No.
of Printed Pages : 8 BECC–102
B. A. (HONOURS) ECONOMICS
(BAECH)
Term-End Examination
December, 2023
BECC–102 : MATHEMATICAL METHODS IN
ECONOMICS–I
Time : 3 Hours Maximum Marks : 100
Note : Answer questions from all the Sections as
directed.
Section—A
Note : Answer any two questions from this Section.
2×20=40
1. (a) The demand and supply function of a
commodity are PD 18 2x x2 and
PS 2 x 3 . Find the consumer’s surplus
and producer’s surplus at equilibrium
price. 15
(b) Marginal cost function of a firm is
MC = 4 + 6x 30 x 2 .Find firm’s total cost
function if the fixed cost is ` 500. 5
P. T. O.
[2] BECC–102
2. What is a linear difference equation ? Why do
we need to linearise non-linear difference
equations ? How is it done ? Explain with the
help of an example. 20
3. The demand and supply curves of a commodity
X are given by the following two equations :
7+7+6
Qd = 200 10 p
Qs = 50 15 p
(a) Determine the equilibrium price and
quantity.
(b) Suppose that the price of factor inputs has
changed, resulting in new supply curve
Qs = 100 15 p . Analyse the new
equilibrium price and new equilibrium
quantity as against the original.
(c) What will happen if government imposes
tax of ` 5 per unit on the commodity X ?
4. A manufacturer has a demand function
Q = 100 0.5P and the total cost function as
C 100 40 Q . 7+7+6
(a) Determine the optimum level of
production.
(b) Show that the second order condition of
profit maximization holds.
[3] BECC–102
(c) What is the maximum profit ?
Section—B
Note : Answer any four questions from this Section.
4×12=48
5. Discuss the methods of proof by contradiction
and proof by inspection. 12
6. Show that the graph of
2 x2 2 y 2 16 x 20 y 64 0 is a circle. Find its
centre and radius. 12
7. (a) What do you understand by Sinking
Funds ? Explain. 6
(b) Find the twelfth term of Geometric
Progression whose third term is 16 and
whose seventh term is 1. 6
8. (a) Evaluate : 6
x3 x 2 16 x 20
f x if x 2
x 2 2
if x 2.
P. T. O.
[4] BECC–102
(b) Find the values of x for which the function
x2
y is discontinuous. 6
x 1 x 3
9. What are the conditions for a function to have :
12
(a) Maxima
(b) Minima
(c) Inflexion
(d) Convex to origin
10. The manufacturing cost of an item consists of
` 1,600 as overhead, material cost of ` 30 per
item and the labour cost ` x 2 /100 for x items
produced. Find how many items can be
produced to have the minimum average cost. 12
Section—C
Note : Answer all questions from this Section.
2×6=12
11. Write notes on the following :
(a) Surjective and bijective functions
(b) Theorems and propositions
12. (a) Find derivative of :
y 3xm1 6 x m
[5] BECC–102
dy
(b) Find when x 8t 2 t 7
dx
y t 2 10t 2 .
BECC–102
2023
–102 I
× =40
PD 18 2x x2 PS 2 x 3
P. T. O.
[6] BECC–102
MC = 4 + 6x 30 x 2
` 5
X
+ +6
Qd = 200 10 p
Qs = 50 15 p
] Qs = 100 15 p
‘X’ `
[7] BECC–102
Q = 100 0.5P
C 100 40 Q + +6
4×12=48
2 x2 2 y 2 16 x 20 y 64 0
P. T. O.
[8] BECC–102
x3 x 2 16 x 20
f x x2
x 2 2
x2
x
x2
y
x 1 x 3
12
` ] ] ]
` x
` x 2 /100
× =12
[9] BECC–102
y 3xm1 6 x m
dy
x 8t 2 t 7
dx
y t 2 10t 2
BECC–102
P. T. O.
