Suppose a firm has a production function with two inputs, capital (K) and labor (L). The production function takes the form: Q = L2K2. Further, let the wage be given by w, the rental rate of capital be given by r, and suppose that the firm wishes to produce Q0 units of output.   Determine the elasticity of substitution for this production function. Explain your answer. Determine the returns to scale for the production function. Solve for the long-run optimal input demand functions for capital and labor as a function of

ENGR.ECONOMIC ANALYSIS
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ISBN:9780190931919
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Chapter1: Making Economics Decisions
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  1. Suppose a firm has a production function with two inputs, capital (K) and labor (L). The production function takes the form: Q = L2K2. Further, let the wage be given by w, the rental rate of capital be given by r, and suppose that the firm wishes to produce Q0 units of output.

 

  1. Determine the elasticity of substitution for this production function. Explain your answer.
  2. Determine the returns to scale for the production function.
  3. Solve for the long-run optimal input demand functions for capital and labor as a function of exogenous variables only.
  4. Derive an expression for long-run total cost as a function of the exogenous variables.
  5. Let w=16, r=25, and Q0 = 10,000. Solve for the long-run cost-minimizing input combination.
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