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.

Applied MathematicsProduction FunctionIsoquantsReturns to ScaleEconomics
2025/7/1

1. Problem Description

The problem describes a production function Q=KaLbQ = K^a L^b, where QQ is the quantity produced, KK is capital, LL is labor, and aa and bb are constants. We are given that a+b>1a + b > 1. The question asks about the spacing of the isoquants.

2. Solution Steps

The condition a+b>1a+b > 1 indicates that the production function exhibits increasing returns to scale. This means that if you increase both inputs KK and LL by the same proportion, the output QQ 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 KK and LL, and a+b>1a+b > 1, QQ more than doubles.

3. Final Answer

d. progressively closer together at higher quantities.

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