Find all the nash equilibrium of the game

Assignment Help Microeconomics

Reference no: EM13697469

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 = √l_b; and ω = 0.5√l_ω

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.

(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:

	Player 2
		Left	Right
Played
	Up	(5,4)	(1,3)
	Down	(4,1)	(2,2)

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.

(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

1135_Find the level of production.png

Let the final demand sector be D = 2475_Find the level of production1.png

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.

X	2	4	6	8	10
Y	5	7	9	8	11

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?

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.

Reference no: EM13697469

Questions Cloud

Investment in debt securities at premium : Investment in debt securities at premium. On April 1, 2014, West Company purchased $400,000 of 6% bonds for $415,750 plus accrued interest as an available-for-sale security. Interest is paid on July 1 and January 1 and the bonds mature on July 1..

What amount should hertz report as deferred income tax : Hertz Co. prepared the following reconciliation of its pretax financial statement income to taxable income for the year ended December 31, 2013, its first year of operations

Recession without increasing countrys foreign indebtedness : What policy options does a government have at its disposal to fight a recession without increasing the country’s foreign indebtedness?

No gift tax was paid with respect to the transfer : Henry receives his 20% partnership interest as a gift from a friend. The friend's basis (without considering partnership liabilities) is $34,000. The FMV of the interest at the time of the gift is $36,000. The partnership has liabilities of $10..

Find all the nash equilibrium of the game : Find the production possibility frontier for this economy and find the competitive equilibrium - Find competitive equilibrium if every consumer owns 100 units of labour and owns one firm.

Omni care is considering improving the accounting system : For the past few years, your client, Omni Care, has operated a small medical practice. Omni Care's current annual revenues are $945,000. Because the accountant has been spending more and more time each month recording all transactions in a two-..

What is decision rule for this optimal firm-level employment : Let us assume that Machineries are the only type of capital that is used in the production function of a competitive firm. We also assume that the price for the products that are sold by this competitive firm is set at $5. Given the production functi..

How does economics tie into business ethics : How does economics tie into business ethics? Explain your answer and provide examples. How does the global marketplace affect business ethics? Support your ideas with outside research. Review the concepts from the "Important Terms for Review," locate..

Actual activity for the period was higher than anticipated : Bunnie's Bakery anticipated making 17,000 fancy cakes during a recent period, requiring 14,000 hours of process time. Each hour of process time was expected to cost the firm $11. Actual activity for the period was higher than anticipated: 18,00..

User Account

All Pages