Consider a market where demand for the good is given by the equation, ?=120−?. There are...
Consider a market where demand for the good is given by the
equation, ?=120−?. There are 3 firms whose outputs are ?1, ?2 and
?3, and there is no further entry. The marginal cost functions for
each of the 3 firms are as follows: ??1=4 ??2=8 ??3=20
Total market output is ?1+?2+?3=?. Marginal revenue for each of the
firms is given below.
??1=120−2?1−?2−?3 ??2=120−?1−2?2−?3 ??3=120−?1−?2−2?3
a. What is the best-response function for each firm?
Part 2 - Solve the 3 BR functions from Part A simultaneously to find each firm’s output. Show your work clearly. Do not skip steps.
(HINT: Plug Firm 2’s BR function into Firm 1’s BR function and solve for ??. Then, plug Firm 3’s BR function into Firm 1’s BR function and solve for ??. Finally, plug each of the resulting equations from the previous 2 steps into Firm 1’s BR function.)
c. Solve for the market price
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Consider a market where demand for the good is given by the
equation, ?=120−?. There are...
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