Directory UMM :Data Elmu:jurnal:S:Structural Change and Economic Dynamics:Vol11.Issue1-2.Jul2000:

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Structural Change and Economic Dynamics 11 (2000) 181 – 184

Hicks-neutral technical progress and relative

price change

Ian Steedman *

Department of Economics,Manchester Metropolitan Uni6ersity,Mabel Tylecote Building, Ca6endish Street,Manchester M15 6BG, UK

Accepted 11 May 1999

Abstract

With constant returns to scale and no produced inputs, relative rates of Hicks-neutral progress predict price changes. With produced inputs they do not; even the direction of relative price changes may fail to be predicted. © 2000 Elsevier Science B.V. All rights reserved.

JEL classification:E10

Keywords:Technical progress; Hicks neutrality; Relative price change

www.elsevier.nl/locate/econbase

In a constant-returns-to-scale production system in which each commodity is produced by primary factors alone and is subject to Hicks-neutral technical progress (HNTP), the relative rates of progress will naturally be correct predictors of the rates of change of all relative prices. When produced inputs are involved, however, a commodity with a ‘high’ rate of progress may perfectly well be rising in relative price. To see this in a very simple way, we shall suppose that all production is instantaneous and that all payments are made immediately; there will thus be no interest/profit elements involved in our ‘price equals unit cost’ equations. To indicate just how simple is the central point, we begin with a system involving just two produced commodities, a single primary factor (homogeneous labour) and Cobb – Douglas unit cost functions.

* Tel.:+44-161-247-3905; fax: +44-161-247-6302. E-mail address:h.dawson@mmu.ac.uk (I. Steedman).

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182 I.Steedman/Structural Change and Economic Dynamics11 (2000) 181 – 184

labelled thatf1\f2 and consider the case

0Bh₂Bh₁B(f₁/f₂)h₂ (3)

It is immediate, from Eqs. (2) and (3), that industry 1 is enjoying the faster rate of HNTP but that (p1/p2) is always rising. The relative rates of HNTP simply do not

predict even the direction of relative price movement, let alone its magnitude. It may be noted that such a predictive failure also arises in a second case.

h1Bh2B(f2/f1)h1B0

Here there is faster regress in 1 and yet (p1/p2) is always falling. From now on,

however, we suppose allhjto be positive, in line with the usual connotation of the

word progress.

2. Many commodities

Generalizing Eq. (1) and dropping the time subscripts, let us now write

ehjt_p

j=cj(p,w); j=1, …,n (4)

where p is the (1×n) price vector and cj( ) is some unit cost function. If w is

constant and p_j is the percentage rate of change ofp_jthen, from Eq. (4),

hj+pj=% i

sijpi

wheresijis the (in general, variable) share of produced inputiin the unit cost ofj;

or in obvious matrix notation

h+p=pS (5)

The rates of percentage price decrease are thus given by

−p=h(I−S)−1

and since each (−p_j) is a different, non-negatively weighted sum of (h₁,h₂, …,h_n)

there is no reason whatever to expect that (p_i−p_j)(h_i−h_j)B0. (Of course, this

relation would hold in the case — utterly irrelevant to a modern economy — of

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We saw in Eq. (2) that the direction of the relative price change depended on whether (h1/f1) was greater than or smaller than (h2/f2) and a generalization of this

result is implicit in Eq. (5). Letfbe the (in general, variable) row vector of primary factor shares and u be the row vector of unit elements (the summation vector). Then

so that relative prices will indeed be constant. This rather ‘Harrodian’ relation betweenh andfthus leads to constant relative prices under Hicks-neutral technical progress.

In general, of course, neither relative prices nor S and f will be constant over time, so that Eq. (7) does not even constitute a fixed relationship between (−p)

and h. When the unit cost functions in Eq. (4) are not all of the Cobb – Douglas form, i.e. always! fixed rates of HNTP presumably need not even imply monotonic-ity of relative price movements.

It will be clear that ifw in Eq. (4) were to represent a vector of primary factor prices rather than a single wage rate, none of our argument would need to be changed provided only thatw; =0. Rather than pursue this point, however, we shall re-emphasize just how simple the role of produced inputs can be and yet upset any (p_i−p_j)(h_i−h_j)B0 result.

(i) Suppose that only commodity 1 is ever used as a produced input, so that each

s1j=1−fj\0 but every other sij=0. Then

presence of just one produced input is enough to break any necessary link between relative rates of HTNP and directions of relative price movements.

(ii) That link can indeed be broken even without there being any ‘inter-industry’ produced input use; it is sufficient that each industry uses some of its own product (and no other product) as an input. ThenSis diagonal and (−p_j)=(h_j/f_j), so that

once again (p_i−p_j)(h_i−h_j)B0 is not ensured. With a Cobb – Douglas unit cost

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there is no reason whatever why the ranking of the (−p_j) should not be exactly the

opposite of that of thehj. Truly, relative rates of HNTP are no guide to movements

of relative prices in even the simplest of systems involving produced means of production. And what system not involving them is worth studying as a representa-tion of a modern economy?

3. Joint products

Let the profit function for the joint products process j be of the strongly separable form

[rj(p)−e

−hjt_c

j(p,w)] (4%)

which generalizes Eq. (4),rj( ) being a convex, linear homogeneous function of the

pi. Then Eq. (5) generalizes to

h+pT=pS (5%)

where the elements of Tj show the shares of the various products in the gross

revenue from process j. Of course, uTu so that uTuuS+f

or

u(T−S)f (6%)

If T and S are square one can simply parallel Eqs. (6) and (7) by replacing (I−S)−1

by (T−S)−1

and little changes except that one cannot now be sure that (T−S)−1

will be non-negative. Of course, ifTandSare not square then even less can be said about any useful connections between (−p) and h.