Consider the following Cobb-Douglas production function:
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In a Cobb-Douglas production function with exponent of labour between 0 and 1, output increases with labour, but marginal product of labour decreases. This shows diminishing marginal returns.
\(\frac{\partial Q}{\partial L}\) increases as \(L\) increases.
\(\frac{\partial Q}{\partial L}\) decreases as \(L\) increases.
As \(L\) increases, \(Q\) increases but at a slower rate.
As \(L\) increases, \(Q\) decreases but at a slower rate.
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The Correct Option isB, C
Solution and Explanation
Step 1: Look at the Cobb Douglas function.
Output is written as a product of inputs raised to powers. The powers tell us the share each input has in production.
Step 2: Use the power rule.
The marginal product of an input is found by differentiating output with respect to that input, which brings its power down as a factor.
Step 3: Apply the needed property.
Adding the powers tells us the returns to scale, and the ratios of marginal products tell us the slope of the isoquant. We use whichever the question asks for.
Step 4: Conclude.
Working the powers through gives the value in the marked option.
\[ \boxed{\text{The value from the Cobb Douglas powers}} \]