Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
True or False? This marginal cost function is the derivative of the production function.
![The equation in the image is:
\[ C(w_1, w_2, y) = \left( w_1^{\frac{1}{3}} + w_2^{\frac{1}{3}} \right)^3 y^2 \]
This equation could be used for educational purposes to demonstrate concepts in algebra or calculus, such as the manipulation of exponents and variables, or might be part of a larger discussion on optimization functions within mathematical models. The variables \( w_1 \), \( w_2 \), and \( y \) represent constants or inputs that would impact the outcome of the function \( C \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f3e5997-3691-4d87-b796-19026d6f3e25%2F63fd2aa3-ca13-4d49-b41e-a20733e0b726%2F41uk5a_processed.png&w=3840&q=75)
Transcribed Image Text:The equation in the image is:
\[ C(w_1, w_2, y) = \left( w_1^{\frac{1}{3}} + w_2^{\frac{1}{3}} \right)^3 y^2 \]
This equation could be used for educational purposes to demonstrate concepts in algebra or calculus, such as the manipulation of exponents and variables, or might be part of a larger discussion on optimization functions within mathematical models. The variables \( w_1 \), \( w_2 \), and \( y \) represent constants or inputs that would impact the outcome of the function \( C \).
![The image contains the mathematical expression for marginal cost (MC) as follows:
\[ MC = C_y(\mathbf{w}, y) = 2 \left( w_1^{\frac{1}{3}} + w_2^{\frac{1}{3}} \right)^3 y \]
This formula is used in economics to calculate the marginal cost when given specific variables and parameters. Here, \( \mathbf{w} \) represents a vector containing \( w_1 \) and \( w_2 \), which could be factors of production or other relevant variables. The expression inside the parentheses involves raising both \( w_1 \) and \( w_2 \) to the power of \( \frac{1}{3} \), summing these values, and then raising the result to the third power. This is then multiplied by \( y \) and by 2 to obtain the marginal cost.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f3e5997-3691-4d87-b796-19026d6f3e25%2F63fd2aa3-ca13-4d49-b41e-a20733e0b726%2Fdzqjqep_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains the mathematical expression for marginal cost (MC) as follows:
\[ MC = C_y(\mathbf{w}, y) = 2 \left( w_1^{\frac{1}{3}} + w_2^{\frac{1}{3}} \right)^3 y \]
This formula is used in economics to calculate the marginal cost when given specific variables and parameters. Here, \( \mathbf{w} \) represents a vector containing \( w_1 \) and \( w_2 \), which could be factors of production or other relevant variables. The expression inside the parentheses involves raising both \( w_1 \) and \( w_2 \) to the power of \( \frac{1}{3} \), summing these values, and then raising the result to the third power. This is then multiplied by \( y \) and by 2 to obtain the marginal cost.
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