Determine the eigenvalues and eigenvectors of the matrix

A =

Singular matrix

Integrate

(i) x Sin x

(ii)

Singular matrix

Decomposable matrix

Adjugate of a matrix

If Z = f(x,y) = xy

Find the maximum value for f(x,y) if x & y are constrained to sum to 1 (That is x+y = 1).

Solve the problem in two ways: by substitution and by using the Lagrangian multiplier method.

If the demand function for a good is Q=280 –10P, what is the price elasticity of demand at P = 30rupees

Evaluate the Limits of

Determine the distance between the points

i)    (3,0,7) and (-4,8,2)

ii) (4,6,7,1) and (-3,0,2,4)

iii)The distance between the points (3,1,2,4) and (4,6,5,) is 200. What can be said about the value of

For what values of x will be the function be discontinuous?

ii) Show that    

tends to a₁/a₂ as x

Discuss the importance of the Hawkins-Simon conditions in input-output analysis

6. Find the short run average cost for the production function q = AL^2/3K^1/3where total cost (TC) = wL + rK, the symbols having their usual meaning.

Using Cramer's rule solve the following equations:

(i) x+y-2 = 0

2x-y+2 = 3

4x+2y-22 = 2

(ii) 2x+4y = 18

4x-6y=8

Discuss the importance of the Hawkins-Simon conditions in input-output analysis

Consider the following Macro-Model (Multiplier –Accelerator Interaction):

Y_t= C_t + I_t+ G_t

C_t= C₀+ Y_t-1

I_t = I₀ + ( C_t–C_t-1)

Where 0 < < 1 ; > 0 ; and G_t= G₀

i) Find the time path Y(t) of national income, and

ii) Comment on the stability conditions.

A firm in a perfectly competitive market has the following cost function:C = 1/3q³–5q²+ 30q +30If the market-clearing price is 9, obtain the profit maximising level of output.

A monopolist faces the demand curve Q = 80-P/2. The cost function is C=Q². Find the output that maximises this monopolist’s profits. What are the prices at profits and that output? Find the elasticity of demand at the profit maximising output

Obedience