Question

The capital cost (CC) of an industrial equipment varies with its capacity (S) as \( CC \propto S^\beta \). The rule-of-thumb value of the exponent \( \beta \) is

• A. 0.4
• B. 0.6
• C. 0.8
• D. 1.0

Hint:

When estimating costs for scaling up production or facility capacities, consider the scaling exponent carefully as it significantly affects financial planning.

Answer 1

The Correct Option is B

The relationship between capital cost and capacity for industrial equipment often follows a power law, known as the scaling law. In this case, the cost-capacity relationship can be described by \( CC = k \times S^\beta \), where \( k \) is a constant and \( \beta \) is the cost-capacity factor. 
Step 1: Understanding the Cost-Capacity Factor: 
The value of \( \beta \) typically ranges between 0.6 and 0.8 for many types of industrial equipment, representing economies of scale. As the capacity increases, the increase in cost is less than proportional. 
Step 2: Rule-of-Thumb for \( \beta \): 
The most commonly used rule-of-thumb for \( \beta \) is 0.6, which suggests that as capacity doubles, the capital cost increases by approximately 60%, not doubling.