1. Two producers of the same good engage in a price fixing by jointly choosing the same price level, which we denote as ?. The

market demand for the good is given by 12 ? ?. Assume that both firms have equal marginal costs of production ? = 2 and

that they can also transfer money (i.e., utility is transferable). If they don't reach an agreement, then they end up with zero

profits (e.g. since they they would end up in the Bertrand duopoly equilibrium) and don't make any transfers. If they agree

on an outcome ? = (?, ?), in which they agree on a price level ? and a transfer ? ? (??,?) from firm 1 to firm 2, their profits

are given by

?1(?, ?) = 1/2(12 ? ?)(? ? 2) ? ?,

?2(?, ?) =1/2(12 ? ?)(? ? 2) + ?.

(a) [0.5pt] Suppose that they can only choose between three price levels ? ? {2, 4, 10}. Formulate this situation as a

bargaining problem by describing the bargaining set ? and the disagreement point ?.

(b) [1pt] Suppose that they can only choose between three price levels ? ? {2, 4, 10}. Calculate the standard bargaining

solution when they have bargaining weights ?1 = 3/4, ?2 = 1/4.

(c) [0.5pt] Suppose that they can choose any price level ? ? [0, 12]. Formulate this situation as a bargaining problem by

describing the bargaining set ? and the disagreement point ?.

(d) [1pt] Suppose that they can choose any price level ? ? [0, 12]. Calculate the standard bargaining solution when they

have bargaining weights ?1 = 3/4, ?2 = 1/4.

1. Two producers of the same good engage in a price xing by jointly choosing the same price level, which we denote as p. The market demand for the good is given by 12 p. Assume that both rms have equal marginal costs of production c = 2 and that they can also transfer money (i.e., utility is transferable). If they don't reach an agreement, then they end up with zero prots (e. g. since they they would end up in the Bertrand duopoly equilibrium) and don't make any transfers. If they agree on an outcome y = (p, t), in which they agree on a price level p and a transfer t E (00, 00) from firm 1 to rm 2, their prots are given by ultp,r)=(12 p)(p 2) t, 1:20), 1:) = $02 p)(p 2) + r. (a) [0.5pt] Suppose that they can only choose between three price levels p 6 {2,4, 10}. Formulate this situation as a bargaining problem by describing the bargaining set V and the disagreement point d. (b) [lpt] Suppose that they can only choose between three price levels p 6 {2,4, 10}. Calculate the standard bargaining solution when they have bargaining weights 11:1 : 3/4, Jr; : 1/4. (c) [0.5pt] Suppose that they can choose any price level 9 E [0, 12]. Formulate this situation as a bargaining problem by describing the bargaining set V and the disagreement point of. (d) [lpt] Suppose that they can choose any price level p E [0, 12]. Calculate the standard bargaining solution when they have bargaining weights in = 3/4, 91'; = 1f4