Apolluter has total abatement cost of t ac = 20a2 , where a is the amount it abates relative to uncontrolled emissions of 100 tons. a performance standard requires it to abate as = 20. the polluter faces a fine of $10,000 if any non-compliance is detected. (a) initially, suppose any noncompliance is detected with certainty. will the polluter comply with the performance standard? what a does the polluter choose? explain with numbers. (b) now suppose the probability of detection increases with the amount of the violation, p = .02v, where v = as − a. does the polluter comply? what level of a does the polluter choose? (c) what are the expected marginal costs to the polluter of violating the standard in part (b)? is this mc increasing, decreasing or constant? suppose the government tightens the standard to some higher as > 30. how will the polluter’s choice of a and v change in response? (d) now suppose the detection returns to being certain. how much will the polluter violate the standard with a fine of $200 per ton of violation? (e) now assume the same $200 per ton fine but detection only occurs with 50% probability? what happens to the marginal cost of violations? what about compliance?