Suppose that the firm’s production activity causes so much pollution that the authorities limit its output to 11 tons in total. By using Lagrangian method, find the number of tons of each of commodity A and B, and the firm’s maximization profit.
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Suppose that the firm’s production activity causes so much pollution that the authorities limit its output to 11 tons in total. By using Lagrangian method, find the number of tons of each of commodity A and B, and the firm’s maximization profit.
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- By selling x tons of the first commodity the firm gets a price per ton given by Px=96-4x By selling y tons of the other commodity the price per ton is given by Py=84-2y The total cost of producing and selling x tons of the first commodity and y tons of the second is given by C(x,y)=2x2+2xy+y2 Suppose that the firm’s production activity causes so much pollution that the authorities limit its output to 11 tons in total. That is x + y = 11. What is the optimal amount of y?Table 17-1Imagine a small town in which only two residents, Rochelle and Alec, own wells that produce safe drinking water. Each week Rochelle and Alec work together to decide how many gallons of water to pump. They bring the water to town and sell it at whatever price the market will bear. To keep things simple, suppose that Rochelle and Alec can pump as much water as they want without cost so that the marginal cost of water equals zero. The weekly town demand schedule and total revenue schedule for water is shown in the table below: Quantity(in gallons) Price Total Revenue(and Total Profit) 0 $60 $0 100 55 5,500 200 50 10,000 300 45 13,500 400 40 16,000 500 35 17,500 600 30 18,000 700 25 17,500 800 20 16,000 900 15 13,500 1,000 10 10,000 1,100 5 5,500 1,200 0 0 Refer to Table 17-1. If this market for water were perfectly competitive instead of…The town has a kayak rental and visitors use the lake for recreation. The town also has a chemical lab that dumps industrial waste into the lake. This pollutes the lake and makes it a less desirable vacation destination. That is, the chemical lab's waste decreases the kayak rental's economic profit. Suppose that the chemical lab could use a different production method that involves recycling water. This would reduce the pollution in the lake to levels safe for recreation, and the kayak rental would no longer be affected. If the chemical lab uses the recycling method, then the chemical lab's economic profit is $900 per week, and the kayak rental's economic profit is $2,600 per week. If the chemical lab does not use the recycling method, then the chemical lab's economic profit is $1,600 per week, and the kayak rental's economic profit is $1,500 per week. These figures are summarized in the following table. Complete the following table by computing the total profit (the chemical lab's…
- The town has a campground whose visitors use the lake for recreation. The town also has a research lab that dumps industrial waste into the lake. This pollutes the lake and makes it a less desirable vacation destination. That is, the research lab's waste decreases the campground's economic profit. Suppose that the research lab could use a different production method that involves recycling water. This would reduce the pollution in the lake to levels safe for recreation, and the campground would no longer be affected. If the research lab uses the recycling method, then the research lab's economic profit is $1,300 per week, and the campground's economic profit is $2,300 per week. If the research lab does not use the recycling method, then the research lab's economic profit is $2,100 per week, and the campground's economic profit is $1,100 per week. These figures are summarized in the following table. NOTE: Choice for first fill-in-blank is (not used or used), for the second its (not use…Consider a lake found in the village of Sturbridge, and then answer the questions that follow. The village has a hiking lodge whose visitors use the lake for recreation. The village also has a chemical plant that dumps industrial waste into the lake. This pollutes the lake and makes it a less desirable vacation destination. That is, the chemical plant's waste decreases the hiking lodge's economic profit. Suppose that the chemical plant could use a different production method that involves recycling water. This would reduce the pollution in the lake to levels safe for recreation, and the hiking lodge would no longer be affected. If the chemical plant uses the recycling method, then the chemical plant economic profit is $1,500 per week, and the hiking lodge's economic profit is $1,800 per week. If the chemical plant does not use the recycling method, then the chemical plant's economic profit is $2,000 per week, and the hiking lodge's economic profit is $1,000 per week. These figures are…Consider a river found in the city of Pittsburgh, and then answer the questions that follow. The city has a water park whose visitors use the river for recreation. The city also has a research facility that dumps industrial waste into the river. This pollutes the river and makes it a less desirable vacation destination. That is, the research facility's waste decreases the water park's economic profit. Suppose that the research facility could use a different production method that involves recycling water. This would reduce the pollution in the river to levels safe for recreation, and the water park would no longer be affected. If the research facility uses the recycling method, then the research facility's economic profit is $1,600 per week, and the water park's economic profit is $2,100 per week. If the research facility does not use the recycling method, then the research facility's economic profit is $2,100 per week, and the water park's economic profit is $1,300 per week. These…
- Consider a river found in the city of Philadelphia, and then answer the questions that follow. The city has a hiking lodge whose visitors use the river for recreation. The city also has a chemical plant that dumps industrial waste into the river. This pollutes the river and makes it a less desirable vacation destination. That is, the chemical plant's waste decreases the hiking lodge's economic profit. Suppose that the chemical plant could use a different production method that involves recycling water. This would reduce the pollution in the river to levels safe for recreation, and the hiking lodge would no longer be affected. If the chemical plant uses the recycling method, then the chemical plant's economic profit is $2,500 per week, and the hiking lodge's economic profit is $2,500 per week. If the chemical plant does not use the recycling method, then the chemical plant's economic profit is $3,000 per week, and the hiking lodge's economic profit is $1,700 per week. These figures…Consider a lake found in the town of Center Barnstead, and then answer the questions that follow. The town has a hiking lodge whose visitors use the lake for recreation. The town also has a tannery that dumps industrial waste into the lake. This pollutes the lake and makes it a less desirable vacation destination. That is, the tannery's waste decreases the hiking lodge's economic profit. Suppose that the tannery could use a different production method that involves recycling water. This would reduce the pollution in the lake to levels safe for recreation, and the hiking lodge would no longer be affected. If the tannery uses the recycling method, then the tannery's economic profit is $1,500 per week, and the hiking lodge's economic profit is $1,800 per week. If the tannery does not use the recycling method, then the tannery's economic profit is $2,000 per week, and the hiking lodge's economic profit is $1,000 per week. These figures are summarized in the following table. Complete the…Differentiate between technical efficiency and economic efficiency with examples
- Assume the firm has historical emissions of 10 units of carbon and the government regulator gives the firm 7 permits to pollute. Each permit allows 1 unit of pollution. Calculate the extra profit (or cost savings) the firm receives from participating in the permit market given their initial allocation of permits (7) and the market price of $8. Show your work. Shade and label the area on the graph that represents your numerical answer from the question above. Upload your graph.Draw a graph with pollution abatement on the horizontal axis (assume a firm can remove up to 100 tons of pollution) and dollars ($) on the vertical axis. Draw one firm's marginal abatement cost curve (MC). Say a pollution tax is imposed on the firm. a. What are the costs the firm would incur if they chose to not reduce pollution at all? b. Is there a different level of pollution abatement the firm could choose that would result in lower costs? c. Label that level of abatement A* on your graph and shade in the area that represents the cost-savings as compared to when they polluted 100 tons (did no abatement)Firm A currently dumps 223 tons of chemicals into the local river. Firm B currently dumps 192 tons of chemicals into the local river. The government has decided to reduce the pollution and from now on will require a pollution permit for each ton of pollution dumped into the river. The government gives each firm 10 pollution permits. The abatement costs of one ton of pollution is $173 for Firm A and $76 for Firm B. What would be the total cost of reducing pollution, if the firms are allowed to trade permits between each other?