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.