Two dairy farmers produce milk for a local town with local milk demand given by Q=100-1/3P (P denotes price measured in Rands, Q denotes the quantity measured in liters). Both farmers have the same cost function given by TC=150 +2q (where denotes output). (a) Determine the reaction function of each farmer. (b) Find the Cournot-Nash equilibrium. (c) Calculate profits for each farmer
Two dairy farmers produce milk for a local town with local milk
(P denotes price measured in Rands, Q denotes the quantity measured in liters). Both farmers have the same cost function given by TC=150
+2q
(where
denotes output).
(a) Determine the reaction function of each farmer.
(b) Find the Cournot-Nash equilibrium.
(c) Calculate profits for each farmer
(d) Suppose that both farmers decide to form a cartel, determine profits
for each farmer under the cartel
(e) What output should farmer 1 produce if he/she expects their rival to produce 20 units?
(f) Calculate the profits if farmer 2 decides to break the cartel agreement
(g) Does joining a cartel offer any benefits to both farmers? Justify your answer
(h) What if farmer 1 is a leader and farmer 2 a follower, determine the price, quantity and profits made by these two farmers.
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