3. (15 points) Consider these examples of utility functions. For each utility function calculate i) the derivative w.r.t (, U ii) the derivative w.r.t c, U., and iii) the rate at which consumer is willing to substitute leisure for consumption, MRSt,c. (a) Log-additive utility, U(c, !) = aln(c) + bln(1) where a, b are some positive constant. (b) Quadratic utility, U(c, l) = ac" + 613 where a, b, a, B are some positive constant. (c) Iso-elastic utility, - 1 U(c, 1) = - 1 + up 1-7 where o, 7, v, are some non-negative constants, o, y / 1. (d) Linear-quadratic utility, U(c, l) = c- a C+ K 2 where a, b, k, are some positive constants