Question

Now suppose country A imposes a tax on A's production of to curb emissions. Country B, however, is not taxed. A's cost function is now , while B's cost function is . World demand is . The amount of greenhouse gas emissions per unit is still , such that total world emissions are given by . What are total world emissions after country A enacts a carbon tax?

Answer 1

286.5

Step-by-step explanation:

P=99-qa-qb

MRa=99-2qb-qb

MCa=48

99-2qa-qb=48

Qa=25.5-0.5qb{ best response function of firm A)

MRb=99-qa-2qb

MCb=4

99-qa-2qb=4

Qb=47.5-0.5qa{ best response function of form b}

Qb=47.5-0.5(25.5-0.5qb)

Qb=34.75/0.75=46.33

Qa=25.5-0.5*46.33=2.33

Total world output=46.33+2.33=48.66

Total world emission=0.5*48.66=24.33

p=1146-qa-qb-qc

MRa=1146-2qa-qb-qc

MCa=0

1146-2qa-qb-qc=0

Qa=573-0.5(qb+qc) best response function of firm a)

By symmetry,

Qb=573-0.5(qa+qc)

Qc=573-0.5(qa+qb)

Qb+qc=1146-qa-0.5(qb+qc)

Qb+qc=764-qa/1.5

Qa=573-0.5(764-qa/1.5)=191+qa/3

Qa=191*3/2=286.5

Qa=Qb=Qc=286.5

Total output=3*286.5=859.5( cournot equilibrium market output)

Cartel output=573

Lower QUANTITY in cartel equilibrium compare to cournot equilibrium

=859.5-573

=286.5