Curvas De Escala

SCALE CURVES

The Concept Unit costs fall as volume increases. Economists call this "increasing returns" and regard it as an exception. In fact, it is the norm.

The Mathematics Scale curves arerepresented by regressing a log-linear relationship on the data:
log(c )  a  b .log( ) v

where: c is a measure of unit cost v is a measure of total volume per period a and b are regressioncoefficients (b is normally negative)

100 logC 

Slope = s c0 s .c 0 s 2 .c 0
10

1 1

v0

102 v

0

  4 0 logV 100 v

The so-called "BCG Slope" of a scale curve (s) is defined as theratio of unit costs after and before volume is doubled. The relationship between b and s is:
s 2
b

s is usually then expressed as a percentage.

2 Discussion The following are the slopes ofsome characteristic scale curves: No scale economies: 100% (as with a pure variable cost business). b = 0, s=

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Perfect scale economies b = -1, s = 50% (as with a purely fixed cost business:total costs are invariant to volume) Negative costs (sign that you did something wrong!) Diseconomies of scale 100% (unit costs rise with volume) b < -1, b > 0, s < 50% s>

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The "Point SixRule" b = - 1/3, s = 79%. (Total volume is proportional to the capacity of a set of vessels; total cost is proportional to their surface area. This rule is so called because total costs increase by 60%[approx. (79% x 2) - 100%] when the volume is doubled. The Point Six Rule commonly applies to capital costs in process industries.)

[You should be able to derive the values of b and s in each case.]Hints Define your measures of unit cost and volume carefully. Do not blindly plot numbers against each other: regress only to validate the relationship that you have hypothesized. Think of a coststructure in terms of cost components, (which add or multiply together to make up total cost) and cost drivers, the determinants of each cost component. Cost components generally relate to each...