The problem describes a production function $Q = K^a L^b$, where $Q$ is the quantity produced, $K$ is capital, $L$ is labor, and $a$ and $b$ are constants. We are given that $a + b > 1$. The question asks about the spacing of the isoquants.
2025/7/1
1. Problem Description
The problem describes a production function , where is the quantity produced, is capital, is labor, and and are constants. We are given that . The question asks about the spacing of the isoquants.
2. Solution Steps
The condition indicates that the production function exhibits increasing returns to scale. This means that if you increase both inputs and by the same proportion, the output will increase by a larger proportion.
To analyze the spacing of isoquants, consider what happens as we move to higher output levels. Because of increasing returns to scale, a given increase in output requires a smaller proportional increase in inputs (K and L) as output increases. Therefore, the isoquants will be progressively closer together at higher quantities.
For example, if we double and , and , more than doubles.
3. Final Answer
d. progressively closer together at higher quantities.