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A bottling company uses two inputs to assemble bottles of the soft drink Squish: bottling machines and workers. Running the bottling machine is an imperfect substitute for the labor performed by the workers. The production function is:
q = 100 K1/4 L½
The implicit rental rate plus hourly operating cost of the machine is r = $15 per hour; and the workers each earn w = $20 per hour.
The current level of input use for the production of q=1000 bottles is:
K=16 machine hours and L=25 labor hours.
Question: Is this firm producing at minimum cost? If it is minimizing costs, explain why. If it is not minimizing costs, explain how the firm should change its input use to lower its costs.
For full credit, you must discuss the two efficiency conditions for minimizing cost. That is:
Is the bundle technologically efficient? (yes/no/why or why not)
Is it economically efficient? (yes/no/why or why not)
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