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 .
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"…
. 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?
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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