Reference no: EM132421853

Problem: Consider the manager of a chair factory who wishes to minimize the cost of production, where the annual level of production is 35000 chairs,i.e. q=35000. Assume for simplicity that there are only two inputs, labour L and capital K ,with wage rate w and capital rental rate r. Thus, the manager's objective is to choose L and K to minimize the total cost wL+rK, given the production function q =f(K,L). Of course, this involves a constrained minimization, and therefore it is appropriate to introduce a third variable, the Lagrange multiplier λ, which corresponds with the production constraint. Suppose that, after a bit of work, the manager finds the following solution: L*=5000 hours,K*=$5 million λ*=$15

Based on this information, is it possible to deduce the marginal cost of production? Discuss, making reference to the envelop theorem.