# ECON 208 Lecture Notes - Root Mean Square, Marginal Product, Diminishing Returns

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Producers in the long-run
Long-run: no ﬁxed factors
- all factors can be varied
- numerous ways to produce any given output
- ﬁrms in the long-run must choose the type/amount of plant/equipment/labor force
- producers aim to be technically efﬁcient (inputs are combined to maximize output)
- technical efﬁciency isn't enough for proﬁt maximization
- the ﬁrm must choose from the many technically efﬁcient options and pick the one that produces a given
level of output at the lowest cost
- choices about how much capital and labor to use are long-run choices because all factors are assumed
to be variable
Proﬁt maximization and cost minimization
- cost minimization = ﬁrms choose the production method that produces a given level of output at the lowest
possible cost
- long-run cost minimization:
- if its possible to substitute one factor for another to keep output constant/reduce total cost the ﬁrm is
not minimizing its costs
- the ﬁrm should substitute one factor for another factor as long as the marginal product of one factor
is greater than the marginal product of another factor
- i.e. if more \$ spent on labor produces more output than more \$ spent on capital would, the ﬁrm can
reduce costs by spending more on labor and reducing expenditure on capital
- MP of capital/price of one unit of capital = MP of labor/price of one unit of labor
- when they are not equal there are possibilities for factor substitutions that will reduce costs
- but will the law of diminishing returns
- new cost-minimizing condition: MP of capital/MP of labor = price of one unit of capital/price of one
unit of labor
- new condition compares contribution to output of the last unit of capital and the last unit of labor
- the right side shows how the cost of an additional unit of capital compares to the cost of an
- if the two sides are the same then the ﬁrm can't make any substitutions between labor/capital to
reduce costs
- if the ratio on the right side < left side then the ﬁrm should switch to a production method that uses
less labor and more capital
- only when the ratio of MPs is exactly = to the ratio of factor prices is when the ﬁrm is using the cost-
minimizing production method
Principle of substitution
- methods of production will change if relative prices of inputs change, with relatively more of the cheaper
input and relatively less of the more expensive input being used
- this principle plays a central role in resource allocation
- it relates to the way ﬁrms respond to changes in relative factor prices that are caused by the changing
scarcities of factors in the economy
- ﬁrms are motivated to use less factors that become scarce and more factors that are plentiful in the
economy
i.e. banks: price of labor has gone up, price of atm equipment has gone down, now employ more
capital than labor
Long-run cost curves
- LRAC: shows lowest possible cost of producing each level of output when all inputs can be varied
- with given factor prices there is a minimum achievable cost for each level of output
- if cost is in \$ per unit of output, we get the LRAC of producing
- LRAC = U shape, part before the minimum = decreasing costs/increasing returns, minimum = constant
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