Part -1:
Question 1. An economy comprises two consumers, 1 and 2, with two consumption goods bi-cycles (b) and wheat(ω). Both consumers have the same utility function it μ(b, ω) = bω. Bi-cycles and wheat are produced by two firms which use only labour according to the production functions.
b = √lb; and ω = 0.5√lω
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.
Question 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 p = 100 - Q, find the equilibrium industry output if the producers are Coumot competitors. What would be the resultant market price? What are the profits of each firm?
Section B
Answer all the questions from this section.
(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:
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Player 2
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Left
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Right
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Played
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Up
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(5,4)
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(1,3)
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Down
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(4,1)
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(2,2)
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3. Discuss the approaches adopted by Pigou and Pareto for analyzing the problem of welfare economics.
4. Write short notes on any two of the following:
(a) Envelope theorem
(b) Hidden information
(c) Actuarially Fair Premium
5. A consumer's utility function is given as
U(x,y) = In (x+2y-y2/2)
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 = I and price of y = P.
(d) Find the Hicksian demand function by (p,u) for commodity y, where the price of x is 1 and the price of y is p.
6. 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 2/3 of remaining in good health is 1/3. Let her utility function be given as U(y) = Y1/2 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:
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 Model
Part -3:
Section A
Answer all the questions from this section.
7. (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?
8. (a) If 2 is the sample mean, prove that the expected value of 2, E (2) equals the population mean (It).
(b) Describe the process of testing hypothesis about population proportion of a given attribute.
Section B
Answer all the questions from this section.
9. Suppose the technology matrix is A
Let the final demand sector be D = 
Find the level of production of the three goods.
10. From the following data, obtain the two regression equations Y on X and X on Y.
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X
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2
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4
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6
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8
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10
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Y
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5
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7
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9
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8
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11
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11. 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?
12. What is a Poisson distribution? Find the mean and variance of a Poisson distribution.
13. (a) Solve the following problem graphically:
Min C = 0.6x1 + x2
Sub to 10 x1 + 4 x2 ≥ 20
5x1+5x2 ≥ 20
2x1+6x2 ≥ 12
x1 , and x2 ≥ O.
(b) Why does the solution occur at a comer point only? Give reasons.