# Econ 2101 Problem Set 6

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Econ 2101 - Hovander Problem Set 6 - Solutions 1) Define the hypothesis of (eventually) diminishing marginal product both mathematically and verbally. Does this hypothesis hold in the short run or the long run? Explain. The long run is defined as a period of time sufficiently long so that all inputs to production can be freely varied. In contrast, the short run is a period of time sufficiently short so that at least one input is fixed (cannot be varied). For simplicity, let’s make the standard assumption that the variable input in the short run is labor and proceed by defining the hypothesis in terms of labor. The hypothesis of eventually diminishing marginal product states that as we increase labor while holding all other inputs fixed, we will eventually reach a point where the additional output gained with each increase in labor gets smaller and smaller. (e.g. the 5th baker increases output by 3 loaves, the 6th baker by 2 loaves, the 7th baker by 1.) Since the hypothesis is regarding what we expect to see when we vary one input while holding others fixed, this hypothesis is relevant in the short run and not in the long run.

Mathematically, the marginal product of labor is MPL =

q( L, K ) . L

Under the hypothesis of eventually diminishing marginal product (of labor), the following will eventually hold:

 2 q( L, K ) 0. L2

(Again, note that this is a partial derivative, so we are hypothesizing this will be true when capital is held fixed, a short-run situation.)

2) Under what conditions will we see an “S-shaped” total product curve? How does this shape relate to the shape of the short-run marginal cost curve? We will see an “S-shaped” total product (of labor) curve when a firm experiences initially increasing and eventually diminishing marginal product (of labor). When wages are fixed, we know that short-run marginal cost is inversely related to

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