A firm uses two inputs to produce a single output. The firm’s technology exhibits constant return to scale (say, if the firm doubles the quantity of inputs it uses, it will double its output). Suppose that we know that in 2021, the firm used 10 units of input 1 and its output was 200 units and in 2022, it used 20 units of input 1 and its output was 500 units. Moreover we know that the quantity of input 2 was the same in 2021 and in 2022 (although the firm could have selected different quantities of input 2 had it wanted to). Using this information, can you tell whether the firm was minimizing its costs in 2021 and in 2022? In other words, could the firm have saved costs in either 2021 or 2022 by producing the same output it did (200 units in 2021 and 500units in 2022) more cheaply? Explain your answer.
A firm uses two inputs to produce a single output. The firm’s technology exhibits constant return to scale (say, if the firm doubles the quantity of inputs it uses, it will double its output). Suppose that we know that in 2021, the firm used 10 units of input 1 and its output was 200 units and in 2022, it used 20 units of input 1 and its output was 500 units. Moreover we know that the quantity of input 2 was the same in 2021 and in 2022 (although the firm could have selected different quantities of input 2 had it wanted to). Using this information, can you tell whether the firm was minimizing its costs in 2021 and in 2022? In other words, could the firm have saved costs in either 2021 or 2022 by producing the same output it did (200 units in 2021 and 500units in 2022) more cheaply? Explain your answer.
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