EBK MICROECONOMICS
5th Edition
ISBN: 9781118883228
Author: David
Publisher: YUZU
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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.
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Students have asked these similar questions
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 .
. Appalachian Coal Mining believes that it can increase labor productivity and, therefore, net revenue by reducing air pollution in its mines. It estimates that the marginal cost function for reducing pollution by installing additional capital equipment is
MC=40P
Where P represents a reduction of one unit of pollution in the mines. It also feels that for every unit of pollution reduction the marginal increase in revenue (MR) is
MR=1000-10P
How much pollution reduction should Appalachian Coal Mining undertake?
Part D E F needed
b) Ana also reads that climate change is caused by carbon emissions from air travel. Two airlines run flights between two cities, Air A and Air B. The government has said that the airlines can produce 100 units of carbon emissions between them, under a carbon permit scheme, and should decide how to split the 100 units between them. Air A and Air B have the same operating costs and the same costs of reducing the amount of carbon that they produce per flight.Say Air A has been operating on the route for over 50 years and the government decides to give all the permits to Air A (based on its long use of the route). Air A offers a proportion R of the 100 units of permits to Air B and Air B can accept the offer or reject it and not fly on the route.• How will the other parameters of the model as discussed in this module affect the value of R* at which Air B accepts the offer?• Say that the government gives the permits to Air A for 5 years, and will gives them to Air B for…
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
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