Two people, Cat and Dog, each start their lives with an inco…

Two people, Cat and Dog, each start their lives with an income of 100, and they don’t discount the future (beta = 1). Life lasts, alas, only two periods, and they can borrow or save at the interest rate of 100% per period–so hypothetically, if they only consumed in the future, they could consume a total of 200 in the future.  Cat’s utility function is square root [c0.5], and Dog’s utility function is natural log [ln(c)]. Like everyone else, they try to maximize their lifetime utility subject to their budget constraint.  Who will consume more in the future, Cat or Dog?