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The given the Cobb-Douglas production function

Q=L2/3K1/3Q = L^{2/3}K^{1/3}, which of the following is correct about this production function?

A. The firm produces Q amount of output using L and K inputs only.

B. The given production function exhibits decreasing returns to scale.

C. The given production function exhibits constant returns to scale.

D. The given production function exhibits increasing returns to scale.

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 3

The function uses only labour and capital as inputs, so A is correct. For a Cobb-Douglas function Q=LaKbQ = L^{a}K^{b}, returns to scale depend on a+ba + b. Here 23+13=1\frac{2}{3} + \frac{1}{3} = 1, so the function shows constant returns to scale (C). Hence A and C only.

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