i am not a spoon feeder, i just don't have any idea about these messy questions.

ASSIGNMENT 5: DUE 4.00PM, 4/09/08
1. A competitive firm uses coal to generate electricity. Its supply curve is Q = 300P
- 1000, where Q is quantity produced (units of electricity per year), and P is
market price of electricity per unit. The production of each unit of electricity
results in a tonne of sulphur dioxide emissions which is estimated to cost the
economy $31. If the market price of electricity is $45 per unit, what is the
optimal level of output from the viewpoint of:
a. The firm? [2 marks]
b. The economy as a whole? [2 marks]
c. If the firm is producing the economy¡¯s optimal output level, what price
should be used to represent the value of an extra unit of output of electricity
to the economy as a whole? [2 marks]
[6 marks]
2. Assuming that shoes have a world price of US$60 a pair, that the EU has a 45%
ad valorem import duty on footwear which applies to all types of footwear and
an Italian company is proposing a project to substitute 150,000 pairs of
imported shoes by domestically produced shoes. The annual cost of the project
(operating cost plus annual equivalent capital cost) at both market and
efficiency prices are $9.4 millions. Apart from the tariff there are no other
distortions to the EU domestic price of shoes. Calculate the net annual benefit
of the project:
a. At market prices. [2 marks]
b. At efficiency prices. [2 marks]

3. An ad valorem tax of 15% applies to sports shoes which have a market price
(i.e. price including the tax) of $46 per pair. What price (give the value in
dollars) should be used for a pair of sport shoes in an efficiency benefit-cost
analysis under each of the following sets of circumstances: [0.25 mark each]
a. The tax is distortionary and the commodity is a project output which
replaces existing supply;
b. The tax is distortionary and the commodity is a project output which satisfies
additional demand;
c. The tax is distortionary and the commodity is a project input which is
sourced from existing supply;
d. The tax is distortionary and the commodity is a project input which is
sourced from additional supply;
e. The tax is corrective and the commodity is a project output which replaces
existing supply;
f. The tax is corrective and the commodity is a project output which satisfies
additional demand;
g. The tax is corrective and the commodity is a project input which is sourced
from existing supply;
h. The tax is corrective and the commodity is a project input which is sourced
from additional supply
[4 marks]

To answer the questions in Assignment 5, let's break them down step-by-step:

1. Optimal level of output:
a. The firm's optimal level of output is determined by setting the marginal cost (MC) equal to the price (P). In this case, the supply curve is Q = 300P - 1000. To find the MC, we take the derivative of the supply curve with respect to quantity (Q): MC = dQ/dP = 300. So, when MC = P, we have 300 = P. Substituting P = $45 into the equation, we find the optimal level of output from the firm's viewpoint is 300 * $45 - 1000 = 13500 units of electricity per year.

b. The economy's optimal level of output is determined by setting the marginal social cost (MSC) equal to the marginal social benefit (MSB). The MSC includes both the firm's marginal cost and the external cost of sulfur dioxide emissions. In this case, the external cost is estimated to be $31 per unit of electricity. So, the MSC is MC + $31 = 300 + $31 = 331. As before, the MSB is equal to the price (P). So, when MSC = MSB, we have 331 = P. Substituting P = $45 into the equation, we find the optimal level of output from the economy's viewpoint is 300 * $45 - 1000 = 13500 units of electricity per year.

c. If the firm is producing the economy's optimal output level, the price that should be used to represent the value of an extra unit of output of electricity to the economy as a whole is the market price of electricity, which is $45 per unit.

2. Net annual benefit of the project:
a. At market prices, we need to calculate the net benefit by subtracting the project cost from the revenue generated by the domestic production of 150,000 pairs of shoes. Since the world price is $60 per pair, the revenue from domestic production would be 150,000 * $60 = $9 million. Subtracting the project cost of $9.4 million, we get a net annual benefit of -$0.4 million.

b. At efficiency prices, we assume that the EU domestic price of shoes is distorted by the import duty. Since the EU has a 45% ad valorem import duty on footwear, the domestic price is 45% higher than the world price. So, the domestic price would be $60 + ($60 * 45%) = $87 per pair. Using the same calculation as in part a, the revenue from domestic production would be 150,000 * $87 = $13.05 million. Subtracting the project cost of $9.4 million, we get a net annual benefit of $3.65 million.

