Supplement%20to%20Handout%206 - Supplement to Handout # 6 1...

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1 Cost Minimization In this handout, we will look at the problem of cost minimization and the techniques to solve them. We will do this exercise using three equivalent methods. We have a production function ( Cobb-Douglas function) which uses two inputs capital K and labor L; q = F ( K;L ) = K a L b where a > 0 ;b > 0 ;a + b 6 1 (1) and r ( rental rate for capital) and w (wage rate for labor) are strictly positive. output, q . The problem under consideration is: min ( K;L ) wL + rK (2) subject to q = K a L b : (3) 1.1 Method 1: Graphical In this method, we refer to the isoquant and isocost curves for two input case. Let us keep labor ( L ) on the horizontal axis and capital ( K ) on the vertical axis. Recall that the slope of the isocost curve is equal to w r : Also the slope of the tangent at any point on the isoquant curve is equal to MP L MP K where MP L and MP K are marginal product of labor and capital respectively. To minimize cost, we need to equate these two ratios,
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Supplement%20to%20Handout%206 - Supplement to Handout # 6 1...

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