The production function is f(x₁, x₂) = ₁ ₂. If the price of factor 1 is $12 and the price of factor 2 is $24, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? A) x₁ = x₂. B) x₁ = 0.50x₂. C) x₁ = 2x₂. D) x₁ = 24x₂. E) We can't tell without knowing the price of the output.

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Quizplus · Accepted Answer

In order to maximize profits, the firm should use factors in the proportion that gives the highest marginal product per dollar spent. The marginal product of factor 1 is 11ea6c55_6e2e_4ef8_9875_f58de9090728_TB6162_11 ₁ per dollar spent, while the marginal product of factor 2 is 11ea6c55_6e2e_7609_9875_d929a80fc21c_TB6162_11 ₂ per dollar spent. Therefore, to maximize profit, the firm should use factor 1 until the marginal product per dollar spent is equal to the marginal product per dollar spent of factor 2, which is at a ratio of 1:2 (since the price of factor 1 is half that of factor 2). Therefore, x₁ should be used in a proportion of 2x₂.

The Production Function Is F(x1, X2) = 1

The Production Function Is F(x₁, X₂) = ₁