, derivation of simple multiplier, Govt. expenditure and tax multiplier, export and import multiplier, super multiplier, employment multiplier, balanced budget multiplier. Budget surplus and full employment.

b) Money in the Keynesian system. Interest rate and aggregate demand, Keynesian theory of interest rate, Keynesian theory of demand for money. Regressive expectation model, portfolio balance approach.

Topic: 4

Theory of Consumption and Their Implications

Theories of Consumption: Duesenbury Hypothesis, Keynesian Consumption Function. Permanent Income Hypothesis / Life Cycle Hypothesis, Beyond Permanent Income Hypothesis, Kuznet's findings and Reconciliation of Marginal Propensity to Consume and Average Propensity to Consume and Evidences. Mathematical derivation of Consumption Models. The MPS Model, Wealth effect in the Static Model. Implications of Consumption Theories for Policy Formulation and Stabilization Policy. Random Walk Model.

Topic: 5

Theory of Investment

Investment VS capital, kinds of investment, determinants of investment MEC VS MEI Present value criterion for investment, Internal Rate of Return Criterion, Neo classical model of fixed business investment. Taxes and investment, Tobin’s q theory, Residential investment model, Acceleration Principle, Rigid and Flexible Accelerator, Inventory Investment Model.

Part B

Topic: 6

IS – LM frame work

IS curve, it derivation, shape of IS curve, factors affecting the slope and position of IS curve (Mathematical version) LM curve, its derivation, factors affecting the slope and position of LM curve. Policy effects in the IS-LM model. Monetary and fiscal policy multipliers in the IS-LM curve model.

Topic: 7

Aggregate Demand and Aggregate Supply Analysis

Keynesian aggregate demand curve, its derivation, factors determining its slope and position. The aggregate demand schedule combined with the classical theory of aggregate supply. The Keynesian contractual view of labor market – a flexible price – fixed money wage model, comparison of classical and Keynesian theories of labor supply. The Keynesian aggregate supply curve with variable money wage. Policy effects in the variable–wage Keynesian model. The effects of shifts in the aggregate supply schedule, factors that shift the aggregate supply schedule. Aggregate supply models. The sticky wage model, the imperfect information model, the sticky – price model, The Worker Misperception Model.

Topic: 8

Inflation

The concept of inflation, Demand pull and Cost push inflation, hyperinflation, social cost of inflation, theory of stagflation, The Relation of Wages Changes to Unemployment. The Philips curve – the theoretical basis for the Philips curve. Unemployment and price expectations. The long-run Philips curve. Deriving the Philips curve from the aggregate supply curve. Adaptive expectations and inflation inertia, The Natural Rate Theory, Monetarist View of the Philips Curve, Keynesian view of the Philips curve.

Topic: 9

Government Debt and Budget Deficits

The size of Government Debt, Measurement Problem: Inflation, Capital Assets, Business Cycle etc, Ricardian view or Debt: Ricardian Equivalence, Consumers and Future Taxes. Tax shooting, Delayed Stabilization, Ricardo and Ricardian Equivalence and Debate. Model or Debt Crises.

Topic: 10

Economic Fluctuations, Long-Term Growth and Full Employment

a) The theory of real business cycles, interpretation, labor market, technology shocks, household behavior, the persistence of output fluctuation, limitations of the models Samualson’s multiplier – accelerator interaction theory of trade cycles, Kaldor’s model of the business cycle. Hicks’s theory of business cycle, AD-AS theories of output functions.

b) Basic neoclassical growth model/Solow growth model – the accumulation of capital, determination of steady state equilibrium in the long-run, how savings affects growth, the golden rule level of capital, how population affects the steady state level, technological progress in the Solow model, policies to promote growth endogenous growth theory.

Recommended Books:

1. Branson, William H., (1979), Macroeconomic Theory and Policy, Harper and Row Publishers, New York / London.

2. Branson, William H., and Litvack James M., Macroeconomics*, (Latest Edition),' Princeton University.

3. Glahe, Fred R., (Latest Edition), Macroeconomics, Theory and Policy, Harcourt Brace Jovanovich Inc.

4. Mankiw, Gregory N., (2000) Macroeconomics*, Worth Publishers, New York.

5. Peel D. and Minfow P., (2002). Advance Macroeconomics, Edward Elgar, Cheltenham, U.K.

6. Romer, David, (200I). Advanced Macroeconomics*, McGraw Hills, New York, London.

7. Sargent, Thomas J., (19XX) Rational Expectations and Inflation*, Harper and Raw Publishers, New York / London.

* Strongly Recommended

Additional Reading Material / Research Papers:

1. Ball, Laurence, Mankiw, N. Gregory, and Romer, David 1988. “The New Keynesian Economics and the Output – Inflation Trade off”. Brookings Papers on Economic Activity. No. 1, 1 -6, Reprinted in Mankiw and Romer (1991)

2. Barro, Robert J 1976. “Rational Expectations and the Role of Monetary Policy”. Journal of Monetary Economics 2 (January): 1 – 32

3. Barro, Robert J. 1989. “Interest – Rate Targeting” Journal of Monetary Economics 23 (January): 3-30

4. Rosalind Leveic arid Alexander Reborens, Macro-economics: An Introduction to Keynesian Neo-Classical Controversies; Macmillan (Latest edition),

5. Barro, Robert, J " and Gordon, David B, 1983b. '"Rules, Discretion and Reputation in a Model of Monetary Policy," Journal of Monetary' Economics 12 (July): 101-121. Reprinted in Persson and Tabellini (1994).

