Given the supply and demand for the
Cobweb model as :
Qst and Qdt 19 — 6Pt
Find the inter temporal equilibrium price and determine whether the equilibrium is stable. Establish the stability condition of Samuelson's multiplier accelerator model.

2. The input coefficient matrix for an economy is given by <img src='./qimages/9908-2.jpg'>

Find the level of output.

3. Consider the Cobb-Douglas production function,

<br><br> <img src='./qimages/9908-3.jpg'>

Prove that,

(a) It is homogeneous of degree 1.

(b) The marginal and average productivities of L and K the two inputs depend on the ratio of the 2 inputs.

(c) Elasticity of substitution is unity.

4.(a) Define standard error of a statistic. Explain how is it useful in testing of hypothesis and decision making.

(b) If xi; i . . n are n sample values from a normal distribution with mean and s.d.cr, derive the pdf of the sample mean x .

5. Find the expected value and variance of the following data <img src='./qimages/9908-5.jpg'>


6. Write short notes on Mean Value Theorem

(b) Taylor's expansion

7. Solve :

Max 10x1 10x2 20x3 20x4

Sub to 12x1 8x2 6x3 4x4 210
3x1 6x2 12x3 24x4 210
x1, x2, x3, x4 0

8. What is a Binomial distribution Find its mean and variance given that the parameters of the distribution are n and p.

9. Assume that on an average one telephone number out of 15 is busy. Find the probability that if 6 randomly selected telephone numbers are picked up not more than 3 are busy

(b) at least 3 of them are busy

10. Find the Inverse of the following matrix :

4 1 —1
0 3 2
3 0 7

11.(a) What is a test statistic Distinguish between one tailed and two
tailed tests.

(c) What is p-value ?

12.(a) If y x1/x1 x2, find the total differential.

(b) Write notes on Eigen value and Eigen vector.