The Rocky Mashed Potato Factory produces output at costs C = Q 2 , where Q is th

Question

The Rocky Mashed Potato Factory produces output at costs C = Q2, where Q is the quantity of mashed potatoes produced, in tons. In addition, 2 units of emissions are produced for each ton of mashed potatoes (E = 2Q). Pollution damage is $2 for each unit of emissions, which leads the government to charge $2 per unit of emissions as a Pigovian fee. The firm’s output sells competitively for $10 per ton.

1. How many tons of mashed potatoes will the Rocky Mashed Potato Factory produce? How much does it pay for emission fees? What are its profits?

2. A device is invented that would reduce the firm’s emissions to one unit for each ton of output (E = Q). How much would the firm be willing to pay for such device?

3. A device is invented that would reduce the firm’s emissions to one unit for each ton of output (E = Q). How much would the firm be willing to pay for such device if there are no government regulation of pollution emissions? What does this lead you to say about the relationship between government regulation and the market for pollution abatement equipment?

Explanation / Answer

The Rocky Mashed Potato factory produces output at costs C=Q2 (marginal cists 2Q), where Q is the quantity of mashed potatoes produced, in tons. In addition, 2 units of emissions are produced for each ton of mashed potatoes (E=2Q). Polluting damage is $2 for each unit of emissions, which leads the government to charge $2 per unit of emissions as a Pigouvian fee. The firm’s output sells competitively for $10 per ton.

a. How many tons of mashed potatoes will the Rock Mashed Potato Factory produce? How much does it pay in emission fees? What are its profits?

MR= P= 10

MC= 2Q

So in equilibrium MR=MC

10= 2Q

Q= 5

Emission fees = 2Q*2 = 5*4 =$20

Profits= TR-TC-taxes = 10*5 – 2*5 -20 = 20
b. A devise is invented that would reduce the firm’s emissions to one unit for each ton of output (E=Q). How much is the firm willing to pay for such a devise?

With new device the firm saves on emission fees

Savings =2E = Q*2 = 2Q

So it if produce Q= 5

Then savings = 2*5 =10

The maximum it will pay id $ 10 for the new device.
c. How would your answer to part B change if there were no government regulation of pollution? What does this lead you to say about the relationship between government and the market for abatement equipment?

With regulation and emission fees the firm pays emission fees and lowers its profits as it earns only $20.

With no regulation the firm pays no emission fees and earns profits=TR-Tc = 50-20 =30, assuming that it does not reduce its production due to regulation. The government indirectly promotes abatement equipment. With no regulation there will be no demand for abatement devices.

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