ch06 - Chapter 6 Inputs and Production Functions Solutions...

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Chapter 6 Inputs and Production Functions Solutions to Review Questions 1. The production function tells us the maximum volume of output that may be produced given a combination of inputs. It is possible that the firm might produce less than this amount of output due to inefficient management of resources. While it is possible to produce many levels of output with the same level of inputs, some of which are less technically efficient than others, the production function gives us the upper bound on (the maximum of) the level of output. 2. The labor requirements function, which is the inverse of the production function, tells us the minimum amount of labor that is required to produce a given amount of output. 0 5 10 15 20 25 30 0 50 100 150 200 250 Q L 3. The average product of labor is the average amount of output per unit of labor. Total Product Quantity of Labor L Q AP L = = The marginal product of labor is the rate at which total output changes as the firm changes its quantity of labor. Change in Total Product Change in Quantity of Labor L Q MP L = = Page 6 - 1
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The total product function in the graph below 3 Q L = , which is linear, would have the average and marginal products coincide. In particular, for all values of Q we would have 3 L L AP MP = = . 0 50 100 150 200 250 0 10 20 30 40 50 60 70 L Q 4. With diminishing total returns to an input, increasing the level of the input will decrease the level of total output holding the other inputs fixed. Diminishing marginal returns to an input means that as the use of that input increases holding the quantities of the other inputs fixed, the marginal product of that input will become less and less. Essentially, diminishing total returns implies that output is decreasing while with diminishing marginal returns we could have output increasing, but at a decreasing rate as the amount of the input increases. It is entirely plausible to have a total product function exhibit diminishing marginal returns but not diminishing total returns. This would occur when each additional unit of an input increased the total level of output, but increased the level of output less than the previous unit of the input did. Essentially, this occurs when output is increasing at a decreasing rate as the level of the input increases. 5. If the marginal product of labor is positive, then when we increase the level of labor holding everything else constant this will increase total output. To keep the level of output at the original level, we need to stay on the same isoquant. To do so, since the marginal product of capital is positive we would then need to reduce the amount of capital being used. So, to keep output constant, when the level of one input increases the level of the other input must decrease. This negative relationship between the inputs implies the isoquant will have a negative slope, i.e., be downward sloping. 6.
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This note was uploaded on 09/24/2008 for the course PAM 2000 taught by Professor Evans,t. during the Fall '07 term at Cornell University (Engineering School).

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ch06 - Chapter 6 Inputs and Production Functions Solutions...

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