# COMMERCE 4FP3 Lecture Notes - Variable Cost, European Cooperation In Science And Technology, Cost Curve

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Published on 31 Jan 2013

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Principles of Economics: Long-run Competitive Equilibrium

LONG-RUN COST

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

Returns (MP)?

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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Principles of Economics: Long-run Competitive Equilibrium

Proof: Recall that Average Cost = ACo = (wL + rK)/q

Define ‘a’ as the % change in inputs and ‘b’ as the % change in outputs.

=> AC1 = (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

Cost

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

AC1(K1>Ko) $30 $20 $12 $8 $10 $14

AC2(K2>K1) $40 $25 $15 $10 $6 $8

AC3(K3>K2) $60 $45 $32 $20 $14 $10

Long-run Average Cost

Cost/unit

Quantity

ACo

AC

1

AC

2

AC

3

LRAC

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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Principles of Economics: Long-run Competitive Equilibrium

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

scale.

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.

Average Cost

q

Increasing

Returns

Minimum

Efficient Scale

Decreasing

Returns

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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