Principles of Economics: Long-run Competitive Equilibrium
Recall that all factors, particularly capital, are variable in the long-run. There are two ways
(plus combinations of the two ways) that Capital can change in the long-run.
1. Change in the size of individual firms through additional or improved equipment and
buildings or through reduction or depreciation of equipment and buildings.
2. Entry into or exit from the industry by firms of the same size as existing firms.
Economies of Scale:
We analyze the effect of changes in the size of individual firm capital through the concept
of economies of scale.
Definition. Economies of Scale (Increasing Returns to Scale) occur when a % increase in all
factor inputs causes a greater % increase in output.
E.g. Suppose that 5 units of Labour and 3 units of Capital produce 100 units of output but that 10
units of Labour and 6 units of Capital produce 250 units of output.
=> 100% increase in factor inputs produces a 150% increase in output.
Why does the concept of Economies of Scale not contradict Eventually Diminishing
Definition: Diseconomies of Scale (Decreasing Returns to Scale) occurs when a % increase in
all factors causes a smaller % increase in output.
Definition: Constant Returns to Scale occurs when a % increase in all factors causes the same
% increase in output.
Average Cost decreases with Economies of Scale
The key element of economies of scale is a decrease in Average Cost with increases in output.
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Proof: Recall that Average Cost = ACo = (wL + rK)/q
Define ‘a’ as the % change in inputs and ‘b’ as the % change in outputs.
=> AC =1(waL + raK)/bq = a/b(wL + rK)/q = a/b * ACo
a < b => Economies of Scale (Increasing Returns to Scale) => Average Cost decreases
a = b => Constant Returns to Scale => no change in Average
a > b => Diseconomies of Scale (Decreasing Returns to Scale) => Average Cost increases
Derivation of Long-run Average Cost from Short-run Average Cost Curves
Since each quantity of capital gives specific short-run cost functions, we can derive long-
run average cost from the short-run average cost function of each capital.
Quantity 20 40 60 80 100 120
ACo (Ko) $20 $14 $10 $15 $22 $30
AC 1K >1o) $30 $20 $12 $8 $10 $14
AC 2K >2 )1 $40 $25 $15 $10 $6 $8
AC 3K >3 )2 $60 $45 $32 $20 $14 $10
Cost/unit Long-run Average Cost
Average Cost falls to minimum and then rises for each Capital. Given that fixed cost is
larger for larger capitals, average cost for small output is greater for larger capitals relative to
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smaller capitals. Average Cost is eventually lower for larger capitals relative to smaller capitals
if there is economies of scale but minimum average cost will rise if there are diseconomies of
Note that falling long-run average cost implies economies of scale and rising long-run
average cost implies diseconomies of scale.
Long-run Average Cost tends to initially decrease due to increasing returns to scale with
increased capital and labour and eventually increase due to decreasing returns to scale with
increased capital and labour. There is only one minimum average cost attainable though it may
occur with different amounts of capital and labour. The smallest capital that gives this minimum
average cost is called Minimum Efficient Scale.
Long-run Average Cost (LRAC)
Long-run Average Cost shows the lowest average cost for each output in the long-run. This
defines the size of capital for lowest average cost for each output.
If capital is infinitely divisible, Long-run Average Cost is a smooth curve with each point
from the short-run average cost of each capital.
Profit Maximization in the long-run implies that firms change capital and labour until they
find the capital with the Short-run Average Cost function that gives minimum Long-run Average
Cost for the desired output.
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The diagram below represents the Long-run Average Cost curve for an industry and three
sizes of capital in the industry with their attendant Short-run Average Cost curves. Provided that
there is no technological change (i.e., no new minimum efficient scale), examination of the
diagram shows that in competitive conditions price will fall from Po to P* as new firms enter the
industry due to economic profits at Po for all capitals and above P* for the minimum efficient
scale capital. In the long-run, no firm could obtain the average return on capital unless the firm
was the size (capital) that permitted Minimum Efficient Scale.
This derivation shows that ‘perfect competition’ – all firms are the same size with similar
cost functions – is an evolutionary result of a competitive market provided that there is no
technological change. The assumption of perfect competition means that we do not need to draw
the Long-run Average Cost function since we know that its minimum is minimum Short-run
Average Cost of the firm.
Technological change alters the minimum efficient scale, usually increasing it but
sometimes decreasing it drastically. Electricity generation was dominated by $Billion plus
plants (Hydro, Nuclear, or Coal) up until the 1970s since these huge plants produced the
cheapest electricity. The development of Co-generation Gas Turbines in the 1970s introduced
small jet engines that could produce electricity competitively because their small size and clean
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combustion of natural gas meant that they could be located in buildings to take advantage of the
heat generated in combustion. The low natural gas prices of the 1980s and 1990s made these co-
generators a formidable competitive of the huge plants, sparking the collapse of monopoly
pricing in various jurisdictions, especially California.
LONG-RUN COMPETITIVE EQUILIBRIUM
We will assume perfect competition without technological change in this course so we can
ignore the possibility of changes in the size of firm capital. Changes in capital can therefore only
occur through the entry into or exit from the industry of perfectly competitive firms.
Long-run Equilibrium => No change in Capital despite the possibility of Capital Change
=> No firms enter or exit the industry
=> 0 Economic Profit
=> P = min AC (Price = minimum Average Cost)
We express long-run equilibrium graphically through the firm/industry diagram Demand
and Supply intersecting at minimum Average Cost as in the following diagram.
q0 qx Q0 Qx
E.g. Suppose that a perfectly competitive firm has the following cost functions.
VC = 2q + 30q FC = 1800 MC = 4q + 30
=> AVC = VC/q = 2q + 30 AC = TC/q = 2q + 30 + 1800/q
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1. What is firm Supply?
Firm Supply = MC > min AVC => P = 4q + 30
2. What is industry Supply if there are n firms