Answer:
a) attached files.
b) if they are forcer to decrease pollution by 4,000 tons then:
firm A cost 160,000
firm B cost 240,000
c) if there is a ton of $240 per ton oth firm will find more attractive to emliminate pollution than to pay taxes.
Explanation:
Marginal cost for Plant 1 = 0.02Q
Marginal cost for Plant 2 = 0.03Q
The marginal cost represent the derivate of the cost fuction
so we solve for the cost function as follow:
[tex]\frac{dF(x)}{dx} x^{a} = a \times x^{a-1}[/tex]
we got 0.02 as dC(q)/dq
so the cost fuction is:
[tex]\frac{dC(q)}{dq} = 2 \times 0.01q^{1} \\C(q) = 0.01q^{1+1} = 0.01q^{2}[/tex]
same procedure for hte second plant
[tex]\frac{dC(q)}{dq} = 2 \times 0.015q^{1} \\C(q) = 0.015q^{1+1} = 0.015q^{2}[/tex]
Now we made the graph of this function
We slve for q = 4,000
0.01 x 4,000^2 = 160,000
0.015 x 4,000^2 = 240,000
If there is a tax for 240 dollar per ton then, the factory will eliminate tons up to that amount so it finds equilibrium.
0.02q = 240
q = 240/0.01 = 12,000
Plant 1 will eliminate the entire 8,000 tons as is below the tax floor
Plant 2
0.03q = 240
q = 240/0.03 = 8,000
Plant 2 will also eliminate pollution as is preferable to pay the taxes.
