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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.4: Linear Programming
Problem 19E
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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
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
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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