If \(Q=L^a\) with \(0<a<1\), the production function is concave. The corresponding cost function often becomes convex because input requirement rises more than proportionately with output.
The cost function is concave and the production function is convex.
The cost function is convex and the production function is concave.
The cost function and the production function are both differentiable and convex.
The cost function and the production function are both differentiable and concave.
Show Solution
The Correct Option isB
Solution and Explanation
Step 1: Look at the single input function.
Output depends on one input, so we can study how output reacts as we add more of that input.
Step 2: Find the marginal product.
The marginal product is the slope of the production function, the extra output from one more unit of the input. We get it by differentiating output with respect to the input.
Step 3: Read its behaviour.
Checking how this slope changes tells us whether the marginal product is rising, falling or turning. This shapes the answer about the stage of production.
Step 4: Conclude.
Using the slope and its change, the property that holds is the one in the marked option.
\[ \boxed{\text{The property fixed by the marginal product}} \]