A firm has a production function given by Q= ALα Kβ and per unit price of capital (K) and Labour  (L) are r and w respectively. Find the Marginal Rate of Technical substitution for capital for this firm If the firm seeks to minimize its cost and its in the short run of production such that K = K, find L and the short run cost function Suppose that the firm can now change all its inputs and it seeks to minimize its cost. Find the input demand functions of K and L; as well as the long run cost 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.