The demand and cost function for a company is estimated to be as follows: P = 100-8Q; TC = 50+80Q-10Q² + 0.6Q³. Suppose the company lacks confidence in the accuracy of cost estimates expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation. What difference would it make on the recommended profit-maximizing and revenue-maximizing prices?

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As a rule, cubic maximizations tend to be more accurate than linear ones when it comes to price estimations due to the fact that they take more variables into account. However, it is possible to use a linear function for ease of usage in order to approximate prices. A linear function is typically represented using this formula: f(x)=a+bx

In order to simplify a cubic function, it is required to leave out the squared and cubic terms. Thus, the new formula for TC would look like this:

TC = 50+80Q

It will help simplify the picture but will also distort some of the projected prices and results. For example, the profit-maximizing price in a linear function would increase from 63.03 to 90 dollars and would no longer be appropriate, as the difference between the two prices would be much too high. However, the revenue-maximizing price will remain the same, meaning that the method would be useful in representing revenue maximization projections.

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Academic.Tips. (2021) 'The demand and cost function for a company is estimated to be as follows: P = 100-8Q; TC = 50+80Q-10Q² + 0.6Q³. Suppose the company lacks confidence in the accuracy of cost estimates expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation. What difference would it make on the recommended profit-maximizing and revenue-maximizing prices'. 18 June.

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Academic.Tips. (2021, June 18). The demand and cost function for a company is estimated to be as follows: P = 100-8Q; TC = 50+80Q-10Q² + 0.6Q³. Suppose the company lacks confidence in the accuracy of cost estimates expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation. What difference would it make on the recommended profit-maximizing and revenue-maximizing prices? https://academic.tips/question/the-demand-and-cost-function-for-a-company-is-estimated-to-be-as-follows-p-100-8q-tc-5080q-10q2-0-6q3-suppose-the-company-lacks-confidence-in-the-accuracy-of-cost-estimates-expressed-in-a-cu/

References

Academic.Tips. 2021. "The demand and cost function for a company is estimated to be as follows: P = 100-8Q; TC = 50+80Q-10Q² + 0.6Q³. Suppose the company lacks confidence in the accuracy of cost estimates expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation. What difference would it make on the recommended profit-maximizing and revenue-maximizing prices?" June 18, 2021. https://academic.tips/question/the-demand-and-cost-function-for-a-company-is-estimated-to-be-as-follows-p-100-8q-tc-5080q-10q2-0-6q3-suppose-the-company-lacks-confidence-in-the-accuracy-of-cost-estimates-expressed-in-a-cu/.

1. Academic.Tips. "The demand and cost function for a company is estimated to be as follows: P = 100-8Q; TC = 50+80Q-10Q² + 0.6Q³. Suppose the company lacks confidence in the accuracy of cost estimates expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation. What difference would it make on the recommended profit-maximizing and revenue-maximizing prices?" June 18, 2021. https://academic.tips/question/the-demand-and-cost-function-for-a-company-is-estimated-to-be-as-follows-p-100-8q-tc-5080q-10q2-0-6q3-suppose-the-company-lacks-confidence-in-the-accuracy-of-cost-estimates-expressed-in-a-cu/.

Bibliography

Academic.Tips. "The demand and cost function for a company is estimated to be as follows: P = 100-8Q; TC = 50+80Q-10Q² + 0.6Q³. Suppose the company lacks confidence in the accuracy of cost estimates expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation. What difference would it make on the recommended profit-maximizing and revenue-maximizing prices?" June 18, 2021. https://academic.tips/question/the-demand-and-cost-function-for-a-company-is-estimated-to-be-as-follows-p-100-8q-tc-5080q-10q2-0-6q3-suppose-the-company-lacks-confidence-in-the-accuracy-of-cost-estimates-expressed-in-a-cu/.

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"The demand and cost function for a company is estimated to be as follows: P = 100-8Q; TC = 50+80Q-10Q² + 0.6Q³. Suppose the company lacks confidence in the accuracy of cost estimates expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation. What difference would it make on the recommended profit-maximizing and revenue-maximizing prices?" Academic.Tips, 18 June 2021, academic.tips/question/the-demand-and-cost-function-for-a-company-is-estimated-to-be-as-follows-p-100-8q-tc-5080q-10q2-0-6q3-suppose-the-company-lacks-confidence-in-the-accuracy-of-cost-estimates-expressed-in-a-cu/.

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