Question

Consider the Cobb-Douglas Production function: P(L,K)=19L⁰.⁵ K⁰.⁵. Find the total units of production when L=13 units of labor and K=12 units of capital are invested.

Answer 1

To calculate the total production with the values L=13 and K=12 in the Cobb-Douglas Production function, numbers are substituted into the function, square roots are determined, and then multiplication gives a total production of approximately 237 units.

Step-by-step explanation:

To find the total units of production using the Cobb-Douglas Production function, we substitute the given values of L (labor) and K (capital) into the function P(L,K) = 19L0.5K0.5. With L = 13 and K = 12, the calculation is:

P(13, 12) = 19 × 130.5 × 120.5

To proceed, we calculate the square roots:

130.5 = 3.60555 (approx) and 120.5 = 3.46410 (approx)

Then we multiply these with the coefficient:

P(13, 12) = 19 × 3.60555 × 3.46410

And finally, we compute the total production:

P(13, 12) ≈ 19 × 12.497 ≈ 237.43

Therefore, the total units of production, when 13 units of labor and 12 units of capital are invested, are approximately 237 units.