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Cobb-Douglas%20Production%20Function

# Cobb-Douglas%20Production%20Function - Cobb-Douglas...

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Cobb-Douglas Production Function Production function of the form q AK L α β = , where q is the rate of output, K is the quantity of capital, and L is the quantity of labor, and where A, α, and β are constants. As in consumer theory, the optimum choice of K and L can be analyzed by the problem of choosing the highest production isoquant tangent to a give isocost line. This gives rise to the same first order conditions as the more usual problem we treated in Class, which was Minimise 0 wL rK C + = Subject to the constraint ( , ) F K L AK L α β = (1) For Cobb-Douglas production function, the firm’s marginal rate of technical substitution between labor and capital is as following dK/dL= 1 1 ( , ) ( , ) K L LK MP K L AK L K MRTS MP K L AK L L α β α β β β α α - - = = = (2) Where 1 ( , ) ( , ) L F K L MP K L AK L L α β β - = = is the marginal product of labor. 1 ( , ) ( , ) K F K L MP K L AK L K α β α - = = is the marginal product of capital.

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