Answer to Question #263846 in Macroeconomics for Ateek

Question #263846

Company A is the only supplier of glass in Big Apple City used for tall buildings’ exteriors. Its marginal cost of production is cA=1, and it has no other production costs. The demand for such glass in Big Apple city is QD=2-P. Company B in Jersey City produces the same glass and is considering whether to expand to Big Apple city. If it enters, it needs to get a permit to allow it to be a supplier in the Big-Apple city at a cost of L=0.5, which does not vary with quantity of output, and its marginal cost of production is cB=0.5. If it expands to the Big-Apple city, companies A and B both supply to the market, and the market price P satisfies QA+QB=2-P, where QA is company A’s production level and QB is company B’s


If company B expands to the Big-Apple city, what is the resulting price in a Nash equilibrium?






1
Expert's answer
2021-11-11T12:14:14-0500

Company A is the only supplier of glass:

QA+QB =2-P


CA=QA, CB=0.5QB


P=2-QA+QB


TR=P.Q

=(2-(QA+QB ))Q


π\piA=(2-(QA+QB ))QA+QA


=2QA-QA2-QAQB-QA


δπAδQA\frac{\delta\pi _{A}}{\delta Q_{A}} =2-2QA-QB-1=0

1QB2=QA\frac{1-Q_{B}}{2}=Q_{A} .....................................................1


π\piB=(2-(QA+QB ))QB-0.5QB


=2QB-QAQB-QB2-0.5QB


δπBδQB=2QA2QB0.5=0\frac{\delta\pi _{B}}{\delta Q_{B}}=2-Q_{A}-2Q_{B}-0.5=0 =2-2QA-QB-1=0


1.5QA2=QB\frac{1.5-Q_{A}}{2}=Q_{B} …......................................................2

Putting QB in QA

21.5QA=2QB2-1.5-Q_{A}=2Q_{B}


0.5=3QA


QA=0.53=0.17\frac{0.5}{3}=0.17


QB=1.50.172=0.67\frac{1.5-0.17}{2}=0.67


\therefore P=2-(0.17+0.67)


P=1.16


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment