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An entrepeneur who wants to maximize profits can solve this problem in two steps:

Cost minimization. An entrepeneur who wants to maximize profits can solve this problem in two steps: 1. Minize production costs for any given output level 2. Using the outcome of the first problem: determine the optimal production level which will maximize profits.

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An entrepeneur who wants to maximize profits can solve this problem in two steps:

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  1. Cost minimization An entrepeneur who wants to maximize profits can solve this problem in two steps: 1. Minize production costs for any given output level 2. Using the outcome of the first problem: determine the optimal production level which will maximize profits. We now address the first problem. Say the entrepreneur wants to produce at least 1 unit of good X with production function The entrepreneur pays the wage rate w for the labor she uses and the rental rate r for the capital she uses, such that the costs are: The entrepreneur cannot influence wage rate w or rental rate r

  2. Kx A Slope = -w/r X = 1 B 0 Lx Cost minimization The production function determines the isoquant X = 1 The wage-rental ratio w/r determines the slope of an isocost line (= all combinations of Kx and Lx with the same level of production costs) The entrepreneur can produce 1 unit of good X at points A and B (same cost level) The objective is, however, to minize the cost level.

  3. Kx A Kx* C X = 1 B 0 Lx* Lx Cost minimization Production costs decrease as the isocost line is closer to the origin. The cost minimizing input combination is therefore at the tangency point C, with Kx* capital and Lx* labor With the production function for good X these are:

  4. Kx D X = 1 0 Lx Cost minimization Clearly, if the wage-rental ratio changes, the cost minimizing input combination changes. If the wage rate decreases, the optimal input combination changes from C to D; you use less capital and more labor The optimal capital-labor ratio therefore depends on the wage-rental ratio. It is: It also depends on the capital intensity parameter alpha. C

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