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In the previous Problem Set question, we started looking at the cost function C (2), 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(r+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' (æ). Use this function in the model below for the Marginal Cost function MC (x) Problem Set question: The cost, in dollars, of producing æ units of a certain item is given by C (x) = 0.02a3 - 15a +200. (a) Find the marginal cost function. va al sin (a) 0.06. -15

In the previous Problem Set question, we started looking at the cost function C (2), 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(r+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' (æ). Use this function in the model below for the Marginal Cost function MC (x) Problem Set question: The cost, in dollars, of producing æ units of a certain item is given by C (x) = 0.02a3 - 15a +200. (a) Find the marginal cost function. va al sin (a) 0.06. -15

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Do you need help with this problem or this material? Remember to use the Academic Support resources vailable on your homepage in Brightspace or r in the learning modules. Remaining "How Did I Do?" Uses: 1/3 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 z 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 x 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 a units of a certain item is given by C (x) = 0.02x - 15a +200. (a) Find the marginal cost function. a a va a sin (a) 2 0.06. - 15 Submit Assignment Quit & Save Back Question Me-
Transcribed Image Text:Do you need help with this problem or this material? Remember to use the Academic Support resources vailable on your homepage in Brightspace or r in the learning modules. Remaining "How Did I Do?" Uses: 1/3 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 z 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 x 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 a units of a certain item is given by C (x) = 0.02x - 15a +200. (a) Find the marginal cost function. a a va a sin (a) 2 0.06. - 15 Submit Assignment Quit & Save Back Question Me-
ules/unproctored Test.QuestionSheet Not The cost, in dollars, of producing a units of a certain item is given by C (x) = 0.023 15x + 200. (a) Find the marginal cost function. a ya a sin (a) 2. 0.06· - 15 MC (z) = (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50 units are produced is $ 135 (c) Find the actual cost of increasing production from 50 units to 51 units. The actual cost of increasing production from 50 units to 51 units is $ 6.06 自
Transcribed Image Text:ules/unproctored Test.QuestionSheet Not The cost, in dollars, of producing a units of a certain item is given by C (x) = 0.023 15x + 200. (a) Find the marginal cost function. a ya a sin (a) 2. 0.06· - 15 MC (z) = (b) Find the marginal cost when 50 units of the item are produced. The marginal cost when 50 units are produced is $ 135 (c) Find the actual cost of increasing production from 50 units to 51 units. The actual cost of increasing production from 50 units to 51 units is $ 6.06 自
Expert Solution
Step 1

The derivative of xn with respect to x is calculated using the formula: ddxxn=nxn-1. The change in the total cost, when one additional unit of a product is sold is called the marginal cost. 

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