Question
Asked Nov 28, 2019
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Let the production function be Q = 4∗K1/4L1/4 assume that both factors are variable.

  1. (a)  Derive the contingent demand functions for K and L

  2. (b)  Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function.

  3. (c)  FindtheamountofKandLnecessarytoproduceQ=8whenv=16andw=1 (with minimal possible cost).

  4. (d)  Find the average and marginal cost functions.

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Expert Answer

Step 1

As per our Honor code, we can attempt only first three parts of the question.

Step 2

Production function is given to be- Q = 4K1/4L1/4

Cost constraint is – C = wL + vK

L = Labor

w = Wage of labor

K = Capital

v = Rent of capital

a) Production function is to be maximized subject to the cost constraint.

Lagrange function to be used for this is-

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Step 3

Now, for maximization, the function is to be differ...

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