In the Cobb-Douglas production function
,defining y = Y/L as output per person and k = K/L as capital per person,the per person production function is:

Question

In the Cobb-Douglas production function 
,defining y = Y/L as output per person and k = K/L as capital per person,the per person production function is:

Quizplus · Accepted Answer

The per-person production function is given by:
y = A * k^α 
where A is the level of technology, k is capital per person, and α is the share of output that goes to capital. From the Cobb-Douglas production function in the question, we have:
Y = A * K^α * L^(1-α)
Dividing both sides by L and expressing K and L in per-person terms, we get:
y = A * (k^α) * (1^1-α)
or simply:
y = A * k^α
This is the same form as the per-person production function given above, with A = 1 and α = 0.3. Therefore, the correct answer is B.

In the Cobb-Douglas Production Function