Math Problem Statement
ข้อ3.5 ถามว่าอะไร
Solution
The question here, 3.35, asks us to calculate two things for the given linear production function:
-
Cost Function: We need to find the cost function associated with the production function. This typically involves expressing the minimum cost required to produce a certain level of output , given input prices.
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Conditional Input Demands: We also need to determine the "conditional input demands," or the demand for each input that minimizes the cost of producing a given output level .
The production function provided is:
where:
- represents the output,
- are the input quantities,
- are the coefficients representing the productivity of each input .
Let me proceed to solve each part.
Solution Outline
- Cost Function: Define the cost function as , where represents the price of each input .
- Conditional Input Demands: Using the cost minimization condition, solve for each in terms of and other parameters.
Would you like the full derivation and explanation for each part?
Additional Questions:
- How do we interpret the cost function in economic terms?
- What are the economic implications of each in the production function?
- How does input price affect conditional input demand?
- How would the analysis change if the production function were non-linear?
- What assumptions underlie the calculation of conditional input demands?
Tip:
For linear production functions, the cost function can often be calculated directly by solving for minimum cost under linear constraints.
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Math Problem Analysis
Mathematical Concepts
Cost Function
Conditional Input Demands
Linear Production Function
Formulas
y = Σ (ai * xi)
C(y) = Σ (wi * xi)
Theorems
-
Suitable Grade Level
Undergraduate Economics or Advanced High School Math
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