Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (x), the cost of a firm producing a items. An important microeconomics concept is the marginal cost, defined in (non-mathematical introductory) economics as the cost of producing one additional item. If the current production level is z items with cost C (x), then the cost of computing h additionial items is C (x + h). The average cost of those h items is (C(x+h)-C(x)) As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (x). Use this function in the model below for the Marginal Cost function MC (x). Problem Set question: The cost, in dollars, of producing x units of a certain item is given by C (x) = 0.04x3 – 15x + 450. (a) Find the marginal cost function. MC (x) = (b) Find the marginal cost when 60 units of the item are produced. The marginal cost when 60 units are produced is $ Number Problem Set question: The cost, in dollars, of producing æ units of a certain item is given by C (x) = 0.04x3 – 15x + 450. (a) Find the marginal cost function. MC (2) = (b) Find the marginal cost when 60 units of the item are produced. The marginal cost when 60 units are produced is $ Number (c) Find the actual cost of increasing production from 60 units to 61 units. The actual cost of increasing production from 60 units to 61 units is $ Number
Introduction to Calculus in Economics (continued): In the previous Problem Set question, we started looking at the cost function C (x), the cost of a firm producing a items. An important microeconomics concept is the marginal cost, defined in (non-mathematical introductory) economics as the cost of producing one additional item. If the current production level is z items with cost C (x), then the cost of computing h additionial items is C (x + h). The average cost of those h items is (C(x+h)-C(x)) As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the derivative C' (x). Use this function in the model below for the Marginal Cost function MC (x). Problem Set question: The cost, in dollars, of producing x units of a certain item is given by C (x) = 0.04x3 – 15x + 450. (a) Find the marginal cost function. MC (x) = (b) Find the marginal cost when 60 units of the item are produced. The marginal cost when 60 units are produced is $ Number Problem Set question: The cost, in dollars, of producing æ units of a certain item is given by C (x) = 0.04x3 – 15x + 450. (a) Find the marginal cost function. MC (2) = (b) Find the marginal cost when 60 units of the item are produced. The marginal cost when 60 units are produced is $ Number (c) Find the actual cost of increasing production from 60 units to 61 units. The actual cost of increasing production from 60 units to 61 units is $ Number
Calculus: Early Transcendentals
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Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![Introduction to Calculus in Economics (continued):
In the previous Problem Set question, we started looking at the cost function C (x), the cost of a firm producing a items. An important microeconomics
concept is the marginal cost, defined in (non-mathematical introductory) economics as the cost of producing one additional item.
If the current production level is z items with cost C (x), then the cost of computing h additionial items is C (x + h). The average cost of those h items is
(C(x+h)-C(x))
As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the
derivative C' (x). Use this function in the model below for the Marginal Cost function MC (x).
Problem Set question:
The cost, in dollars, of producing x units of a certain item is given by
C (x) = 0.04x3 – 15x + 450.
(a) Find the marginal cost function.
MC (x) =
(b) Find the marginal cost when 60 units of the item are produced.
The marginal cost when 60 units are produced is $ Number](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66a2cee6-12ef-4906-a343-96f32a210b9a%2Fd5ab778c-edc0-4c0a-a403-c9d258c470d2%2Ffarnwj7.jpeg&w=3840&q=75)
Transcribed Image Text:Introduction to Calculus in Economics (continued):
In the previous Problem Set question, we started looking at the cost function C (x), the cost of a firm producing a items. An important microeconomics
concept is the marginal cost, defined in (non-mathematical introductory) economics as the cost of producing one additional item.
If the current production level is z items with cost C (x), then the cost of computing h additionial items is C (x + h). The average cost of those h items is
(C(x+h)-C(x))
As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h → 0, i.e. the
derivative C' (x). Use this function in the model below for the Marginal Cost function MC (x).
Problem Set question:
The cost, in dollars, of producing x units of a certain item is given by
C (x) = 0.04x3 – 15x + 450.
(a) Find the marginal cost function.
MC (x) =
(b) Find the marginal cost when 60 units of the item are produced.
The marginal cost when 60 units are produced is $ Number
![Problem Set question:
The cost, in dollars, of producing æ units of a certain item is given by
C (x) = 0.04x3 – 15x + 450.
(a) Find the marginal cost function.
MC (2) =
(b) Find the marginal cost when 60 units of the item are produced.
The marginal cost when 60 units are produced is $ Number
(c) Find the actual cost of increasing production from 60 units to 61 units.
The actual cost of increasing production from 60 units to 61 units is $ Number](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66a2cee6-12ef-4906-a343-96f32a210b9a%2Fd5ab778c-edc0-4c0a-a403-c9d258c470d2%2Fksfpmv9.jpeg&w=3840&q=75)
Transcribed Image Text:Problem Set question:
The cost, in dollars, of producing æ units of a certain item is given by
C (x) = 0.04x3 – 15x + 450.
(a) Find the marginal cost function.
MC (2) =
(b) Find the marginal cost when 60 units of the item are produced.
The marginal cost when 60 units are produced is $ Number
(c) Find the actual cost of increasing production from 60 units to 61 units.
The actual cost of increasing production from 60 units to 61 units is $ Number
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