The cost of pollution (in billions of dollars) originating in the paper industry

Question

The cost of pollution (in billions of dollars) originating in the paper industry is
Cp = 2P + P^2
where P is the quantity of pollutants emitted (in thousands of tons). The cost of pollution control (in billions of dollars) for this industry is
Cc = 5 - 3P
A) What is the optimal level of pollution?
P = 2P + P^2
=> MC = 2 + 2P
CC = 5 - 3P
=> MC = -3
to find the optimal level of pollution as recommended, we need to set total marginal cost = 0, then I have
2 + 2P -3 = 0 => 2P -1 = 0 => P = 0.5
You have already evaluated MCP = 2 + 2P and MCC = -3

B) At this level of pollution, what is the marginal cost of pollution?
Part b. now requires you to evaluate MCP when P = 0.5

C) At this level of pollution, what is the marginal cost of pollution control?
Part c. requires you to evaluate MCC when P = 0.5

NOT SURE HOW TO SOLVE B AND C. HELP

Explanation / Answer

b. just plug p=.5 into the first marginal cost equation MC=2+2P MC=2+2(.5) = 3 c. plug p=.5 into the 2nd marginal cost equation MC=5-3P = 5-3(.5) = 3.5

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