A firm currently uses 40 units of labor (L) and 20 units of capital (K) to produce 400 units of output. Input prices equal $30 for labor and $60 for capital, while the marginal products are 6 for labor and 3 for capital. To minimize the cost of producing its current level of output, should the firm use more L and less K, more K and less L, or leave its input combination unchanged? Explain your answer.

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Q: production function

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Isocost and Isoprofit Curve Analysis

An isocost curve in the production theory that is a crucial part of economics depicts different combinations of factor inputs at a given market cost. In other words, this shows all the combinations of production factors that cost the same for the firm to employ. Usually, this can be depicted as a downward sloping straight line when the firms act as the price-takers in the factor markets. The slope of this mainly depicts the relative prices of different production factors.