Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Find the supply function for the (attached) production function.
![The function presented in this image is:
\[ f(x_1, x_2) = (x_1 - 1)^{0.25} \cdot x_2^{0.5} \]
This mathematical expression specifies a function \( f \) dependent on two variables, \( x_1 \) and \( x_2 \). The function can be interpreted as follows:
- The term \( (x_1 - 1)^{0.25} \) indicates taking the base \( (x_1 - 1) \) to the power of 0.25, which is equivalent to the fourth root of \( (x_1 - 1) \).
- The term \( x_2^{0.5} \) indicates taking \( x_2 \) to the power of 0.5, which is equivalent to the square root of \( x_2 \).
- The two terms are then multiplied together to produce the value of the function \( f(x_1, x_2) \).
This function is useful in mathematical analysis and can be applied in various contexts within fields such as algebra, calculus, and optimization.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0f3e5997-3691-4d87-b796-19026d6f3e25%2F155ef7c3-4488-4569-9bc6-15033335dde6%2Fhjwg3jp_processed.png&w=3840&q=75)
Transcribed Image Text:The function presented in this image is:
\[ f(x_1, x_2) = (x_1 - 1)^{0.25} \cdot x_2^{0.5} \]
This mathematical expression specifies a function \( f \) dependent on two variables, \( x_1 \) and \( x_2 \). The function can be interpreted as follows:
- The term \( (x_1 - 1)^{0.25} \) indicates taking the base \( (x_1 - 1) \) to the power of 0.25, which is equivalent to the fourth root of \( (x_1 - 1) \).
- The term \( x_2^{0.5} \) indicates taking \( x_2 \) to the power of 0.5, which is equivalent to the square root of \( x_2 \).
- The two terms are then multiplied together to produce the value of the function \( f(x_1, x_2) \).
This function is useful in mathematical analysis and can be applied in various contexts within fields such as algebra, calculus, and optimization.
Expert Solution

Introduction:
We are going to use the relationship between upward sloping marginal cost curve and supply curve to answer this question
Approach:
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