Which utility function yields a constant price elasticity of demand function?

Question

How do I know which utility function I can use to find an isoelastic demand function. And similarly, which cost function can I use to find an isoelastic supply function?Does it work through trial and error, or is there a particular method?

Answer 1

any constant elasticity of substitution utiltity will generate an MRS = (Y/X)^k where k is the elasticity of substitution. the demand curves will be iso elastic