Ques 1.

A monopolist faces the demand curve Q = 60-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.

Ques 2.

A monopolist firm has the following total revenue and total cost functions:
R = -mQ²+ nQ          ( m,n > 0)

C = aQ²+ bQ + c       (a,b,c > 0)
Suppose that the government plans to levy an excise tax on the product of this firm and
wishes to maximise the total tax revenue T from this source. What tax rate t ( rupees per
unit of output) should the government choose? 

Ques 3.

 A firm in a perfectly competitive market has the following cost function: C = 1/3q³ – 5q² + 30q +10 If the market-clearing price is 6, obtain the profit maximising level of output.

                                       OR

Given the demand function PD = 27 – Q ² and supply function P_s = 2Q + 3. Assuming perfect competition, find (i) the consumers’ surplus, (ii) the producers’ surplus.

Ques 4.

Given the total cost function TC = 9q²+ 2q + 8100
(a) Find marginal cost (MC) and average coat (AC) as functions of q
(b) Show that when MC < AC, AC is falling, and when MC > AC, AC is rising

Ques 5.

Given the aggregate consumption function C = 0.9Y + 100(where C is aggregate consumption
and Y is aggregate income)
(a) Find the marginal propensity to consume (MPC) and average propensity to consume (APC)
(b) Find the elasticity of consumption with respect to income, and show that it equals MPC/APC

Ques 6.

Let X = and Y =
Find, X U Y and the Cartesian Product of
X and Y .

Ques 7.

Given A= { 1, 2, }, B= { 3, 4, 5 } and C= { 3, 5, 6, 7, 8 }, show that
 (i) 
 (ii) 

Ques 8.

Create a truth table for
(a)
(b) the converse of ‘A implies B’.

Ques 9.

Find the Euclidean distance between
(i) (2, 3) and (4, 1)
(ii) (2, 3, 4) and (4, 1, -5)

Ques 10.

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

Ques 11.

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

Ques 12.

Evaluate the Limits of

Ques 13.

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

Ques 14.

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?

Ques 15.

Discuss the Classical Theory of Economic growth. Discuss the Marxian criticism of the Classical Theory of growth.

Ques 16.

Explain the concept of economic inequality. Explain the various methods of measuring economic inequality.