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microbook_3e-page91 - x You can trade one unit of labor for...

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isoquants Recall the production function I used above: X = K 2/3 *L 1/3 and solve for K: K = X 3/2 *L –1/2 This second equation shows us how much we need to increase use of kapital as labor inputs decrease in order to hold output constant. This relationship gives us an “isoquant.” isoquant – shows all combinations of kapital and labor that can be used to produce a given level of output. Kapital Output of X Labor slope 22.36 15.87 8 -1.40 21.08 15.87 9 -1.17 20.00 15.87 10 -1.00 19.07 15.87 11 -0.87 18.26 15.87 12 -0.76 Slope of isoquant: marginal rate of technical substitution slope = MPK MPL ǻ L ǻ K 0 L K isocosts x Recall that the wage rate and the rental rate were both equal to $0.53 x So what’s the relative wage?
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Unformatted text preview: x You can trade one unit of labor for one unit of capital at a one-to-one ratio, so the relative wage is: labor of unit kapital of unit 1 kapital of $0.53/unit labor of $0.53/unit r w x The relative wage gives us the slope of the isocost line. Isocost line shows all possible quantities of labor and kapital which yield the same total cost. The optimal employment levels of kapital and labor are given by at the point where the isoquant is tangent to (just touches) the isoquant. Note that the isocost line looks just like a budget constraint. Note that the isoquant curve looks just like an indifference curve. L K 20 10 Page 91...
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