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# BECC 102 Mathematical Methods for Economics-I SOLVED ASSIGNMENT 2020-21 (ENGLISH MEDIUM)

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## BECC 102 SOLVED ASSIGNMENT 2020-21

Course Code: BECC 102
Assignment Code: BECC 102/TMA/January 2020 & July 2020
Total Marks: 100

Assignment A

Answer the following Long Category questions in about 500 words each. Each question carries 20 marks. Word limit will not apply in the case of numerical questions.

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.

OR

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?

2. 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 – Q2 and supply function Ps = 2Q + 3. Assuming perfect competition, find (i) the consumers’ surplus, (ii) the producers’ surplus.

BECC 102 SOLVED ASSIGNMENT 2020-21

Assignment B

Answer the following Middle Category questions in about 250 words each. Each question carries 10 marks. Word limit will not apply in the case of numerical questions. 3X10=30

3. 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

OR

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

4 Let X = 1,3,5 and Y = 2,4,6
Find, X U Y and the Cartesian Product of X and Y .

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

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

OR

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

BECC 102 SOLVED ASSIGNMENT 2020-21

Assignment C

Answer the following Short Category questions in about 100 words each 5X 6=30
6. What is a point of inflexion ? Does f(x) = x3 have a point of inflexion at x = 0?
7. Find the integral of (y2-1) dx-2dy = 0
8. Evaluate the Limits of 2.
8. Evaluate the Limits of
9. If the demand function for a good is Q=140 – 5P, what is the price elasticity of demand at P=15 rupees?
10. 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?

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