### Section - A

1. Answer all the following seven parts in about 100 words each.

Marks: 5 × 7 = 35

#### (a) Show that the ordinary demand curve will have a greater demand elasticity than the compensated demand curve.

(Comment for solution.)

#### (b) Discuss the Lerner Index of monopoly power.

(Comment for solution.)

#### (c) Illustrate graphically the effects of advertising on price and output in monopolistic competition.

(Comment for solution.)

#### (d) Distinguish between Partial Equilibrium and General Equilibrium Approaches.

(Comment for solution.)

#### (e) "The social optimal output occurs where Marginal Social Benefits (MSBs) equal Marginal Social Costs (MSCs)." Examine the statement.

(Comment for solution.)

#### (f) Solve the following 2 × 2 game :

(Comment for solution.)

#### (g) Show that

(Comment for solution.)

### Section - A

Answer any five out of the following seven questions :

Marks: 18 × 5 = 90

#### 2. Consider the 2-variable linear regression model : (a) Estimate the parameters Alfa and Bita by the OLS method. Also estimate the standard errors of these estimates. (b) Describe the testing procedure of Bita and estimate the 95% confidence interval of Bita.

(Comment for solution.)

#### 3. (a) Define Indirect Utility Function. Derive the Indirect Utility Function from the Direct Utility Function.

(Comment for solution.)

#### (b) Consider the Indirect utility Function : Where notations have their usual meanings. Derive the demand functions for x1 and x2

(Comment for solution.)

#### (c) Consider the utility function and budget equation of a consumer respectively : Where notations have their usual meanings. Derive the expenditure function of the consumer.

(Comment for solution.)

#### 4. (a) Show that a monopolist produces output in the elastic range of demand.

(Comment for solution.)

#### (b) The demand and the total cost function of a firm respectively are given by: where notations have their usual meanings. (i) Show that a monopolist produces output in the elastic range of demand. (ii) Calculate the efficiency loss of monopoly.

(Comment for solution.)

#### 5. (a) Consider the 3-variable linear regression model in deviation from : Would you estimate the parameters B2 and B3 ?

(Comment for solution.)

#### (b) Consider the following data : (i) Estimate the parameters alfa and Bita of the model : (ii) Estimate the standard errors of these estimates. (iii) How would test Bita?

(Comment for solution.)

#### 6. Consider an economy consisting of two consumers, one producer, one ordinary good, one public good and one primary factor. Show that Pareto optimality conditions are not valid for the public good.

(Comment for solution.)

#### 7. (a) Explain the concept of stability and and its different types.

(Comment for solution.)

#### (b) Explain the stability conditions in a single market both in the Walrasian process and Marshallian process.

(Comment for solution.)

#### 8. (a) Consider the production function: How would you restrict the values of alfa and Bita So that there occrs constant returns to scale and decreasing returns to scale ?

(Comment for solution.)

#### (b) Consider the production function and cost function of a ompetitive firm respectively : where notations have their usual meanings. Derive the supply function of the competitive firm.

(Comment for solution.)

### Section - A

Answer any three out of the following five questions :

Marks: 25 × 3 = 75

#### 9. (a) Consider the first-order autoregressive scheme in the generl regression model. How would you estimate the variance, covariance and autocorrelation coefficient of the disturbance term of the model ?

(Comment for solution.)

#### (b) Describe the Durbin-Watson (DW) test of autocorrelation.

(Comment for solution.)

#### (c) Given a sample of 50 observations and 4 explanatory variables, what can you say about autocorrelation if the computed Durbin-Watson (DW) values are :

(Comment for solution.)

#### 10. (a) Graphically explain the Lorenz curve as a measure of income inequalit.

(Comment for solution.)

#### (b) How would you derive the Gini coefficient from the Lorenz curve ?

(Comment for solution.)

#### (c) How would you derive the Gini coefficient from the Pareto law of income distribution ?

(Comment for solution.)

#### 11. (a) "It is not possible to construct social preferences from individual preferences without violating one or more of the five axioms." Examine the statement given by Arrow.

(Comment for solution.)

#### (b) Consider the economy with two goods and fixed factor supplies. Assume that the social welfare function defined in commodity space : and that society's implicit production function Find the values of x1 and x2 that maximize social welfare.

(Comment for solution.)

#### (c) Explain 'Compensation Principle' and 'Test Criteria' formulated by Hicks-Scitovsky.

(Comment for solution.)

#### 12. (a) What is the Leontief inverse matrix ? What are the mathematical properties of it ?

(Comment for solution.)

#### (b) State and prove graphically the Hawkins-Simon condition in case of 2 × 2 industries in the static open input-output model. Give an economic interpretation of it.

(Comment for solution.)

#### (c) Consider the Leontief input coefficient matrix : (i) Test the viability condition of the system. (ii) Test the properties of Leontief inverse.

(Comment for solution.)

#### 13. (a) Show that MC cuts ATC at its lowest point.

(Comment for solution.)

#### (b) The short-run cost function of a competitive firm is given by Where notations have their usual meanings. Derive the short-run supply function of the firm.

(Comment for solution.)

#### (c) Show that the elasticity of demand is the same at all point on the demand curve :

(Comment for solution.)

#### (d) Consider the demand function of two goods, x1 and x2 respectively : where P1 and P2 are prices of x1 and x2 respectively. Determine whether the commodities are complementary or competitive.

(Comment for solution.)