6. Bernheim, B. Douglas. 1987, "Ricardian Equivalence: An Evaluation of Theory and Evidence." NBER Macroeconomics Annual 2: 263 – 304

7. Blanchard, Olivier J. 1984. "The Lucas Critique and the Volcker Deflation." American Economic Review' 74 (May): 211-215.

8. Denison, Edward F. 1985. Trends in American Economic Growth. /lJ2lJ-1IJ82. Washing/oil: The Brookings Institution. .

9. Fischer, Stanley. 1993. "The Role of Macroeconomic Factors in Growth." Journal Of Monetary Economics 32 (December): 485-512.

10. Friedman, Milton, 1968. 'The 13--ole of Monetary Policy". American Economic Review 58 (March): 1-17.

11. Genberg, Hans 1978. "Purchasing Power Parity under Fixed and Flexible Exchange Rates."- - (Journal of international Economics 8 (May): 247-276.

12. Long, John B., and Plosser, Charles I. 1983. "Real Business Cycles." Journal of Political Economy 91 (February): 39-69.

13. Mankiv, G., N. (1990), A quick Refresher Course in Macroeconomics, Journal of Economic Literature , Vol. XXVIII, 1645-60. .

14. Romer, Christina D. 1999. "Changes in Business Cycles: Journal of Economic Perspectives 13 (spring): 23-44.

15. Romer, Paul M. I.990, "Endogenous Technological Change." 1998 (October, Part 2): S71-S 102.

NOTE: Assignment No. 1 will be formulated from Part A and Assignment No. 2 will be based on Part B.

BAHAUDDIN ZAKARIYA UNIVERSITY, MULTAN

DEPARTMENT OF ECONOMICS

Note: Attempt all questions. Answers should be brief and relevant.

MACRO ECONOMICS: ASSIGNMENT NO: 1

Q1. Define the terms personal income and personal disposable income. Conceptually, how do these income measures differ from national income? Of what usefulness are these measures?

Q2. Three price indices were considered in this chapter: the GDP deflator, the consumer price index, and the producer price index. Explain the differences among these different measures of the price level.

Q3. What are the major policy conclusions of classical economics? Explain how these policy conclusions follow from the key assumptions of the classical theoretical system.

Q4. Suppose that for a particular economy and period, investment was equal to 100, government expenditure was equal to 75, net taxes were fixed at 100, and consumption (c) was given by the consumption function.

C = 25 + 0.8 YD

Where YD is disposable income and Y is GDP.

a. What is the level of equilibrium income (Y)?

b. What is the value of the government expenditure multiplier ([pic])? Of the tax multiplier ([pic])?

Q5. Explain the permanent income hypothesis of consumer behavior. Compare the permanent income hypothesis with the life cycle hypothesis of consumption.

BAHAUDDIN ZAKARIYA UNIVERSITY, MULTAN

DEPARTMENT OF ECONOMICS

Note: Attempt all questions. Answers should be brief and relevant.

MACRO ECONOMICS: ASSIGNMENT NO: 2

Q1. Explain the Keynesian theory of interest-rate determination. What differences do you see between this theory and the classical theory of the interest rate?

Q2. Explain the relationship between the effectiveness of monetary policy and the interest elasticity of money demand. Will monetary policy be more or less effective the higher the interest elasticity of money demand? Explain. Now explain the relationship between fiscal policy and the interest elasticity of money demand. Why do the two relationships differ?

Q3. Within the variable price – variable wage version of the Keynesian model, analyze the effects that an unfavorable supply shock, such as a rise in the price of oil, would have on the rate of interest. Would the equilibrium rate of interest rise or fall?

Q4. Explain the concept of the Phillips curve. Is there any difference between monetarist and Keynesian views of the Phillips curve?

Q5. Explain why, in a model with endogenous technological change, a rise in the saving rate may lead to a permanent rise in the long run growth rate in output.

Paper 3: MATHEMATICAL ECONOMICS

PART A

Topic: 1

The Nature of Mathematical Economics

Ingredients of mathematical models. Derivations: Equation of a straight line and its forms: Two points, intercept, point slope and slope intercept. Types of functions: constant, polynomial, rational, non-algebraic. Relationships and functions. Indices & their rules. Functions of more than two independent variables. Logarithms & the rules of logarithms.

Topic: 2

Equilibrium Analysis in Economics

A linear partial equilibrium market model. The effect of an excise tax in a competitive market. Non linear market model General Market Equilibrium. Equilibrium in a linear. National Income Model

Topic: 3

Linear Models and Matrix Algebra

Theory of matrix multiplication. Laws of matrix operations. Types of matrices: Square, identity, null, idempotent, diagonal, transpose and their properties. Conditions for non singularity of a matrix. Minors and cofactors. Determinant & its properties. Solution of linear equations through Gaussian method, Cramer's rule and Inverse of a matrix method. Properties of inverse of a matrix. Use of matrix approach in market & national income models.

