Ch.7&8 Notes

Ch.7&8 Notes - Intermediate Microeconomics Professor...

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Intermediate Microeconomics Professor Yongmin Chen Topic 6: Input Choices and the Cost of Production The Optimal combination of Inputs We have seen that in order to produce certain amount of output, it is often possible to use different combinations of inputs, as is represented by the isoquant. Now the question is: what input combination should a firm choose to produce the desired output? This is the problem of determining the optimal combination of inputs. Suppose the production uses two inputs: labor (L) and capital (K). The price of labor is w, and the price of K is r. That is, each unit of labor costs w, and each unit of capital costs r. If L units of labor and K units of capital are used, the total cost would be wL + rK = C Clearly, given w , r, and C, there are different combinations of (L,K) that would require the same total cost C. The line that represents all the input combinations with a total cost C is called the isocost line. For different C, there corresponds to different isocost lines. An isocost line that is closer to the origin represents a lower level of total cost. The slope of the isocost line is -w/r. To produce a certain amount of output, one essentially selects a point on an isoquant. Of course, different points on an isoquant will generally have different costs. To choose the optimal input combination is to choose the input combination that requires least cost. This is achieved by finding out the point on the isoquant that is tangent to an isocost line. See illustration in class. Since MRTS LK = -slope of the isoquant, and since the slope of the isocost line is -w/r, the conditions for cost minimization in producing certain output X * can be written as: MRTS LK = w/r X(L,K) = X * Since MRTS LK = MP L /MP K , the above condition can also be written as MP L /MP K = w/r, and X(L,K) = X * . Example 6-1. Suppose the production function is X = L
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Ch.7&8 Notes - Intermediate Microeconomics Professor...

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