Part 1:
1. An economy comprises two consumers, 1 and 2, with two consumption goods bi-cycles (b) and wheat. Both consumers have the same utility function μ , ω . Bi-cycles and wheat are produced by two firms which use only labour according to the production functions. b =!l" and ω 0.5!l% Both firms are owned by consumer 1, and consumer 2 owns 200 units of labour.
(a) Find the production possibility frontier for this economy.
(b) Find the competitive equilibrium.
(c) Find competitive equilibrium if every consumer owns 100 units of labour and owns one firm.
(d) Find the Pareto efficient allocations for this economy.
2. Assume that there are four firms supplying a homogenous product. They have identical cost functions given by C (Q) = 40 Q. If the demand curve for the industry is given by µ = 100 - Q, find the equilibrium industry output if the producers are Cournot competitors. What would be the resultant market price? What are the profits of each firm?
3.
(a) Distinguish between pure strategy Nash equilibrium and mixed strategy equilibrium. When would you use mixed strategy equilibrium?
(b) Find all the Nash equilibrium of the following game: Player1 Player 2 Left Right Up (5,4) (1,3) Down (4,1) (2,2) 4
4. Discuss the approaches adopted by Pigou and Pareto for analyzing the problem of welfare economics.
5. Write short notes on any two of the following:
(a) Envelope theorem
(b) Hidden information
(c) Actuarially Fair Premium
6. A consumer's utility function is given as U(x,y) = In (x+2y- * + , ) Where x and y are two goods of consumption.
(a) Find the indirect utility function of the consumer.
(b) Examine if Roy's law is satisfied by the consumer's demand function for y.
(c) Find the expenditure function of the consumer e(p,u) where price of x = 1 and price of y = p.
(d) Find the Hicksian demand function hy (p,u) for commodity y, where the price of x is 1 and the price of y is p.
7. Sita expects her future earnings to be worth Rs. 100. If she falls ill, her expected future earning will be Rs. 25. There is a belief that she may fall ill with probability of , - while the probability of remaining in good health is . - . Let her utility function be given as U(y) = / 0 +. suppose that an insurance company offers to fully insure Sita against loss of earnings caused by illness against an actuarially fair premium.
(a) Will Sita accept the insurance? Explain.
(b) What is the maximum amount that Sita would pay for the insurance?
Part 2:
In the case of numerical questions word limits do not apply.
Section A
1. Derive the conditions for steady state in the Solow model. What are its implications? In what respects is the golden rule different from the steady state?
2. Explain how IS and LM curves are derived. What are the implications of IS and LM curves? What are the factors on which the shape of the IS and LM curves depend?
Section B
3. What does the Phillips curve signify? How do you reconcile the difference in the shape of the curve in the short run and the long run?
4. Lucas' point of view, what are the limitations of the Keynesian model? What improvements does he suggest?
5. What is meant by endogenous growth? Explain the main features of endogenous growth models.
6. An economy with fixed exchange rate cannot maintain an independent monetary policy. Do you agree with the above statement? Substantiate your answer with appropriate diagrams.
7. Write short notes on the following.
a) Rational Expectations
b) Search and Matching
Part 3:
1. (a) Write a linear first - order differential equation and work out its general solution.
(b) How will you solve the Harrod-Domar formulation of steady growth through differential equations?
2. (a) If 1¯ is the sample mean, prove that the expected value of 1¯, E 1¯ equals the population mean (μ).
(b) Describe the process of testing hypothesis about population proportion of a given attribute.
Section B
3. Suppose the technology matrix is A 50.2 0.3 0.2 0.4 0.1 0.2 0.1 0.3 0.2 9
Let the final demand sector be D = 5 10 5 6 9 Find the level of production of the three goods.
4. From the following data, obtain the two regression equations Y on X and X on Y. X 2 4 6 8 10 Y 5 7 9 8 11
5. A monopolist's demand curve is given by P = 100 - 2q.
(a) Find his marginal revenue function.
(b) At what price is marginal revenue zero?
(c) What is the relationship between the slopes of the average and marginal revenue curves?
6. What is a Poisson distribution? Find the mean and variance of a Poisson distribution.
7. (a) Solve the following problem graphically: Min C = 0.6x1 + x2 Sub to 10 x1 + 4 x2 ≥ 20 5 x1 + 5 x2 ≥ 20 2 x1 + 6 x2 ≥ 12 x1 , and x2 ≥ 0.
(b) Why does the solution occur at a corner point only? Give reasons.
Part 4:
SECTION A
1) Examine the effect of population growth in the Solow model of economic growth. Discuss how the Solow model could be used to explain poverty traps in developing nations.
2) Describe the Mankiw-Romer-Weil extension to the neoclassical model to include human capital. Explain why diminishing returns to capital do not take place in the AK model.
SECTION B
3) Distinguish between economic growth and development. Briefly mention the main benefits that economic growth confers upon society.
4) Describe Pasinetti's theory of economic growth and distribution.
5) Describe the various approaches to the measurement of total factor productivity.
6) What are the main propositions of the Real Business Cycle model? Describe the basic structure of a prototype Real Business Cycle model.
7) Compare and contrast the Uzawa two-sector growth model with the Feldman model.
Part 5:
Section-A
1. Distinguish between "economic growth" and "economic development". How is economic development a better measure of economic welfare?
2. What are the constituents of financial system? Critically evaluate the impact of reforms introduced in the equity and foreign exchange market. OR Give an account of major changes that have taken place in Indian economy over the last six decades. What are the implications of expansion in the services sector for employment and poverty?
Section-B
3. "More people mean more resources". Comment on the above statement.
4. Explain the important issues which are crucial for promotion of Indian exports and hence need to be addressed in India's trade policy.
5. Explain the role of agricultural policy in raising public investment in agriculture.
6. Which changes would you like to make in trade and industrial policies to ensure rapid growth of GDP while maintaining adequate macro-economic balance?
7. Do you think that existing institutional structure in India has not led to good governance? Give reasons in support of your answer.