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Cobb-douglas production function of the form

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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.

Reference no: EM131293296

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