The Rocky Mashed Potato factory produces output at costs C=Q2 (marginal cists 2Q

Question

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 selsl competitively for $10 per ton. ( at least 250 words total)

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?

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?

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?

Explanation / Answer

Given that c=Q2 and the emissions per unit of production is 2Q and the government charges 2$ for each unit of emission and Price=$10

a)Thus the profit function is

Profit=Price*Quantity- Cost

10*Q-Q2 -2*2Q

Now differentiating this we have

10-2Q-4=0

Solving this we get Q=3

Putting Q=3, in the profit function we get

10(3)-3*3-4(3)=9

The emission fee is 4*3=12

b)Now if E=Q due to introduction of a new machine, Then the firm saves 2Q of the emission fees. So the firm will be willing to pay at maximum 2Q or less than that.

c)If there were no Government regulation,then the firm would not buy the machine. It would pollute the environment and maximize its profit.

In this case, if the firm is to run in the market based approach, then it would ignore the pollution or its emmsssion and thus degrade the environment. This would cause harmful effects on other people. This is the example of negative externality. Here comes the necessity of the intervention of the government. The Government will force the market or the firm to bear its external cost.

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