The Cobb–Douglas production function Y = K2/3 L1/3 can be rearranged into the output per worker function:y = k1/3.y = k2/3.y = k3.y = k2.
Question
The Cobb–Douglas production function
Y = K<sup>2/3</sup> L<sup>1/3</sup> can be rearranged into the output per worker function:
y = k<sup>1/3</sup>. y = k<sup>2/3</sup>. y = k<sup>3</sup>. y = k<sup>2</sup>.
Solution
The Cobb-Douglas production function Y = K^(2/3) L^(1/3) can be rearranged into the output per worker function by dividing both sides of the equation by L (the number of workers).
Step 1: Divide both sides of the equation by L Y/L = K^(2/3) L^(1/3) / L
Step 2: Simplify the right side of the equation Y/L = K^(2/3) * L^(-2/3)
Step 3: Rewrite the equation with y = Y/L and k = K/L y = k^(2/3)
So, the output per worker function is y = k^(2/3). The other options y = k^(1/3), y = k^3, and y = k^2 are not correct rearrangements of the original Cobb-Douglas production function.
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