Answer to Question #263846 in Macroeconomics for Ateek

Question

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?

Answer 1

Company A is the only supplier of glass:

Q_A+Q_B =2-P

C_A=Q_A, C_B=0.5Q_B

P=2-Q_A+Q_B

_TR=P.Q

=(2-(Q_A+Q_B ))Q

$\pi$_A=(2-(Q_A+Q_B ))Q_A+Q_A

=2Q_A-Q_A²-Q_AQ_B-Q_A

$\frac{\delta\pi _{A}}{\delta Q_{A}}$ =2-2Q_A-Q_B-1=0

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

$\pi$_B=(2-(Q_A+Q_B ))Q_B-0.5Q_B

=2Q_B-Q_AQ_B-Q_B²-0.5Q_B

$\frac{\delta\pi _{B}}{\delta Q_{B}}=2-Q_{A}-2Q_{B}-0.5=0$ =2-2Q_A-Q_B-1=0

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

Putting Q_B in Q_A

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

0.5=3Q_A

Q_A=$\frac{0.5}{3}=0.17$

Q_B=$\frac{1.5-0.17}{2}=0.67$

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

P=1.16