Question

All firms produce according to a Cobb-Douglas production function. This production function should look familiar to you. It says that output Q is related to inputs K and L as: This production function implies that the cost-minimizing demand for capital will be Ou where w is the wage rate, r is the cost of capital, Q is output level, and α and β are parameters We will assume that α + β 1; this is the constant-returns-to-scale assumption we saw earlier in the course. Ά ls a technical parameter: an increase în means that the same amount o inputs elds more output. You should be able to see that A is another name for the total factor productivity figure in earlier problem sets Similarly, Oru Note that this function already takes the optimal combinations of capital and labor into account; thi:s assumes that the firm is producing as chcaply as possible, given its technology and factor costs. If you take math econ you will learn how to derive all of this. In this problem set, you can take theso formulas as given and use them answer the questions of this problem set Note that by assumption, an increase in α mplies a reduction in . For given values of r and u, a higher α necessarily means that the firm uses relatively more capital în its production process. Make sure you understand this point.

Answer 1

To prove this, we will consider $\alpha +\beta = 1$ as mentioned in the question

Here is the proof,

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as a+p1 Proved