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


"\\pi"A=(2-(QA+QB ))QA+QA


=2QA-QA2-QAQB-QA


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

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


"\\pi"B=(2-(QA+QB ))QB-0.5QB


=2QB-QAQB-QB2-0.5QB


"\\frac{\\delta\\pi _{B}}{\\delta Q_{B}}=2-Q_{A}-2Q_{B}-0.5=0" =2-2QA-QB-1=0


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

Putting QB in QA

"2-1.5-Q_{A}=2Q_{B}"


0.5=3QA


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


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


"\\therefore" P=2-(0.17+0.67)


P=1.16


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