EBK MICROECONOMICS
5th Edition
ISBN: 9781118883228
Author: David
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Question
Chapter 1, Problem 1.17P
To determine
(a)
The objective function for the given problem.
Expert Solution
Answer to Problem 1.17P
The objective function for the given problem is to minimize
Explanation of Solution
The objective function is the relationship that is maximized (or minimized) by the decision-maker.
Here, in the given case, the firm is seeking to minimize the total cost to operate plant one and two. Therefore, the objective function will be:
To determine
(b)
The constraints for the given problem.
Expert Solution
Answer to Problem 1.17P
The constraints for the given problem is:
Explanation of Solution
A constraint is a restriction that will be placed on the firm.
Here, in the given case the firm will have 1 million metric tons of emission. Therefore, the constraint can be given as:
To determine
(c)
The statement of constrained optimization.
Expert Solution
Answer to Problem 1.17P
The statement of constrained optimization is:
Explanation of Solution
A statement of constrained optimization states the kind of functions a decision-maker wants to minimize or maximize along with the constraints.
In this, the perspective of the decision-maker must be considered.
In the given case, the objective function is
The given constraint is
. Therefore, the statement for the constraint optimization can be given as:
To determine
(d)
The emission level from each plant chosen by the firm.
Expert Solution
Answer to Problem 1.17P
The emission level from each plant chosen by the firm is given as:
| Emission plant 1 (X) | TC plant 1 | Emission plant 2 (Y) | TC plant 2 | TC |
| 0 | $490 | 1,000,000 | $10 | $500 |
| 250,000 | $360 | 750,000 | $40 | $400 |
| 500,000 | $250 | 500,000 | $90 | $340 |
| 750,000 | $160 | 250,000 | $160 | $320 |
| 1,000,000 | $90 | 0 | $250 | $340 |
Explanation of Solution
The allocation of operating cost for plant 1 and plant 2 can be represented in the following tabular form:
| Emission plant 1 (X) | TC plant 1 | Emission plant 2 (Y) | TC plant 2 | TC |
| 0 | $490 | 1,000,000 | $10 | $500 |
| 250,000 | $360 | 750,000 | $40 | $400 |
| 500,000 | $250 | 500,000 | $90 | $340 |
| 750,000 | $160 | 250,000 | $160 | $320 |
| 1,000,000 | $90 | 0 | $250 | $340 |
From the above table, it is concluded that when X =750,000 metric tons and Y = 250,000 metric ton, then the total operating cost is minimized.
Want to see more full solutions like this?
Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Portland is trying to reduce annual NOx emissions by 200 units. Its environmental
planners are now deciding how to allocate the abatement mandate between cars and
power plants. The marginal costs of abatement from cars (Qc) and abatement from
plants (Qp) are MACC = 3Qc and MACP = Qp. Each source is currently emitting 200
units (so total emission from both sources are 400). (Note: Q is the quantity of
abatement and the goal is to abate a total of 200 units).
%3D
(a) On your work sheet Graph the two marginal cost lines (on two separate graphs).
(b) The traditional approach has been to assign all 200 units of abatement to the
power plants, i.e. Qc = 0 and Qp = 200. What is the total cost of abatement under
this system?
Show your calculations on your work sheet and enter the total cost in the blank
below.
(c) The planners have hired you to tell them what the cheapest way is for the city to
divide the 200 units of abatement between the two sources. What do you tell them?
(ie. what are Qc"…
Following are the marginal abatement costs of three firms . Suppose each firm is currently emitting 10 tons / week , so the total emissions are 30 tons / week . Suppose we wish to reduce total emissions by 50 % , to 15 tons per week . The following table provides marginal abatement costs for each firm .
a ) What is the total cost if each firm cuts total emission by 50 % from their current levels .
b ) What is the total cost if the total emissions decrease by 50 % ( to 15 tons per week ) that meets the equi - marginal principle .
c ) From the society's point , which method of reducing ( a or b above ) emissions is better ? Provide a reason .
The local environmental authority levied an emissions fee of $30 per ton of waste on a firm that has the marginal cost of abatement (MCA) curve displayed in the figure below. What level of emissions will the firm release? How much will it pay in emissions fees?
