Cobb douglas example2/29/2024 Therefore, to find the optimal bundle, we will set the MRS equal to the price ratio and plug the result back into the budget constraint. It is very flexible, allowing one to make adjustments to it. A Cobb-Douglas utility function is a sub-category of utility functions. Suppose a consumer, David, is shopping for a refrigerator. The partial derivative of Y with respect to X2, keeping other. Let us look at a few utility function examples to understand the topic better. It’s easy to see that all the conditions for using the Lagrange method are met: the MRS is infinite when $x_1 = 0$, zero when $x_2 = 0$, and smoothly descends along any budget line. Therefore, the marginal product of labour goes on diminishing with the increase in labour input. Demand Functions and Their Representations 8.2 Demand Functions for Cobb-Douglas Utility Functionsįor a generic Cobb-Douglas utility function Cobb-Douglas is an example: MRS ( / ) (Y / X) Useful properties: 1 Tangency condition solves to Relative demand function Y / X f(P X / P Y) The elasticity of this function is the elasticity of substitution in consumption.
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