The production function is f(x₁, x₂)= x^1/2₁x^1/2₂.If the price of factor 1 is $10 and the price of factor 2 is $15, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? A)x₁ = 1.50x₂. B)x₁ = x₂. C)x₁ = 15x₂. D)x₁ = 0.67x₂. E)We can't tell without knowing the price of the output.

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Quizplus · Accepted Answer

The profit-maximizing condition is MP₁/P₁ = MP₂/P₂. Substituting the given production function and factor prices, we get:(1/2)x₁^-1/2x₂^1/2 / 10 = (1/2)x₁^1/2x₂^-1/2 / 15Simplifying, we get:x₁ = 1.5x₂

The Production Function Is F(x1, X2)= X1/21x1/22

The Production Function Is F(x₁, X₂)= X^1/2₁x^1/2₂