Understanding Production Function Returns to Scale

Returns to scale is a concept in economics that describes how a production function changes as all input factors are proportionally increased or decreased. It helps understand the efficiency and output changes at different scales of operation.

Analyzing Returns to Scale Types

Let's examine the different types of returns to scale:

• Constant Returns to Scale: If all inputs are increased by a certain proportion (e.g., multiplied by factor k), the output increases by the exact same proportion. If inputs increase by factor k, output increases by factor k.
• Increasing Returns to Scale: If all inputs are increased by a certain proportion (e.g., multiplied by factor k), the output increases by a larger proportion. If inputs increase by factor k (where k > 1), output increases by a factor greater than k. Mathematically, if inputs change by k, output changes by a factor > k.
• Decreasing Returns to Scale: If all inputs are increased by a certain proportion (e.g., multiplied by factor k), the output increases by a smaller proportion. If inputs increase by factor k, output increases by a factor less than k. Mathematically, if inputs change by k, output changes by a factor < k.

Matching the Scenario

The question specifies that a proportional increase in all inputs leads to an increase in output by a larger proportion. This scenario directly aligns with the definition of increasing returns to scale.

Therefore, the production function is said to display increasing returns to scale.