Eco 201
Spring 2009
Lecture 4.2b
Cost Functions
Long-run Cost Curve
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The marginal cost curve (MC)
• A marginal cost represents the relation
between marginal cost incurred by a firm
in the short-run production of a good and
the quantity of output produced.
– holding other variables, like technology and
resource prices, constant.
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The marginal cost curve (MC)
• Marginal Cost = Difference in total costs in going from
producing Q -> Q+1 units
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The marginal cost curve (MC)
• The marginal cost curve is U-shaped.
Marginal cost is relatively high at small
quantities of output, then as production
increases, declines, reaches a minimum
value, then rises.
– Shape of the marginal cost curve is due: 1)
first, increasing; 2) then decreasing marginal
returns (and the law of diminishing marginal
returns - Diminishing returns).
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Diminishing Marginal Returns
• In economics, diminishing returns is also
called diminishing marginal returns or
the law of diminishing returns.
– In a production system with fixed and variable
inputs (say factory size and labor), beyond
some point, each additional unit of variable
input yields less and less additional output
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A Little History
Malthus
• The concept of diminishing returns can be traced back to
the concerns of early economists such as Johann
Heinrich von Thünen, Turgot, Thomas Malthus and
David Ricardo.
• Malthus and Ricardo, who lived in 19th century England,
were worried that land, a factor of production in limited
supply, would lead to diminishing returns. In order to
increase output from agriculture, farmers would have to
farm less fertile land or farm existing land with more
intensive production methods. In both cases, the returns
from agriculture would diminish over time, causing
Malthus and Ricardo to predict population would outstrip
the capacity of land to produce, causing a Malthusian
catastrophe. (Case & Fair, 1999: 790).
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In Terms of Cost
• Producing one more unit of output costs
more and more in variable inputs.
– Law of increasing relative cost, or law of
increasing opportunity cost.
– Diminishing marginal returns also implies a
technological relationship.
• Decreased “specialization” or productivity of an
input, e.g., labor
– Less well-suited for production of this good
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An Example
• Suppose that one kilogram (kg) of seed applied to a plot of land of a
fixed size produces one ton of crop.
– You might expect that an additional kilogram of seed would produce an
additional ton of output.
• If there are diminishing marginal returns, that additional kilogram will
produce less than one additional ton of crop (on the same land,
during the same growing season, and with nothing else but the
amount of seeds planted changing).
– “crowding out” from sunlight, competition for water and nutrients –
increased “seed density” decreases production
• For example, the second kilogram of seed may only produce a half
ton of extra output.
• Diminishing marginal returns also implies that a third kilogram of
seed will produce an additional crop that is even less than a half ton
of additional output. Assume that it is one quarter of a ton.
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Combining cost curves:
MC and TC (ATC)
• Combine marginal, total cost curves to provide
information about firms.
– Assume that the firm is in a perfectly competitive market.
• Marginal revenue equals market equilibrium price
• Marginal cost curve will cut the average cost curve at its
lowest point.
• In a perfectly competitive market a firm's profit
maximizing price would be above the price at which the
average cost curve cuts the marginal cost curve.
– If the marginal revenue is above the average total cost price the
firm is deriving an economic profit.
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Combining cost curves
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A good link for cost curves
• http://www.whitenova.com/thinkEconomics
/lrac.html
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The long-run average cost curve
(LRAC)
• LRAC is U-shaped
– Since all factors are variable, U-shape reflects (dis)economies of scale
or scope
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Long-run/short-run Cost Curves
• Long-run average cost curve is the envelope of
an infinite number of short-run average total cost
curves,
– Each short-run average total cost curve tangent to, or
just touching, the long-run average cost curve at a
single point corresponding to a single output quantity.
– The key to the derivation of the long-run average cost
curve is that each short-run average total cost curve
is constructed based on a given amount of the fixed
input, usually capital.
• when the quantity of the fixed input changes, the short-run
average total cost curve shifts to a new location.
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Relationship between SRAC and
LRAC curves
• In the SR one factor (K) is fixed
– Chose K to minimize costs for a given level of output
• http://www.amosweb.com/cgibin/awb_nav.pl?s=wpd&c=dsp&k=longrun+average+cost+curve,+derivation
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Envelope Theorem
• Long-run cost curve when K is completely
variable
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Long-run <-> Short-run
Cost Curves
• Long-run average cost curve is the factory size
(or quantity of capital) that can produce each
quantity of output at the lowest short-run
average total cost.
• Five short-run average total cost curves
– corresponds to five alternative factory sizes that could
be used to produce Stuffed Amigos--10,000 square
feet, 20,000 square feet, 30,000 square feet, 40,000
square feet, and 50,000 square feet. These five
factors reach minimum short-run average total cost at
production levels of 100, 200, 300, 400, and 500
Stuffed Amigos, respectively.
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The long-run average cost curve
(LRAC)
• The LRAC curve is U-shaped
• As a firm in the long-run increases the quantities of all
factors employed, other things being equal:
– the output may increase initially at a more rapid rate (economies
of scale) than the rate of increase in inputs,
– then output may increase in the same proportion of the input
(constant returns to scale),
– and ultimately, output increases less proportionately
(diseconomies).
• economies of scale when negatively-sloped
• diseconomies of scale when positively sloped.
• Constant returns to scale when no slope
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Review
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