A firm in a perfect competitive market structure faces a marginal cost function given by

                   MC(Q) = 4Q + 5

where Q represents quantity of output produced. This firm earns marginal revenue of Rs 25 oneach unit sale of its output. Suppose this firm decides to produce 3 units of output, is this a profit maximisingdecision by the firm? If not, how much should this firm produce to earn maximum profits? In the long-run will this firm earn negative economic profits, positive economic profits, or zero economic profits? 

Explain the concept of maximum value function.

. Define

a. Adjugate of a matrix

b. Decomposable matrix

c. Singular matrix

If Z = f(x,y) = xy

Find the maximum value for f(x,y) if x and 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.

. Let Z = f(x,y) = 3x3 -5y2 -225x + 70y + 23.

(i) Find the stationary points of z.

(ii) Determine if at these points the function is at a relative maximum, relative minimum, infixion point, or saddle point.

Consider two countries I and II producing two commodities A and B. There is only one factor of production, that is, Labour hours. The table below gives labour hours required by each
country to produce a unit of commodities A and B.

Labour hours needed to produce a unit of

Answer the following:

 (i) Which country has an absolute advantage in producing commodity A? Give reason. 

 (ii) Which country has a comparative advantage in producing commodity B? Give reason.

 (iii) If trade takes place between both the given countries, which country will export commodity A?

How long will it take a given sum of money (Say in Rupees) to increase 4 times its present value when compounded half yearly at 7% rate of interest?

If the demand function for a good is Q=140 – 5P, what is the price elasticity of demand at P = 15 rupees?

Find the integral of (y2 -1) dx-2dy = 0

 What is a point of inflexion ? Does f(x) = x3 have a point of inflexion at x = 0?

Let X{1,3,5 and Y{2,4,6} Find, X U Y and the Cartesian Product of X and Y.

OR

Heckscher-Ohlin theory of international trade begins where the Ricardian theory of international trade ends. Elucidate.

(b) With regards the Kinked demand curve theory given by Paul Sweezy, answer the following:

(i) The demand curve facing an oligopolist has a kink at the level of the prevailing price. Discuss.

 (ii) Why does the slope of the demand curve vary on the both sides of the kink? Give reason.