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In the following videos, we try to find MRS for several utility functions, say, cobb douglas, perfect complements, perfect substitutes. MRS calculates the rate at which one good is substituted for another, keeping utility constant. MRS for Cobb Douglas changes at every point along an indifference curve. MRS for perfect complements is same along a vertical or horizontal strip, while it is not defined at the kink. In case of perfect substitutes, MRS is same along the entire indifference curve.

In the last video, we do one small application related to cobb douglas, where expenditure shares of both goods are found. But to do this application, you should have little knowledge about, how to find, marshallian demand curve of cobb douglas, which you can see here. You can carry this application and do it for perfect complements and perfect substitutes too.

Calculate MRS for the cobb-douglas utility function, u=xy, at the point (5,10)

 

Show by an example that MRS for perfect substitutes is a constant.

 

Derive the MRS in case of perfect complements.

 

Calculate the expenditure share of x and y if the utility function is cobb douglas, u=xy