Question 4 Consider the production process with 2 inputs and 1 output. The production function is...

 

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Question 4 Consider the production process with 2 inputs and 1 output. The production function is given by y = x The input prices are w, and w, respectively. Consider the case of long run where both factors are variable. The output price is denoted as p. (Please leave the numbers in decimals or fractions.) (a) First, consider the profit maximization problem directly. Derive the input demand functions and output function in terms of input prices w₁, ₂ and output price p. How do they change with the input and output prices? (b) Now, consider the cost minimization problem. Derive the conditional input demand functions and the cost function in terms of w₁, ₂ and y. How do they change with input prices and output level? (c) Based on the cost function in (b), solve for the profit maximizing output level in terms of input prices and output price. Does it provide the same output supply function as in (a)? Question 4 Consider the production process with 2 inputs and 1 output. The production function is given by y = x The input prices are w, and w, respectively. Consider the case of long run where both factors are variable. The output price is denoted as p. (Please leave the numbers in decimals or fractions.) (a) First, consider the profit maximization problem directly. Derive the input demand functions and output function in terms of input prices w₁, ₂ and output price p. How do they change with the input and output prices? (b) Now, consider the cost minimization problem. Derive the conditional input demand functions and the cost function in terms of w₁, ₂ and y. How do they change with input prices and output level? (c) Based on the cost function in (b), solve for the profit maximizing output level in terms of input prices and output price. Does it provide the same output supply function as in (a)?