(Answered) Assume that a firm has cobb-douglas production function of

Economics

Assume that a firm has Cobb-Douglas Production function of the form q = (3LK). Thus her marginal productivity of labor is 3K and the marginal productivity of capital is 3L. Further assume that Sarah has costs such that C = wL + rK where C is some fixed total costs, w is the wage rate and r is the rental rate on capital.

What is the optimal bundle of labor and capital ? What is the output level for this bundle? This can be done (and attempted) in three ways which should all give the same answers.

Book's Substitution method
MRTS = Wage/Rental ratio and Cost constraint method
Lagraingian method.

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