LaborDemand2011A - Econ145.LaborDemand2011A John Pencavel...

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Econ145.LaborDemand2011A John Pencavel THE DEMAND FOR LABOR Property rights : assume those who supply capital “own” the firm & organize production to maximize net returns. Employment relationships are assumed to be governed by the employment- at-will doctrine. X = output , p = price per unit of output, E = labor input, w = price per unit of E , K = non-labor input (“capital”) , r = price per unit of K net returns or profits = Π = p.X - w.E - r.K Inputs and outputs are not independent of one another: X = f( E , K ) is the production function which shows the maximum output attainable from given inputs. Inputs and outputs are flows per unit of time (not stocks). All marginal products are non-negative: M X / M E $ 0, M X / M K $ 0 . To model the demand for labor, three classes of assumptions are needed: assumptions about technology, prices, and objectives.
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2   ( / ) X E E X E 2 2 0 Reference Model assumptions about technology : eventually diminishing returns obtains, i.e., after a point, marginal products decline - Here diminishing returns operates at all E , i.e., the slope of the production function falls as E increases. At a , the average product of labor APE is X o / E o which exceeds the marginal product of labor, MPE, at that point. Of course, the shape of the output-labor relations depends on the level at which other inputs (here K ) are held fixed.
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3 2 2 2 2 2 2 0 X E X K X E K . In this case, diminishing returns operates only after E^ . At E o , marginal and average products are the same. When the level of not merely one input is changed but when all inputs are changed, the corresponding change in output is expressed in terms of returns to scale. Suppose all inputs are increased by factor a > 1. Then output increases by the proportion b: b. X = f( a. E , a. K ) . If b < a, the production function displays decreasing returns to scale; if b > a, the production function displays increasing returns to scale; if b = a, the production function reveals constant returns to scale. For this Reference Model we assume decreasing returns to scale - also called generalized diminishing returns or the production function is strictly concave which means:
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