In class we learned about the Cobb-Douglas utility function, which is sometimes assumed by economists. Another is called the CES (stands for Constant Elasticity of Substitution) utility function: U=U(x,y)=(x^+y^)^(1/) where , and are constants.

(a) Just as we have a "shortcut formula" for the MRS for the Cobb-Douglas utility function

MRS=-(y/x)

we can derive a shortcut formula for the MRS for the CES utility function. Do so, showing your work

(b) Actually, the Cobb-Douglas utility function is a special case of the CES utility function. That is, when you assume particular value(s) for the parameter(s) ( , and/or ) you get the Cobb-Douglas function. Based on your answer to (a), what assumption(s) about the parameter(s) give you the Cobb-Douglas function? Explain.