A baker uses labor (L) and raw materials (M) to produce mini Muhlenberg Mule sugar figurines (q). The process is fairly simple as workers only must make the sugar mixture and pour the mixture into the mule molds. The baker’s production function is as follows f(L, M) = L 0.50M. Let wL and wM denote the prices of a unit of L and M, respectively. (a) Write the firm’s cost minimization problem if it wants to produce q units of output. (b) Write the Lagrangian function that describes the cost minimization problem. (c) Derive the long run conditional factor input demands for L and M as a function of wL, wM, and q; L ∗ (wL, wM, q) and M∗ (wL, wM, q).
A baker uses labor (L) and raw materials (M) to produce mini Muhlenberg Mule sugar figurines (q). The process is fairly simple as workers only must make the sugar mixture and pour the mixture into the mule molds. The baker’s production function is as follows f(L, M) = L 0.50M. Let wL and wM denote the prices of a unit of L and M, respectively. (a) Write the firm’s cost minimization problem if it wants to produce q units of output. (b) Write the Lagrangian function that describes the cost minimization problem. (c) Derive the long run conditional factor input demands for L and M as a function of wL, wM, and q; L ∗ (wL, wM, q) and M∗ (wL, wM, q). (d) Suppose wL = $25 and wM = $2. Determine the cost-minimizing combination of inputs if the baker wants to produce 200 mules. (e) Using wL = $25 and wM = $2 and the demand functions from part (c), write the firm’s long run cost function CLR(q).
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