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Technology
I. Describing technological constraints
- production set: combinations of inputs and outputs that are
feasible patterns of production
- production function: upper boundary of production set
- isoquants: all combinations of inputs that produce a
constant level of output, which are just like indifference
curves (constant utility)
II. Examples of isoquants
- can't take monotonic transformations any more!
- fixed proportions: one man, one shovel
- perfect substitutes: pencils
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III. Well-behaved technologies
- monotonic: more inputs produce more output
- convex: averages produce more than extremes
IV. Marginal product
- MP1 is how much extra output you get from increasing the
input of good 1, holding good 2 fixed
V. Technical rate of substitution
- like the marginal rate of substitution
- given by the ratio of marginal products
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VI. Diminishing marginal product
- more and more of a single input produces more output, but
at a decreasing rate. See Figure 18.5.
- law of diminishing returns
VII. Diminishing technical rate of substitution
- equivalent to convexity
- note difference between diminishing MP and diminishing
TRS
VIII. Long run and short run
- All factors varied in the long run
- Some factors fixed in the short run
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IIX. Returns to scale
- constant returns: baseline case
- increasing returns
- decreasing returns
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Profit Maximization
I. Profits defined to be revenues minus costs
- value each output and input at its market price: even if it is
not sold on a market.
- it could be sold, so using it in production rather than
somewhere else is an opportunity cost.
II. Short-run and long-run maximization
- variable factor
- the least profits a firm can make in the long run are zero
- fixed factors: plant and equipment
- the profits can be negative in the short run
- quasi-fixed factors: can be eliminated if operate at zero
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output (advertising, lights, heat, etc.)
III. Short-run profit maximization.
- max pf(x) − wx
- the optimal condition imply that the value of the marginal
product equals wage rate
- comparative statics: change w and p and see how x and f(x)
respond
IV. Long-run profit maximization
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V. Profit maximization and returns to scale
- constant returns to scale implies profits are zero
a) note that this doesn't mean that economic factors
aren't all appropriately rewarded
b) use examples
- increasing returns to scale implies competitive model
doesn't make sense
VI. Revealed profitability
- simple, rigorous way to do comparative statics
- observe two choices, at time t and time s: (pt, wt, yt, xt) and (ps,
ws, ys, xs)
- if firm is profit maximizing, then must have
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- The above two inequalities are referred to as the Weak
Axiom of Profit Maximization (WAPM)
- add these two inequalities:
- rearrange:
or
- implications for changing output and factor prices