The Employment Impact of Differences in Dmand and Production

Appendix 3:   On the Independence of the Employment

Matrix from the Price Level

To show this, we again use a closed input-output system, similar to the one used in Appendix 2.
Each nominal entry Xij is now split into its two components, a quantity q, and its price p.

We will consider two goods only, with prices p1 for good 1 and p2 for good 2. The quantities q
of each good are evaluated at the same price regardless of their destination (to other firms as
intermediate products or to final demand). This system can be written as follows:

^q11 ^p1               ^q12 ^p1          ^(q11^+q12^)p1

q₂₁ p₂             q₂₂ p₂         (q₂₁ +q₂₂)p₂

(q₁₁p₁+q₂₁p₂)(q₁₂p₁+q₂₂p₂)

v₁p₁               v₂p₂

g₁p₁             g₂p₂

f₁ p₁                g₁ p₁

f₂p₂             g₂p₂

(g₁p₁+g₂p₂)

where the subscripts 1 and 2 denote the two goods, f final demand, v value added, and g gross

output.

The employment matrix N can be written as:

	^ N1	0	1 - q22 p2	‰ P1 "
N= 1	g1P1		g 2 P 2	g 2 P 2   Г Â P1    0
DET	0	N2	q 21 p 2	1  q11 P1     0    f2 P 2 1-
	L	g 2 P 2 _	_ g1P1	g 1P1 _

where N represent employment in the two industries and DET is the determinant of the

coefficients matrix. DET is independent of the price level of the two goods:

DET =

∖ _- q11 Pi Y_{1 -} q22 p 2 Y ‰ p q 21 p 2

l g1P1 Jl g 2 P 2 J g 1P1 g 2 P 2

which simplifies to

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