Exam Details
| Subject | Quantitative Methods | |
| Paper | ||
| Exam / Course | Master of Arts in Economics | |
| Department | School of Social Sciences (SOSS) | |
| Organization | indira gandhi national open university | |
| Position | ||
| Exam Date | December, 2015 | |
| City, State | new delhi, |
Question Paper
Answer any two questions from this section.
Discuss the Hawkins-Simon condition in the context of input-output analysis.
From the following technology matrix find equilibrium prices if the wage rate is Rs100 per day:
Steel Coal Final Demand
Steel 0·4 0·1 50
Coal 0·7 0·6 100
Labour 5 2
Given demand and supply for cobweb model as Qdt =18 -Pt and Qst 3 4 Pt Find the intertemporal equilibrium price and determine whether the equilibrium is stable.
Establish the stability condition of Samuelson's multiplier-accelerator interaction model.
Consider the aggregate production function Q Ka where K and L are all functions of time. Depict and solve for the time path of capital output ratio.
Solve:
2y) dy dt
If x is the sample mean, prove that the expected value of x is equal to u(the population mean).
Describe the process of testing hypotheses about population proportion of a given attribute.
Answer any five questions from this section.
5. A monopolists demand curve is P =100 -2Q.
Find her MR function.
What is the relation between slopes of AR and MR curves?
At what price is MR
[AR Average Revenue; MR Marginal Revenue]
6. Suppose we roll a die and are told that the number is even. What is the probability that it was
7. Solve the following linear programming model in x1 and x2:
Maximize z =45x1 55x2
subject to 6x1 4x2 120, x1 0
3x1 10x2 180, 0
8. The SD of output per acre from a sample of 34 representative firms producing paddy is 83 kg. Is the hypothesis that SD of output per acre for all firms producing paddy is 107 kg rejected at level of significance (Use large sample test) [SD =Standard Deviation].
9. What is a binomial distribution Find the mean and standard deviation of it with n and p as the two parameters.
10. Write short notes on the following:
Eigenvalue and Eigenvector
Rank of a matrix
Taylor's expansion
11. Find the inverse of
4 1
0 3 2
3 0 7
12.(a) What is a test statistic?
Distinguish between one-tailed and two-tailed tests.
What is p-value
Discuss the Hawkins-Simon condition in the context of input-output analysis.
From the following technology matrix find equilibrium prices if the wage rate is Rs100 per day:
Steel Coal Final Demand
Steel 0·4 0·1 50
Coal 0·7 0·6 100
Labour 5 2
Given demand and supply for cobweb model as Qdt =18 -Pt and Qst 3 4 Pt Find the intertemporal equilibrium price and determine whether the equilibrium is stable.
Establish the stability condition of Samuelson's multiplier-accelerator interaction model.
Consider the aggregate production function Q Ka where K and L are all functions of time. Depict and solve for the time path of capital output ratio.
Solve:
2y) dy dt
If x is the sample mean, prove that the expected value of x is equal to u(the population mean).
Describe the process of testing hypotheses about population proportion of a given attribute.
Answer any five questions from this section.
5. A monopolists demand curve is P =100 -2Q.
Find her MR function.
What is the relation between slopes of AR and MR curves?
At what price is MR
[AR Average Revenue; MR Marginal Revenue]
6. Suppose we roll a die and are told that the number is even. What is the probability that it was
7. Solve the following linear programming model in x1 and x2:
Maximize z =45x1 55x2
subject to 6x1 4x2 120, x1 0
3x1 10x2 180, 0
8. The SD of output per acre from a sample of 34 representative firms producing paddy is 83 kg. Is the hypothesis that SD of output per acre for all firms producing paddy is 107 kg rejected at level of significance (Use large sample test) [SD =Standard Deviation].
9. What is a binomial distribution Find the mean and standard deviation of it with n and p as the two parameters.
10. Write short notes on the following:
Eigenvalue and Eigenvector
Rank of a matrix
Taylor's expansion
11. Find the inverse of
4 1
0 3 2
3 0 7
12.(a) What is a test statistic?
Distinguish between one-tailed and two-tailed tests.
What is p-value
Other Question Papers
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- Actuarial Economics: Theory and Practice
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