A two person partnership between a coder and a marketer yields profits (a, b) = 6a 1/3 b 1/3 where: a 0 is the measure of the coders effort; b 0 is the measure of the marketers effort. The profits are evenly split between the two partners.
- a 2 D. A two person partnership between a coder and a marketer yields profits #(a,b) = 6a1/351/3 where: a> 0 is the measure of the coder's effort; b > 0 is the measure of the marketer's effort. The profits are evenly split between the two parters. The coder's utility is ue(a,b) = }#(a,b) a and the marketer's utility is um(a,b) = z(a, b) b. This problem asks you to compare three different vectors of choices by the two. You may use the fact that the function (:,:) is strictly concave for a, b >0. The efficient choices of efforts are the pair (a, be) that solve the problem maxa,b20 [ue(a,b) + Um(a, b)]. The equilibrium choices of efforts are pair(s) (a*, b*) that simultaneously solve maxa>o uc(a,b*) and maxb>0 Um(a*, b). The leader-follower quantities are the subgame perfect equilibrium (a$9P, 689P) for the game in which the coder chooses a before the marketer, the marketer learns what a is before they choose b, and b*(a) denotes the marketer's best choice given a. D.1. Give and solve the FOCs for the efficient choices, (a,b). D.2. Find both Nash equilibria. (Hint: if the other is putting in no effort, ... ] D.3. Show that the equilibrium levels of effort are inefficient. D.4. Show that the subgame perfect levels of effort are inefficient. D.5. What is the ranking of the utility levels in the positive equilibrium, the subgame perfect equilibrium, and the efficient outcomes? Explain. - a 2 D. A two person partnership between a coder and a marketer yields profits #(a,b) = 6a1/351/3 where: a> 0 is the measure of the coder's effort; b > 0 is the measure of the marketer's effort. The profits are evenly split between the two parters. The coder's utility is ue(a,b) = }#(a,b) a and the marketer's utility is um(a,b) = z(a, b) b. This problem asks you to compare three different vectors of choices by the two. You may use the fact that the function (:,:) is strictly concave for a, b >0. The efficient choices of efforts are the pair (a, be) that solve the problem maxa,b20 [ue(a,b) + Um(a, b)]. The equilibrium choices of efforts are pair(s) (a*, b*) that simultaneously solve maxa>o uc(a,b*) and maxb>0 Um(a*, b). The leader-follower quantities are the subgame perfect equilibrium (a$9P, 689P) for the game in which the coder chooses a before the marketer, the marketer learns what a is before they choose b, and b*(a) denotes the marketer's best choice given a. D.1. Give and solve the FOCs for the efficient choices, (a,b). D.2. Find both Nash equilibria. (Hint: if the other is putting in no effort, ... ] D.3. Show that the equilibrium levels of effort are inefficient. D.4. Show that the subgame perfect levels of effort are inefficient. D.5. What is the ranking of the utility levels in the positive equilibrium, the subgame perfect equilibrium, and the efficient outcomes? Explain
