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]
1. To find the optimal level of output, we need to equate the marginal cost of production with the marginal benefit to determine where the firm and the economy as a whole can maximize their benefits.
a. From the firm's perspective, the optimal level of output is where marginal cost (MC) equals market price (P). MC is given by the derivative of the supply curve, so we have: MC = dQ/dP = 300.
300 = P
P = 300.
Therefore, the firm's optimal level of output is 300 units of electricity per year.
b. From the economy's perspective, the optimal level of output is where the marginal benefit (MB) equals the marginal cost (MC) of production. MB is equal to the market price (P) minus the cost of the emissions.
MB = P - $31.
Setting MB equal to MC, we have:
P - $31 = 300.
P = $331.
Therefore, the optimal level of output from the economy as a whole is 300 units of electricity per year, with a market price of $331 per unit.
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 is the marginal benefit (MB) to the economy. As discussed in part b, MB is equal to the market price (P) minus the cost of the emissions.
MB = P - $31 = $331 - $31 = $300.
Therefore, 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 $300.
2. To calculate the net annual benefit of the project, we need to compare the costs saved by producing domestically to the benefits of substituting imported shoes.
a. At market prices, the cost of the project is $9.4 million. Since the shoes have a world price of $60 per pair, the total cost savings from substituting 150,000 pairs of imported shoes is:
Total cost savings = 150,000 * $60 = $9 million.
The net annual benefit of the project at market prices is:
Net benefit = Total cost savings - Cost of the project = $9 million - $9.4 million = -$0.4 million.
b. At efficiency prices, we assume that there are no distortions to the EU domestic price of shoes. Therefore, the cost of the project remains at $9.4 million, but the benefits of substituting imported shoes are calculated based on the efficiency price of $60 per pair.
Total cost savings = 150,000 * $60 = $9 million.
The net annual benefit of the project at efficiency prices is:
Net benefit = Total cost savings - Cost of the project = $9 million - $9.4 million = -$0.4 million.
Therefore, the net annual benefit of the project remains the same at both market and efficiency prices: -$0.4 million.
3. The value used for a pair of sport shoes in an efficiency benefit-cost analysis depends on 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, the price used should include the tax, which is 15% of the market price.
Tax = 15% * $46 = $6.9.
Price = $46 + $6.9 = $52.9.
b. If the tax is distortionary and the commodity is a project output that satisfies additional demand, the price used should also include the tax, which is 15% of the market price.
Price = $46 + $6.9 = $52.9 (same as in part a).
c. If the tax is distortionary and the commodity is a project input sourced from existing supply, the price used should be the market price plus the tax.
Price = $46 + $6.9 = $52.9 (same as in part a).
d. If the tax is distortionary and the commodity is a project input sourced from additional supply, the price used should also be the market price plus the tax.
Price = $46 + $6.9 = $52.9 (same as in part a).
e. If the tax is corrective and the commodity is a project output that replaces existing supply, the price used should exclude the tax.
Price = $46.
f. If the tax is corrective and the commodity is a project output that satisfies additional demand, the price used should also exclude the tax.
Price = $46.
g. If the tax is corrective and the commodity is a project input sourced from existing supply, the price used should also exclude the tax.
Price = $46.
h. If the tax is corrective and the commodity is a project input sourced from additional supply, the price used should also exclude the tax.
Price = $46.
Therefore, the prices used in an efficiency benefit-cost analysis under each set of circumstances are:
a. $52.9.
b. $52.9.
c. $52.9.
d. $52.9.
e. $46.
f. $46.
g. $46.
h. $46.
To solve these messy questions, we can break them down and tackle each part step by step. I will guide you through the process of solving each question.
1. For the first question, we are given a supply curve for a competitive firm using coal to generate electricity, which is Q = 300P - 1000, where Q is the quantity produced (units of electricity per year), and P is the market price of electricity per unit.
a. To find the optimal level of output from the viewpoint of the firm, we need to maximize the firm's profit. Profit is equal to the difference between total revenue and total cost. Total revenue is given by P * Q, and total cost is given by the cost of emissions, which is 31 * Q (since each unit of electricity produced results in a tonne of sulfur dioxide emissions costing $31).
So, the profit function for the firm is: Profit = P * Q - 31 * Q
To find the optimal level of output, we need to find the quantity at which the firm's profit is maximized. This can be done by taking the derivative of the profit function with respect to Q, setting it equal to zero, and solving for Q.
b. To find the optimal level of output from the viewpoint of the economy as a whole, we need to consider the external cost of emissions. The external cost of emissions is the cost imposed on society due to pollution. In this case, it is given as $31 per tonne of sulfur dioxide emissions.
To find the optimal level of output for the economy as a whole, we need to include the external cost in the firm's cost function. The new cost function is given by: Cost = 31 * Q.
Similar to part a, we can find the optimal level of output by maximizing the difference between total revenue and total cost. Total revenue is still given by P * Q, and total cost now includes the external cost of emissions, which is 31 * Q.
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 price at which the firm's marginal cost equals the external cost. In other words, it is the price at which the firm is willing to produce an additional unit of electricity, taking into account the external cost.
2. For the second question, we are given information about a proposed project to substitute imported shoes by domestically produced shoes. We are also given the world price of shoes, the EU's import duty, and the costs of the project.
a. To calculate the net annual benefit of the project at market prices, we need to consider the difference between the costs of producing the shoes domestically and the benefits gained from substituting the imported shoes. Subtract the costs of the project from the value of the substituted imported shoes at market prices.
b. To calculate the net annual benefit of the project at efficiency prices, we need to consider the difference between the costs of producing the shoes domestically and the benefits gained from substituting the imported shoes. Subtract the costs of the project from the value of the substituted imported shoes at efficiency prices.
3. For the third question, we are given an ad valorem tax on sports shoes and asked to determine the price to be used in an efficiency benefit-cost analysis under different circumstances.
a. If the tax is distortionary and the commodity is a project output replacing existing supply, the price to be used should be the market price without the tax.
b. If the tax is distortionary and the commodity is a project output satisfying additional demand, the price to be used should be the market price without the tax.
c. If the tax is distortionary and the commodity is a project input sourced from existing supply, the price to be used should be the market price without the tax.
d. If the tax is distortionary and the commodity is a project input sourced from additional supply, the price to be used should be the market price without the tax.
e. If the tax is corrective and the commodity is a project output replacing existing supply, the price to be used should be the market price without the tax.
f. If the tax is corrective and the commodity is a project output satisfying additional demand, the price to be used should be the market price without the tax.
g. If the tax is corrective and the commodity is a project input sourced from existing supply, the price to be used should be the market price without the tax.
h. If the tax is corrective and the commodity is a project input sourced from additional supply, the price to be used should be the market price without the tax.
These are the steps to solve each part of the questions. By following these steps and applying the given information, you should be able to find the answers.