Linear Model Equation with Examples Statistical Economics

Linear Model Equation with Examples Statistical Economics of Quantity and Supply

Linear Model Equation 3.2

Qd=a-bP

Qs= -C+dP

If b+d = 0

d = -b

b = -d

now we are putting the value of d in Qs

Qs = -C + dP

= -C + (-b) P

= – C – bP ——– Qs

= – bP –bP ——– Qd.

According to this case, the slope of both equations is the same and Qs do not intercept each other at any point.

So quantity and price are not an equilibrium.

Linear Model Equation with Examples  Statistical Economics 3.3

Qd      =          4-P2, Qs=4P-1

Qd       =          Qs

4-P2    =          4P-1    ——— 4+1     =          P2 + 4P

P2 + 4P – 5    = 0       ——— 5          =          P2 + 4P

P2 + 4P – 5    = 0

Example 3.3(i)

f(x)      =          x2-7x+10

dy/9x   =          2x-7+0

dy/9x   =          2-0

dy/9x   =          0-0

formula X1 and X2    where a = 1, b= -7, C=10

= -b± √b2 -4ac/2a

= -(-7) ± √(-7)2 – 4(1)(10)/2(1)

= 7 ± √49-40/2

= 7± 3/2

= 7 ± √9/2

X2=10/2

=4/2= X1

g(x) = 2x2 – 4x -16                a=2, b=-4, c=-16

= -b ± √b2-4ac/2a

= -(-4) ± √(-4)2 – 4(2)(-16)/2(2)

= 4 ± √16-8(-16)/4

= 4 ± √16+128/4

= 4 ± √144/4

= 4 ± 12/4

= 8/4 after divide X1

= 16/4 after divide X2

X1=2 , X2= 4

Qd       =          Qs

3-P2    =          6P-4

P2        =          6P – 4 – 3

P2        =          6P – 7

P2+6P-7=0

= -b ± √b2-4ac/2a      a=1, b=6, c=-7

= -6 ± √(6)2-4(1)(-7)/2(1)

= -6 ± √36+28/2

= -6 ± 64/2

= -6 ± 8/2

= 2/2= 1

= -14/2= -7

P1= 1

P2= -7

Putting the value of P1 in equation 1

Qd       = 3-P2

= 3-(1)2

Q         = 2

P         = 1

Putting the value of P in equation 1

Qd       = 8-P2

= 8-(√5)2

= 8- (2.24)2

= 8-5

Q         = 3

 

So P=√5

Qd       =          Qs

8-P2    =          P2-2

-P2-P2 = -8-2

2P2      = 10

P2        =10/2

P2        = 5

P          =√5

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