In period 1, the economy has two possible states a and b, with equal probability of occurrence. Consider the following utility functions defined in the consumption plan c= = [co; Cla; C16]: U(C) 1-7 1-7 U(C) = 1 logco +5 (logcia + logcb) 2 1 1 1 1 + 1 7 2 1 7 1 -e (e-acia +e-4c1b), a > 0 2 Cla'+ 1-7 -aco U(C) Prove that they satisfy: insatiability, continuity and convexity. In period 1, the economy has two possible states a and b, with equal probability of occurrence. Consider the following utility functions defined in the consumption plan c= = [co; Cla; C16]: U(C) 1-7 1-7 U(C) = 1 logco +5 (logcia + logcb) 2 1 1 1 1 + 1 7 2 1 7 1 -e (e-acia +e-4c1b), a > 0 2 Cla'+ 1-7 -aco U(C) Prove that they satisfy: insatiability, continuity and convexity