Question

For a production function $Q = 3L^{1/3}K^{1/3}$, the maximum possible output that the farmer can produce with 125 units of Labour (L) and 125 units of Capital (K) will be:

• A. 75 units
• B. 125 units
• C. 375 units
• D. 27 units

Hint:

To simplify, combine variables with common exponents:
$L^{1/3}K^{1/3} = (L \times K)^{1/3}$.
$(125 \times 125)^{1/3} = 25$.
Then multiply by 3: $3 \times 25 = 75$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The Cobb-Douglas production function determines the maximum output ($Q$) that can be produced using specific levels of inputs like Labour ($L$) and Capital ($K$).
Key Formula or Approach:
Substitute the given values of $L$ and $K$ into the function:
\[ Q = 3L^{1/3}K^{1/3} \]

Step 2: Detailed Explanation:
The inputs are:
- $L = 125$
- $K = 125$
Substitute these values into the production function:
\[ Q = 3 \times (125)^{1/3} \times (125)^{1/3} \] Calculate the cube root of 125:
\[ 125 = 5^3 \implies (125)^{1/3} = 5 \] Substitute the simplified values back into the equation:
\[ Q = 3 \times 5 \times 5 \] \[ Q = 75 \] Therefore, the maximum output is 75 units.

Step 3: Final Answer:
The maximum possible output is 75 units, corresponding to Option (A).