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A cost minimizing firm’s production function is Q=2KL. The price of labor, w, is currently $4, and the price of capital, r, is currently $1. At the firm’s current level of output, it has total costs of $160. Input prices change such that the wage rate is now 8 times the rental rate. The firm adjusts its input combination, but leaves total output unchanged.
Answer the questions below as you solve for the cost - minimizing input combination after the price changes.
1. Solve for the initial input combination and the initial level of output (before the price change). Hint: you must maximize output subject to a “total cost” constraint...think utility optimization.
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