When the sum of exponents exceeds one (a+b>1) in the Cobb - Douglas production function, it causes which one of the following?

Correct option is C

The Cobb-Douglas production function is generally expressed as:

​Q = AL^aK^b​

where:
• Q = Output
• A = Total Factor Productivity (a constant)
• L = Labor input
• K = Capital input
• a and b are the output elasticities of labor and capital, respectively

Returns to Scale (RTS):
Returns to scale measure how output changes when all inputs are scaled by a common factor. The sum of the exponents (a+b) determines the type of returns to scale:
1. If a+b=1→ Constant Returns to Scale (CRS)
Doubling inputs leads to exactly double output.
2. If a+b<1 → Decreasing Returns to Scale (DRS)
Doubling inputs leads to less than double output, indicating inefficiencies.
3. If a+b>1 → Increasing Returns to Scale (IRS)
Doubling inputs leads to more than double output, meaning the firm benefits from economies of scale.

When a+b>1, increasing all inputs by a certain percentage results in an even larger percentage increase in output. This happens due to factors such as specialization, better coordination, or improved efficiency at a larger scale of production.

Information Booster:

• Increasing Returns to Scale (IRS) indicate that a firm's productivity improves as it expands.
• Causes of IRS include:
  • Specialization of Labor: More workers allow for division of labor, improving efficiency.
  • Bulk Purchasing: Large-scale production reduces per-unit costs.
  • Technological Advancements: Larger firms can invest more in technology, enhancing productivity.
  • Better Resource Utilization: Larger firms can use machinery and capital more efficiently.
• Industries that typically experience IRS:
  • Software development
  • Heavy manufacturing
  • Telecommunications

Additional Knowledge:

​(a) Constant Returns to Scale (CRS)
• This occurs when a+b=1, meaning input and output increase in the same proportion.
• Example: A firm doubling its capital and labor sees exactly double the output.
(b) Decreasing Returns to Scale (DRS)
• Happens when a+b<1, meaning input increases lead to proportionally smaller output increases.
(d) Variable Returns to Scale (VRS)
• "Variable Returns to Scale" is not a specific category of RTS.
• It is a broad term describing situations where the returns to scale might vary at different levels of production.
• The correct term for increasing or decreasing returns would be IRS or DRS.