Chapter 1 Solutions
EBK MICROECONOMICS
Ch. 1 - Prob. 1RECh. 1 - Prob. 2RECh. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 1.1PCh. 1 - Prob. 1.2PCh. 1 - Prob. 1.3P
Ch. 1 - Prob. 1.4PCh. 1 - Prob. 1.5PCh. 1 - Prob. 1.6PCh. 1 - Prob. 1.7PCh. 1 - Prob. 1.8PCh. 1 - Prob. 1.9PCh. 1 - Prob. 1.10PCh. 1 - Prob. 1.11PCh. 1 - Prob. 1.12PCh. 1 - Prob. 1.13PCh. 1 - Prob. 1.14PCh. 1 - Prob. 1.15PCh. 1 - Prob. 1.16PCh. 1 - Prob. 1.17PCh. 1 - Prob. 1.18PCh. 1 - Prob. 1.19PCh. 1 - Prob. 1.20PCh. 1 - Prob. 1.21P
Knowledge Booster
Similar questions
- questions 3a and 3barrow_forwardam. 337.arrow_forwardGlobal warming is mainly caused by Greenhouse gas (GHG) (i.e., CO2) emission. Aiming to be carbon neutral by 2060, China starts penalizing the polluting firms by introducing a specific tax to those firms. (Source: https://www.nature.com/articles/d41586-020-02927-9)Suppose you are the owner of a profit-maximizing firm in China that produces goods with carbon emission. The specific tax (with tax rate t) is imposed in proportion to the quantity of your firm’s output (q). The market of your firm’s product is assumed to be perfectly competitive. Assume there is no fixed cost: use a fully labelled diagram to show the effect of the tax on the cost curves, and briefly discuss the movement of the curves. (10 marks) Suppose China government decides to raise the tax rate. Discuss the impact of the rise on your firm's output level with economic models wherever necessary. (20 marks)arrow_forward
- Two coal-burning electric power plants are emitting mercury which impairs cognitive development in children. Plant A's marginal abatement cost is MCA= 1.2q and plant B's marginal abatement cost is MCB = 0.3q. Each firm initially emits 50 units and the EPA would like to reduce total emissions to 40. If the EPA follows a command-and-control policy and tells each firm to abate by the same amount, what will be the total costs? If firms could trade permits, what would happen to total costs? Why?arrow_forwardImagine a firm's marginal abatement cost function with existing technologies is: MAC = 20 E. If the firm adopts new pollution abatement technologies, its marginal abatement cost function will be: MAC = 100.5E. The adoption costs for the new technology are $4. If the government raises the tax on emissions from $2 to $4, the firm's total costs increase by $ HINT: Total costs include tax payments, total abatement costs, and (if relevant) adoption costs for the new technology. Question 14Select one: a. $20. b. $ 24. c. $10. d. $30.arrow_forwardConsider two firms with the following marginal abatement costs (MAC) as a function of emissions (E): MAC 110-2E_1 MAC 2 = 16-4E_2. If both firms were forced to eliminate all of their emissions, their combined total abatement costs (TAC) would be Answer:arrow_forward
- The following accompanying table shows the relationship between the speed of a computer's CPU and its benefits and costs. Assume that all other features of the computer are the same (that is, CPU speed is the only source of variation), and only the CPU speeds listed below are available for purchase. CPU Total Marginal Total |Marginal GHz Benefit Benefit Cost Costs 2.0 $1,000 $900 2.5 $1,400 $100 3.0 $300 $1,200 3.5 $1,900 $1,500 4.0 $2,000 $400 Application of the Cost-Benefit Principle would lead one to purchase a computer.arrow_forwardImagine a firm’s marginal abatement cost function with existing technologies is: MAC = 12 – E. If the firm adopts new pollution abatement technologies, its marginal abatement cost function will be: MAC = 6 – 0.5E. The adoption costs for the new technology are $6. If the government raises the tax on emissions from $2 to $4, the firm's total costs increase by $_____. HINT: Total costs include tax payments, total abatement costs, and (if relevant) adoption costs for the new technology. Select one: a. $12. b. $8. c. $10. d. $16.arrow_forwardGive only typing answer with explanation and conclusion Suppose there are two industries with MAC functions as follows: MACA = 240-3EA and MACB=160-2EB And suppose the local government wished to reduce the total industry emissions by 50% (from the uncontrolled level) by implementing a uniform standard. How much emission would be reduced and what would be the total abatement costs for each industry under this uniform standard?arrow_forward
- A river is being used by both a chemical factory for waste disposal and a salmon fishery for fish reproduction. Waste emissions from the factory detrimentally affect fish reproduction at the downstream salmon fishery. The chemical factory's emission levels are currently unregulated. The marginal damage caused to the salmon fishery is given by MD=4e, where e is the level of emissions discharged into the river per month by the chemical factory. To reduce its emissions, the chemical factory would face marginal abatement costs of MAC=800-16e. Suppose that instead of a constant tax of $T per unit of emissions, the government enacts a two- rate tax system, where the higher rate (call it TH) is designed to achieve the efficient level of emissions, and the lower rate (call it T1) is designed to collect just enough tax revenues to cover the damages from remaining emissions. 23. At what amount per unit should the government set for the higher rate? $ 24. At what amount per unit should the…arrow_forward6 A coal-fired power plant produces powerp with costs c(p) = . Each unit of power earns the plant $11. Burning coal releases particulate matter (PM2.5), a pollutant that is known to cause heart disease, lung disease, and birth defects. The coal plant borders a wildlife sanctuary which sells tourism visits t for a price $30. However, the sanctuary's animals are getting sick due to the negative externality of PM2.5, such that the costs to the sanctuary are c(t) = +². The local government decides to tax the coal plant to internalize its negative externality. What tax will restore the social optimum? (Round answers to 2 decimal places) Answer: Checkarrow_forwardHighFlyer Airlines wants to build new airplanes with greatly increased cabin space. This will allow HighFlyer Airlines to give passengers more comfort and sell more tickets at a higher price. However, redesigning the cabin means rethinking many other elements of the airplane as well, like engine and luggage placement, and the most efficient shape of the plane for moving through the air. HighFlyer Airlines has developed a list of possible methods to increase cabin space, along with estimates of how these approaches would affect the planes operating costs and ticket sales. Based on these estimates, Table 13.5 shows the value of R, how much should the firm invest in R on top of the private return; that is, an R private return to HighFlyer Airlines would have a 9 social return. How much investment is socially optimal at the 6 interest rate?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Economics 2eEconomicsISBN:9781947172364Author:Steven A. Greenlaw; David ShapiroPublisher:OpenStax
Principles of Economics 2e
Economics
ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:OpenStax