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Illustrative calculation of skilled labour multiplier

This appendix explains in more detail the calculation of the skilled labour mul-

tiplier discussed in the text. We first illustrate the calculation of the total

embodied labour content of skilled labour.

(1) On the part of the student. Assume 4 years of study at 40 hours per week

for 45 weeks per year.

Total: 7200 hours.

(2) Classroom teaching. Assume 15 hours per week, 35 weeks per year, for

4 years, distributed across an average class size of 30 (average of large

lecture classes and smaller labs, seminars etc.).

Total per student: 70 hours.

(3) Tutorial work. Assume 2 hours per week, 30 weeks per year of one-on-one

tutorials.

Over 4 years, total = 240 hours.

(4) Educational overheads. Let us suppose this amounts to a contribution

equal to the classroom teaching labour.

Total 70 hours.

Now examine the breakdown of this total labour content into simple and

skilled. The student’s own contribution is simple; the teachers’ contribution is

skilled; and let us assume for the sake of argument that the ‘overhead’ contri-

bution breaks down 50:50 skilled and unskilled. We then arrive at the follow-

ing: total labour content of skill production equals approximately 7,600 hours

(rounding up), of which skilled labour makes up around 5 percent (rounding up

again).

The total embodied hours figure quoted above is a first approximation (in

fact an underestimate, as we shall see). Let us denote this approximation by

TH 0 . Using TH 0 we can construct a first approximation to the transmission

rate of embodied labour on the part of skilled labour:40

Chapter 2. Eliminating Inequalities

R 0 = TH 0 /AH.D

where AH represents the annual hours the skilled worker will work once qualified,

and D is the depreciation horizon in years. We can now use R 0 to re-evaluate

the total hours embodied (on the assumption that the transmission rate for the

teachers and others who supply the skilled input into the production of skilled

labour is the same as that for their students, once qualified). If the proportion of

TH 0 accounted for by skilled labour input is denoted by SP, our revised estimate

of the total embodied labour is

(1 + R 0 )SP.TH 0 + (1 − SP)TH 0 = (1 + R 0 SP)TH 0 .

But this new figure for total hours embodied can now be used to re-estimate

the transmission rate, permitting a further re-estimation of total hours-and so

on, recursively. The resulting successive approximations to the total labour

embodied in the production of skilled labour form a geometric expansion, the

nth term of which is

(1 + R 0 SP + R 20 SP 2 + R 30 SP 3 + · · · + R n 0 SP n )TH 0 .

Letting n tend to infinity, we can deduce the final limiting value of the total

hours estimate, namely (1-R 0 SP) −1 TH 0 , and the corresponding final estimate

of the transmission rate for embodied labour:

R f = (1−R 0 SP) −1 TH 0 /AH.D.

Remembering that R 0 = TH 0 /AH.D, R f may be rewritten as

R f = TH 0 /(AH.D−SP.TH 0 ),

enabling us to calculate the final transmission rate directly. Using the above

illustrative figures of TH 0 = 7600, AH = 1575 and SP = 0.05 we find that

R f = 0.50 for D = 10,

R f = 0.33 for D = 15,

R f = 0.24 for D = 20,

as quoted in the text. In each case the skilled labour multiplier is simply 1 plus

R f

a rough copy if you have it pages 46-48