Statistics Solutions

[Steps Shown] A firm uses inputs x_1 and x_2 to produce output y according to the following production function: f(x_1, x_2)= x_I^I / 2 x_2^1 / 2. The factor

Question: A firm uses inputs \(x_{1}\) and \(x_{2}\) to produce output \(y\) according to the following production function: \(f\left(x_{1}, x_{2}\right)=\) \(x_{I}^{I / 2} x_{2}^{1 / 2}\). The factor prices are \(p_{1}=\\) 10$ and \(p_{2}=\\) 15$ and the firm can hire as much of either factor it wants at these prices. (i) Determine whether the firms Marginal Cost (MC) is increasing, decreasing or constant. (ii) Can you find the profit maximizing or cost minimizing level of (a) output and (b) inputs? If your answer is YES, find the answers. If your answer is NO, justify your answer. (iii) Can you find in what proportions should the firm use factors 1 and 2 ? If your answer is YES, find the answers. If your answer is NO, justify your answer.

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