Economics - Find increase of cost

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Homework Help Overview

The discussion revolves around a problem in economics related to calculating the increase in cost based on a given marginal cost function. The marginal cost is expressed as a polynomial function of the number of units produced, and the specific task is to determine the cost increase when production levels change from 1200 to 1600 units.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the interpretation of marginal cost and its relationship to cost calculation, with some suggesting integration while others propose alternative methods such as summation or approximation techniques.

Discussion Status

The conversation includes various interpretations of the problem, with participants exploring different mathematical approaches. Some guidance has been offered regarding the integration process and the potential need for approximation methods, but no consensus has been reached on the correct approach.

Contextual Notes

There is a noted uncertainty regarding the correct method to apply, as participants question the assumptions about the marginal cost definition and its application in this context.

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Im not sure if anyone can help me with this, I haven't seen a question like this I am guessing its easy. I tried just taking the integral and evaluating, bu tthat gave me a wrong answer.

Q:The marginal cost of producing x units of a certain product is 74+1.1x-0.002x^2+0.00004x^3. Find the increase in cost if the production level is raise from 1200 to 1600
 
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Well, isn't marginal cost the derivative of the cost with respect to the number of goods produced??

In that case, you integrated incorrectly.
 
Yes that is what I thought, but the answer I got was slightly off the given answer
 
Well, IF you integrated correctly, then maybe the problem meant for you to take "marginal cost" literally as the cost of producing one more unit. In this case you would have to take a sum rather than an integral. Or maybe they wanted you to approximate by considering the cost of the nth unit to be the integral from n-.5 to n+.5 of the marginal cost--in this case you would integrate from 1200.5 to 1600.5
 
Last edited:
Oops..Must have made a mistake..Integration from 1600 to 1200 yields the correct answer
 

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