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show step and ans 16 The duopolists Carl and Simon face a demand function for pu

ID: 1217910 • Letter: S

Question

show step and ans

16 The duopolists Carl and Simon face a demand function for pumpkins of 2,200 400 where Dis the total number of pumpkins that reach the market and P is the price of pumpkins Suppose further that each farmer has a constant marginal cost of $1.50 for each pumpkin produced If Carl believes that Simon is going to produce os pumpkins this year, then the reaction function tells us how many pumpkins Carl should produce in order to maximize his profits. Carl's reaction function is a. Rc (OS) 400-gs/2 b. Re (OS) 2,200- 8000s Re (os) 800-os/2 d. RC (OS) 2,200-4000s e. RC (OS) 400-os

Explanation / Answer

Ans: 800 - Qs/2

Explanation:

Q = 2200 - 400P

The inverse demand function: P = 5.5 - 0.0025Q

Q = Qc + Qs

P = 5.5 - 0.0025(Qc + Qs)

   = 5.5 - 0.0025Qc - 0.0025Qs

TR for Carl = P * Qc = 5.5Qc - 0.0025Qc2 - 0.0025QcQs

MRc =5.5 - 0.005Qc - 0.0025Qs

MC = 1.50

for equilibrium condition is MRc = MC

5.5 - 0.005Qc - 0.0025Qs = 1.50

=> 0.005Qc = 4 - 0.0025Qs

=> Qc = 800 - 0.5Qs or 800 - Qs/2