Econ302-hw3-fall08-solutions - Econ302 Homework Assignment...

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Econ302 Homework Assignment 3 Solutions 1.  Diminishing returns to a single factor of production and constant returns to scale are  not inconsistent.  Discuss. Diminishing returns to a single factor are observable in all production processes at  some level of inputs.  This fact is so pervasive that economists have named it the “law  of diminishing marginal productivity.”  By definition, the marginal product of an input  is the additional output generated by employing one more unit of the input, all other  inputs held fixed.  The extra output, or returns, to the single input diminish because all  other inputs are held fixed.  For example, when holding the level of capital constant,  each additional unit of labor has less capital to work with. Unlike the returns to a single factor, returns to scale are proportional increases in  all  inputs.  While each factor by itself exhibits diminishing returns, output may more than  double, less than double, or exactly double when all the inputs are doubled.   The  distinction again is that with returns to scale, all inputs are increased in the same  proportion and no input is held fixed. 2.  For each of the following examples, draw a representative isoquant.  What can you say  about the marginal rate of technical substitution in each case? a. A firm can hire only full-time employees to produce its output, or it can hire some  combination of full-time and part-time employees.  For each full-time worker let  go, the firm must hire an increasing number of temporary employees to maintain  the same level of output. Place part time workers on the vertical axis and full time workers on the horizontal  axis.  The slope of the isoquant measures the number of part time workers that can  be exchanged for a full time worker, while still maintaining output.  When we are at  the bottom end of the isoquant we have a lot of full time workers and few part time  workers.  As we move up the isoquant and give up full time workers, we must hire  more and more part time workers to replace each full time worker.   The slope  increases (in absolute value terms) as we move up the isoquant.   The isoquant is  therefore convex and we have diminishing marginal rate of technical substitution. b. A firm finds they it can always trade two units of labor for one unit of capital and  still keep output constant.
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