What is the overall cost to society from the regulators

Question

1. Suppose each individual in the class represents a firm, which, in the process of producing its output, also produces pollution (designated at ej for firm j). The total cost to the firm from setting it's pollution level at ej is given by

C(ej ) = 1/2(αj - ej )2             (1)

where αj > 0. Your specific value for αj is posted on D2L in the Excel spreadsheet EX450 HW2.xlsx in the Problem Set folder. Suppose the total damages done by emissions is given by

D(E) = 1/2 E2

where E =∑_j=1^N ej denotes total emissions.

(a) Assuming that you are a cost minimizing firm, how much pollution would your firm emit (call this e_j^o ) and what would be the total cost to your firm from those emissions?

(b) What would the total of these costs across all the firms?

(c) What would be the total damages to society from these emissions?

(d) What is the overall cost to society from emissions; i.e., the sum of parts (b) and (c)?

2. Suppose that a regulator comes along and decides that total pollution needs to be reduced to 3050 units (i.e., they set an emissions standard for each firm of ¯ej = 50 units of pollution, with total allowable pollution of E¯ ≡ ∑_j=1^Ne¯j )

(a) What would be the total cost to your firm of the regulator's emissions goal?

(b) What would be the total cost to all firms of the regulator's emissions goal?

(c) What would be the total damages to society of allowed emissions?

(d) What is the overall cost to society from the regulator's emissions goal; i.e., the sum of parts (b) and (c)? Is this an improvement from the unregulated results from part 1.d?

(e) Is this solution a least cost solution? Explain your reasoning.

3. Suppose that a regulator decides to instead set an emissions tax of $25 per unit of emissions

(a) Facing this tax, how much pollution would your firm choose to emit? What would be the total cost to your firm from these emissions?

(b) What would be the total emissions and what would be the total cost to all firms from their emissions?

(c) What would be the total damages to society of allowed emissions?

(d) What is the overall cost to society from the emissions; i.e., the sum of parts (b) and (c)? Is this an improvement from the unregulated results from part 1.d? Is this an improvement over the command and control results from part 2.d?

(e) Is this solution a least cost solution? Explain your reasoning.

Attachment:- 1443298_2_EC450-HW2.xlsx