Transcript Long-run average cost

CHAPTER 7
Costs and supply
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The complete theory of supply (1)
• Short-run and long-run cost curves and output
decisions need to be carefully distinguished
when we study the determinants of supply.
• The profit-maximizing firm will choose the lowest
cost way of producing any given level output,
given the technology available and factor input
costs.
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The complete theory of supply (2)
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The production function
• The amount of output produced depends
upon the inputs used in the production
process.
• A factor of production (“input”) is any
good or service used to produce output.
• The production function specifies the
maximum output which can be produced
given inputs.
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Short run vs long run
• The short run is the period in which a firm can
make only partial adjustment of inputs, e.g. the
firm may be able to vary the amount of labour,
but cannot change capital.
• The long run is the period in which a firm can
adjust all inputs to changed conditions.
• The long run total cost curve describes the
minimum cost of producing each output level
when the firm is free to vary all input levels.
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The short run
• Fixed factor of production
– a factor whose input level cannot be varied
• Fixed costs
– costs that do not vary with output levels
• Variable costs
– costs that do vary with output levels
• Short-run total cost (STC) = short-run fixed cost
(SFC) + short-run variable cost (SVC)
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The marginal product of labour
• The marginal product of labour is the
increase in output obtained by
adding 1 unit of the variable factor
but holding constant the inputs of all
other factors.
• Labour is often assumed to be the
variable factor, with capital fixed.
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The law of diminishing
marginal returns
• Holding all factors constant except one, the law of
diminishing marginal returns implies that beyond
some value of the variable input further increases in
the variable input lead to steadily decreasing
marginal product of that input.
• For example, trying to increase labour input without
also increasing capital will bring diminishing
marginal returns.
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The firm’s short-run output decision
£
SATC1
SAVC1
SMC = MR
MR
Q1
Output
• Firm sets output at Q1,
where SMC=MR
• subject to checking the
average condition:
– if price is above SATC1
firm produces Q1 at a
profit
– if price is between
SATC1 and SAVC1 firm
produces Q1 at a loss
– if price is below SAVC1
firm produces zero
output.
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Costs in the long run: Average cost
The average cost of production is total cost divided by
the level of output.
Long-run average cost (LAC) is often assumed to be Ushaped:
Output
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Costs in the long run: Economies of
scale
Economies of scale – or increasing returns to scale –
occur when long-run average costs decline as output
rises:
Output
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Costs in the long run: Decreasing
returns to scale
Decreasing returns to scale occur when long-run
average costs rise as output rises:
Output
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Costs in the long run: Constant
returns to scale
Constant returns to scale occur when long-run average
costs are constant as output rises:
Output
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The firm’s long-run output decision
£
LMC = MR
MR
• The decision:
– If the price is at or
above LAC1 the firm
produces Q1
– If the price is below
LAC1 the firm goes
out of business
• NB: LMC always passes
through the minimum
point of LAC.
Output
(goods per week)
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Average cost
The long-run average cost curve (LAC)
SATC2
SATC1
Each plant size
is designed for
a given output
level.
SATC4
SATC3
Output
So there is a
sequence of SATC
curves, each
corresponding to
a different plant
size.
In the long-run, plant size itself is variable, and the long-run
average cost curve LAC is found to be the ‘envelope’ of
the SATCs.
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The firm’s output decisions – a summary
Marginal
condition
Check whether to
produce
Short-run decision Choose the
output at which
MR=SMC
Produce this
output unless
price lower than
SAVC, in which
case produce
zero
Long-run decision Choose the
output at which
MR=LMC
Produce this
output unless
price is lower
than LAC, in
which case
produce zero.
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Some maths
• An example of a short-run total cost
function: STC  F  cQ  dQ 2
• Where SFC=F and SVC = cQ+ Dq2
• and
dSTC
SMC 
 c  2dQ
dQ
SFC F
SAFC 

Q
Q
• Thus the short-run average fixed cost
decreases steadily as Q increases.
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Some maths (2)
• Short run average variable cost is:
SVC
SAVC 
 c  dQ
Q
• And short run average total cost:
STC F
SATC 
  c  dQ
Q
Q
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Concluding comments (1)
• In the long run, a firm can fully adjust all its inputs.
• In the short run, some inputs are fixed.
• The production function shows the maximum
output that can be produced using given
quantities of inputs.
• The total cost curve is derived from the
production function, for given wages and rental
rates of factors of production.
• The short-run marginal cost curve (SMC) reflects
the marginal product of the variable factor,
holding other factors fixed.
• The SMC curve cuts both the SATC and SAVC
curves at their minimum points.
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Concluding comments (2)
• The long-run total cost curve is obtained by
finding, for each output, the least-cost method
of production when all inputs can be varied.
• Average cost is total cost divided by output.
• LAC is typically U-shaped.
• Much of manufacturing has economies of
scale.
• When marginal cost is below average cost,
average cost is falling.
• In the long run, the firm supplies the output at
which long-run marginal cost (LMC) equals MR
provided price is not less than the level of longrun average cost at that level of output.
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