3. Price for efficiency benefit-cost analysis:
a. When the tax is distortionary and the commodity is a project output that replaces existing supply, the price used in the analysis should be the market price minus the tax. In this case, the market price is $46 per pair, so the price used would be $46 - ($46 * 15%) = $39.10.

b. When the tax is distortionary and the commodity is a project output that satisfies additional demand, the price used should be the market price plus the tax. In this case, the price used would be $46 + ($46 * 15%) = $52.90.

c. When the tax is distortionary and the commodity is a project input that is sourced from existing supply, the price used should be the market price plus the tax. In this case, the price used would be $46 + ($46 * 15%) = $52.90.

d. When the tax is distortionary and the commodity is a project input that is sourced from additional supply, the price used in the analysis should be the market price minus the tax. In this case, the market price is $46 per pair, so the price used would be $46 - ($46 * 15%) = $39.10.

e. When the tax is corrective and the commodity is a project output that replaces existing supply, the price used would be the market price.

f. When the tax is corrective and the commodity is a project output that satisfies additional demand, the price used would be the market price.

g. When the tax is corrective and the commodity is a project input that is sourced from existing supply, the price used would be the market price.

h. When the tax is corrective and the commodity is a project input that is sourced from additional supply, the price used would be the market price.

I hope this helps! Let me know if you have any further questions.

To answer these questions, you will need to understand some basic economic concepts and use relevant formulas. I will guide you through the process of finding the answers.

1. a. To find the optimal level of output for the firm, you need to maximize its profit. Profit is calculated as total revenue minus total cost.
- Total revenue (TR) is equal to the quantity produced (Q) multiplied by the price (P): TR = Q * P.
- Total cost (TC) consists of the production cost and the cost of emissions. The cost of emissions is the quantity produced (Q) multiplied by the cost per unit of emissions ($31).
- Profit (π) is calculated as π = TR - TC.
- To maximize profit, take the derivative of profit with respect to Q and set it equal to zero. Solve for Q.

b. To find the optimal level of output for the economy as a whole, you need to take into account the cost of emissions. The social cost of emissions is the cost to the economy per unit of emissions. Multiply the quantity produced (Q) by the cost per unit of emissions ($31) to find the total cost of emissions. Subtract this cost from the total revenue (TR) to find the net benefit to the economy. Again, maximize net benefit by taking the derivative with respect to Q and setting it equal to zero. Solve for Q.

c. The price that represents the value of an extra unit of output to the economy as a whole can be found by taking the derivative of net benefit with respect to Q and setting it equal to zero. Solve for P.

2. To calculate the net annual benefit of the project, you need to consider the difference in costs between imported shoes and domestically produced shoes. Subtract the cost of producing domestically from the cost of importing. Multiply this difference by the number of pairs of shoes (150,000) to find the net annual benefit.

a. The net annual benefit at market prices is the difference in costs at the market price of shoes.

b. The net annual benefit at efficiency prices is the difference in costs at the efficiency price of shoes.

3. To find the price that should be used in an efficiency benefit-cost analysis under different circumstances, you need to consider whether the tax is distortionary or corrective and whether the commodity is a project output or input.

a. If the tax is distortionary and the commodity is a project output that replaces existing supply, subtract the tax rate (15%) from the market price ($46).

b. If the tax is distortionary and the commodity is a project output that satisfies additional demand, subtract the tax rate from the market price.

c. If the tax is distortionary and the commodity is a project input sourced from existing supply, add the tax rate to the market price.

d. If the tax is distortionary and the commodity is a project input sourced from additional supply, add the tax rate to the market price.

e. If the tax is corrective and the commodity is a project output that replaces existing supply, subtract the tax rate from the market price.

f. If the tax is corrective and the commodity is a project output that satisfies additional demand, subtract the tax rate from the market price.

g. If the tax is corrective and the commodity is a project input sourced from existing supply, add the tax rate to the market price.

h. If the tax is corrective and the commodity is a project input sourced from additional supply, add the tax rate to the market price.

By following these steps and using the relevant formulas, you should be able to find the answers to the questions. Remember to show your calculations and clearly explain your reasoning to receive the full marks. Good luck with your assignment!