Nonetheless, the Cobb–Douglas function has been applied to many other contexts besides production. It can be applied to utility as follows: U(x1,x2)=x1αx 2β; ...
These two expressions are mathemat- ically equivalent. The Cobb-Douglas function is three dimensional with utility or output mea- sured along the vertical axis.
calculus. For example, if the utility function is. U = xy then. MRS = y x. This is a special case of the "Cobb-Douglas" utility function, which has the form: U = xayb.