Economics Homework Solutions
Problem
#3934

The six-tenths rule

Question:

The six-tenths rule quantifies the relationship between the relevant costs of a firm's decision to expand and the increased internal economies that result from that expansion.

As a result of an expanding printing industry, the owner is considering taking on new business, which will necessitate a dramatic increase in processing capacity. This will require the installation of additional technical capacity at a cost of £30000 and will entail the employment of three additional workers to deal with the increased processing capacity. An adjacent unused building, which is also owned by the firm, will need to be refurbished at a cost of £22500 to accommodate the additional technical capacity. The new expansion is not likely to incur additional increases in the owner's nor the part-time worker's annual salaries.

On the basis of the owner's desire to go ahead with the expansion:

i) Identify with reasons, the relevant costs associated with this decision  
ii) Calculate the new average unit cost of each document  
iii) If n, the scale factor is 0.6, calculate the new processing capacity associated with this decision;    
iv) Calculate the new profit/loss made on each processed document.

I appreciate your help in answering this question; will you please also be able to explain to me how you got to the answer you will be sending me, please? Thank you for your help.

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Useful information:

The most well known kind of technical (internal) economy of scale arises
because the capacity of a small set of technical units frequently rises
in greater proportion than their cost as the set of technical units
becomes larger. This technological relationship is of prime importance
and is known as the six-tenths rule.

The “six-tenths rule” stated mathematically is:

C2 = C1 [Y2/Y1]0.6

Where:

C1 is the total cost of a small set of technical units

C2 is the total cost of a larger set of technical units

Y1 is the capacity of a small set of technical units

Y2 is the capacity of a large set of technical units

In the six-tenths rule a technical unit is the unit cost of say:

A software package

A personal computer

A microprocessor

An oil tanker

An EPOS
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