# ECON 208 Chapter Notes - Chapter 8: Profit Maximization, Marginal Product, Dofasco

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School
McGill University
Department
Economics (Arts)
Course
ECON 208
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Chapter 8 Producers in the Long Run
8.1 The Long Run: No Fixed Factors
SR = at least one factor is fixed = must adjust the input of the variable factors to produce output
LR = all factors can be varied = must choose the type and amount of plant and equipment and
the size of their labour force
Technical efficiency: when a given number of inputs are combined in such a way as to maximize
the level of output
to maximize profits, firm must choose from among the many technically efficient options that
produces a given level of output at the lowest cost = combo that minimizes TC
how much capital/labour to use = LR choices = all factors of production are assumed to be
variable
Profit Maximization and Cost Minimization
Cost minimization: an implication of profit maximization that firms choose the production
method that produces any given level of output at the lowest possible cost
Long-Run Cost Minimization
Firm should substitute one factor for another as long as the marginal product of the one factor
per dollar spent on it is greater than the marginal product of the other factor per dollar spent on
it. If these 2 aren’t equal, firm isn’t minimizing costs.
K = capital, L = labour, pL and pK = prices per unit of the 2 factors; cost minimization occurs when
MPK = MPL
pK pL
Law of diminishing marginal returns says that, with other inputs held constant, an increase in
the amount of one factor used will decrease that factor’s marginal product
Reduce K and increase L, MPk rises, MPL falls
Whenever the ratio of the marginal product of each factor to its price isn’t equal for all factors,
there are possibilities for factor substitutions that will reduce costs (for a given level of output)
MPK = pK Left side: compares the contribution to output of the last unit of capital and last unit of
MPL = pL labour; Right side: how the cost of an additional unit of capital compares to the cost of
If the left < right, it would pay the firm to switch to a method of production that uses less capital
and more labour; but if left>right, then it would pay the firm to switch to a method of
production that uses less labour and more capital. Only when left=right is the firm using the
cost-minimizing production method.
Profit-maximizing firms adjust the quantities of factors they use to the prices of the factors given
by the market
The Principle of Substitution
Principle of Substitution: the principle that 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; profit-maximizing/cost-minimizing firms will react to changes in
factor process by changing their methods of production
Methods of production will change if the relative prices of factors change. Relatively more of the
cheaper factor and relatively less of the more expensive factors will be used.
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Principle of substitution plays a central role in resource allocation because it relates to the way
in which individual firms respond to changes in relative factor prices that are caused by the
changing relative scarcities of factors in the economy as a whole. Individual firms are motivated
to use less of factors that become scarcer to the economy and more of factors that become
plentiful
1st example: customer transactions in banks before bank hired many tellers to deal with the
hundreds of customers, now banking transactions facilitated with computers and dealt with
ATMs, automated telephone banking, or internet banking. Dramatic reduction in price of comps
and modest increase in wages = encouraged bankers to make this substitution of capital for
labour
2nd: producing same product differs across countries. Canada, labour is highly skilled and
expensive, farmers use machinery; developing countries, labour abundant and capital scarce,
less mechanized. Where factor scarcities differ across nations, so will the cost-minimizing
methods of production
3rd: firms can also be induced to substitute between capital and material inputs (fuel); increase
in price of oil = change in type of capital equipment to substitute away from jets that use a lot of
fuel toward ones that are more fuel efficient
Long-Run Cost Curves
With given factor prices, there is a minimum achievable cost for each level of output; if this cost
is expressed in terms of dollars per unit of output, we obtain the LR avg cost of producing each
level of output.
Long-run average cost (LRAC) curve: the curve showing the lowest possible cost of producing
each level of output when all inputs can be varied; determined by the firm’s current technology
and by the prices of the factors of production
The LRAC curve is the boundary between cost levels that are attainable (points on it; only if
sufficient time elapses for all inputs to be adjusted), with known technology and given factor
prices, and those that are unattainable (points below it). To move from one point on the curve
to another requires an adjustment in all factor inputs
In deriving the LRAC curve, unlike the SR cost curve, there are no fixed factors of production and
all costs are variable in the LR, so no AVC, AFC, ATC, only LRAC for any given set of input prices.
The Shape of the Long-Run Average Cost Curve
LRAC First falls and then rises; saucer/U-shaped
Decreasing Costs
From 0 to Qm (quantity at minimum price) the firm has falling LRAC: an expansion of output
permits a reduction of average costs.
Economies of scale: reduction of long-run avg costs resulting from an expansion in the scale of a
firm’s operations so that more of all inputs is being used
since the LRAC curve is draw assuming constant factor prices, the decline in LRAC occurs
because output is increasing more than in proportion to inputs as the scale of the firm’s
production expands.
3
Increasing returns (to scale): a situation in which output increases more than in proportion to
inputs as the scale of a firm’s production increases. A firm in this situation is a decreasing-cost
firm.
Increasing returns may occur due to increased opportunities for specialization of tasks made
possible by the division of labour; larger plants used greater specialization since large,
specialized equipment is useful only when the volume of output that the firm can sell justifies
using that equipment
Constant Costs
Minimum efficient scale (MES): the smallest output at which LRAC reaches its minimum. All
available economies of scale have been realized at this point; LRAC fall until output reaches Qm.
the LRAC curve is then flat over some range of output = firm encounters constant costs over the
relevant range of output so the LRAV font change as its output changes; since factor prices are
assumed to be fixed, the firm’s output must be increasing exactly in proportion to the increase
in inputs
Constant returns (to scale): a situation in which output increases in proportion to inputs as the
scale of production is increased. A firm in this situation is a constant-cost firm.
Increasing Costs
When the LRAC curve is rising, a LR expansion in production is accompanied by a rise in avg
costs
Decreasing returns (to scale): a situation in which output increases less than in proportion to
inputs as the scale of a firm’s production increases. A firm in this situation is an increasing-cost
firm
^firm suffers some diseconomies of scale = difficulties of managing and controlling an enterprise
as its size increases; at first scale economies as firm grows and benefits from greater
specialization, but after, planning and coordination problems may multiply more than in
proportion to the growth in size = management costs per unit of output^
Other diseconomies = possible alienation of the labour force as size^ = harder to supervise
because too many supervisors and middle managers who are hard to control; managers might
begin to pursue their own goals
SR one factor is fixed and law of diminishing returns ensures that returns to the variable factor
will eventually diminish. LR all factors variable and possible that diminishing returns never
encountered as long as it is genuinely possible to ^inputs of all factors
The Relationship between Long-Run and Short-Run Costs
Each curve assumes given prices for all factor inputs.
LRAC curve shows the lowest cost of producing any output when all factors are variable
SRATC curve shows the lowest cost of producing any output when one/more factors fixed
No short-run cost curve can fall below the long-run cost curve because the LRAC curve
represents the lowest attainable cost for each possible output.
As the level of output is changed, a diff-size plant is normally required to achieve the lowest
attainable cost;

## Document Summary

Sr = at least one factor is fixed = must adjust the input of the variable factors to produce output. Lr = all factors can be varied = must choose the type and amount of plant and equipment and the size of their labour force. How much capital/labour to use = lr choices = all factors of production are assumed to be variable. Cost minimization: an implication of profit maximization that firms choose the production method that produces any given level of output at the lowest possible cost. Firm should substitute one factor for another as long as the marginal product of the one factor per dollar spent on it is greater than the marginal product of the other factor per dollar spent on it. If these 2 aren"t equal, firm isn"t minimizing costs. K = capital, l = labour, pl and pk = prices per unit of the 2 factors; cost minimization occurs when.