SEMESTER FALL 2020
MATHEMATICAL ECONOMICS(ECO406)
ASSIGNMENT NO.2
DUE DATE: 21 DECEMBER, 2020
TOTAL MARKS:15
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ECO406 Assignment 2 Solution Fall 2020-VU-Digilearnerspoint
Question No.1 (Mark5)
A linear function is one in which the power of an
independent variable is equal to one. Given below is an example of a linear
function showing the relationship between demand and price.
Derive the linear equation of demand function from the following
table:
P
550
225
Q
100
150
Question No.2: (Mark:5)
Solve the following equations using the substitution method
and find the values of the unknown.
6x – 2y = 12
– 8x + 4y = –16
Question No.3: (Mark5)
Solve the following equation by the factorizing method and find the values of X.
2X2 -X-15=0
Solution#01
The general form of linear demand function or equation is
Qd= a-bP A
By Plugin in values of given table in A we get
100 = a-b550 1
150 = a-b225 2
By subtracting 1 from 2
150 = a-b225
-(100=a-b550)
50=b325
b = 50/325=0.15
Put value of b in equation 1
100 = a – 0.15*550
100 = a – 84
a=100+84=184
Thus linear demand function is
Qd = 184-0.15P
Solution#02
6x – 2y = 12 A
– 8x + 4y = –16 B
Divide equation A by 2 and B by 4, we get
3x - y = 6 1
-2x + y = -4 2
By adding 1 and 2
3x – y = 6
-2x +y = -4
X = 2
To find the value of y, substitute value of x either in 1, we get
3*2 – y = 6
6 – y = 6
By subtracting 6 from both sides
6-6-y = 6-6
-y = 0
Multiplying both sides by minus 1, we get
-1*-y = 0*-1
Y = 0
Thus solution set is (2,0)
Verification
Put x=2 and y=0 in equation B
-8*2 + 4*0 = -16
-16 = -16
As both sides are same, hence proved
Solution#03
2X2 -X-15=0 A
2X2 -6X + 5x -15=0
2x(x-3) + 5 (x-3) = 0
(2x + 5)*(x – 3) = 0
2x + 5 = 0 x
– 3 =0
Subtracting 5 from both side Adding
3 on both side
2x + 5 -5 = 0 - 5 x
– 3+3 =0+3
2x = -5 x
= 3
Dividing both side by 2
X = -5/2
Thus solution set is (-5/2, 3)
Verification
Put value of x=-5/2 in A
2(-5/2)^2 –(-5/2)-15=0
25/2 +5/2 – 15 = 0
(25+5-30)/2 =0
0/2=0
0=0