Topic: 4

Input–Output Analysis

Input-output model, its structure and its derivation. The use of input output model in Economics.

Topic: 5

Differentiation

Rules of differentiation. Differentiation of a function .of one variable. Sum, difference, product, quotient, chain, power, inverse, logarithmic & exponential. Functions, Combinations of rules. Higher order derivatives. Economic applications of derivative. Concept of maxima & minima, elasticity and point of inflection. Profit & Revenue maximization under perfect competition, under monopoly. Maximizing. excise tax revenue in monopolistic competitive market, Minimization of cost etc.

PART B

| |

Topic: 6

Partial & Total Differentiation

Partial differentiation & its rules. Higher order & cross partial derivatives (Young's theorem). Total differential & total derivatives. Implicit functions rule of differentiation. Optimizing cubic functions & their economic application.

Topic: 7

Economic Applications of Partial & Total Differentiation

Comparative static analysis: a linear Partial equilibrium market model, a linear National Income model. Partial Elasticities. Production functions Analysis. Maximization & Minimization of unconstrained functions & their economic. applications: Profit maximization by a multi-product firm under perfect Competition & monopoly, Price discrimination, Multi-plant monopoly, .input decisions etc.

Topic: 8

Optimization: Constrained & Extrema

Free and constrained optimization, extrema of a function of two variables: graphical analysis, Lagrange method. Utility maximization & Cost minimization. Homogenous Production function, Cobb Douglas Production function. Jaccobian determinants. CES Production Function. Translog Function.

Topic: 9

Linear Programming

Ingredients of linear Programming. Graphical approach, simplex method, economic application of linear programming. Concept of primal & dual. Duality theorems. Solving of Primal via dual. Economic interpretation of a dual.

Recommended books:

1. Chiang, A.C., Fundamental Methods of Mathematical Economics, McGraw Hills, (Latest Edition).

2. Baumol W. L., Economic Dynamics, Macmillan, (Latest edition).

3. Budnick, Frank, Applied Mathematics for Business, Economics and Social Sciences.

4. Dowling E. T., Mathematics for economists, Schum Series (latest edition).

5. Weber E. Jean, Mathematical Analysis, Business and Economic Applications (Latest Edition) I-Harper and Row Publishers, New York.

NOTE: Assignment No. 1 will be formulated from Part A and Assignment No. 2 will be based on Part B.

DEPARTMENT OF ECONOMICS

BAHAUDDIN ZAKARIYA UNIVERSITY, MULTAN

ASSIGNMENT NO.1

M.A. ECONOMICS, PART-I, MATHEMATICAL ECONOMICS, PAPER - 4, INSTRUCTOR: DR. IMRAN SHARIF CHAUDHRY

Q1:(a) Explain the different types of function and give examples from economics.

(b) If A = {2, 3, 4, 5}, B = {3, 5, 7}, C = {1, 2, 3, 4, 5, 6} verify the distributive laws.

Marks:10+10

Q2:(a) Differentiate between partial and general market equilibrium. Also construct the two-commodity model to find out equilibrium level of prices.

(b) If the national income model is as:

Y = C + I° + G°

C = a + b (Y – T)

T = d + ty

(i) List out parametric, their sign and economic meaning

(ii) Identify the exogenous variables

(iii) Find the equilibrium level of national income Marks:10+10

Q3:(a) Write out the advantages and disadvantages of matrix algebra

b) State and prove the properties of transpose of a matrix

c) If A = I – X (XX)-1X, then verify that A is an idempotent matrix Marks:10+10

Q4:(a) State and prove the first prove properties of determinant by using the following matrix

2 3 1

A = 0 5 6

3 1 1

b) If input matrix and final demand vector

0.2 0.3 0.2 10

A = 0.4 0.1 0.2 d = 5

0.1 0.3 0.2 6

i) Explain the economic meanings of 0.4 and 6

ii) Explain the economic meanings of third column sum

iii) Find the solution output levels of three industries Marks:10+10

Q5: Write short note of the following:- Marks:04+04+04+04+04

i) Input – output model

ii) Rank of a matrix

iii) Derivation of quadratic formula

iv) Theorems of polynomial equation

v) Mathematical and non-mathematical economics

DEPARTMENT OF ECONOMICS

BAHAUDDIN ZAKARIYA UNIVERSITY, MULTAN

ASSIGNMENT NO.2

M.A. ECONOMICS, PART-I, MATHEMATICAL ECONOMICS, PAPER - 4, INSTRUCTOR: DR. IMRAN SHARIF CHAUDHRY

Q1:(a) Analyze the comparative static with its limitation and compare with static analysis.

(b) State the limit theorems involving a single and two functions. Why is this concept of limit important in Economics? Marks:10+10

Q2:(a) Write out different rules of differentiation with numerical examples.

(b) Explain the economic uses of derivative with examples.

(c) The total money supply has two components: bank deposits D and Cash holding C, which we assume to bear a constant ratio C/D = c, 0 ................
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