chapter 6_the theory of cost

7/29/2019 Chapter 6_the Theory of Cost

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Written by: Edmund Quek

2011 Economics CafeAll rights reserved. Page 1

CHAPTER 6

THE THEORY OF COST

LECTURE OUTLINE

1 INTRODUCTION

2 SHORT-RUN THEORY OF COST

2.1 Distinction between fixed cost and variable cost

2.2 Total cost

2.3 Marginal cost2.4 Average cost

2.5 Relationship between marginal cost and average cost

2.6 Optimum capacity

3 LONG-RUN THEORY OF COST

3.1 Cost minimisation in the long run3.2 Long-run average cost

3.3 Productive efficiency

References

John Sloman, Economics

William A. McEachern, EconomicsRichard G. Lipsey and K. Alec Chrystal, Positive Economics

G. F. Stanlake and Susan Grant, Introductory Economics

Michael Parkin, EconomicsDavid Begg, Stanley Fischer and Rudiger Dornbusch, Economics


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1 INTRODUCTION

Explicit costs are costs that involve monetary payments such as the costs of materials and

labour. Accounting costs include only explicit costs. Implicit costs are costs that do notinvolve monetary payments such as the costs of the owners labour and financial capital.

Economic costs include both explicit costs and implicit costs. Economists are concernedwith economic profit and hence economic costs. An increase in output will require anincrease in the quantity of factor inputs which will lead to an increase in costs. The theory

of cost is the study of how the cost of production changes as the output level changes. This

chapter gives an exposition of the theory of cost.

2 SHORT-RUN THEORY OF COST

2.1 Distinction between fixed costs and variable costs

Fixed costs are costs that do not vary with the output level as they are associated with fixedfactor inputs. In other words, an increase in the output level will not lead to an increase in

fixed costs. Fixed costs will still be incurred even if the firm shuts down production.

Examples of fixed costs are interest payments on loans for the purchase of capital goods

(factories and machinery), insurance premiums and rent.

Variable costs are costs that vary directly with the output level as they are associated with

variable factor inputs. In other words, an increase in the output level will lead to an increasein variable costs since more variable factor inputs are needed to produce more output.

Variable costs will not be incurred if the firm shuts down production. Examples of variable

costs are the costs of materials and direct labour (labour provided by factory workers).

2.2 Total cost

Total cost (TC) is the cost of all the factor inputs needed to produce an amount of output. In

the short run, total cost is the sum of total fixed cost (TFC) and total variable cost (TVC)

and is positively related to the output level.


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TC Curve

In the above diagram, since fixed costs do not vary with the output level, the TFC curve is

horizontal. However, since more variable factor inputs are needed to produce more output,

the TVC curve is upward-sloping. Since TC is the sum of TFC and TVC, the TC curve isgeometrically similar to the TVC curve, except that the former is higher than the latter by

TFC at each output level.

From the first unit of output to Q0, the firm is experiencing increasing marginal returns. In

other words, each additional unit of the variable factor input is adding more to total output

than the previous additional unit. Therefore, each additional unit of output requires fewer

units of the variable factor input to produce and this makes the TC and the TVC curves riseat a decreasing rate (i.e. the slopes of the TC and the TVC curves are decreasing).

After Q0, the firm is experiencing diminishing marginal returns. In other words, eachadditional unit of the variable factor is adding less to total output than the previous

additional unit. Therefore, each additional unit of output requires more units of the variable

factor input to produce and this causes the TC and the TVC curves to rise at an increasing

rate (i.e. the slopes of the TC and the TVC curves are increasing).

2.3 Marginal cost

Marginal cost (MC) is the additional cost resulting from producing one more unit of output.

Mathematically,

TC TVC

MC -------- or ----------

Q Q


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Therefore, marginal cost is the slope of the TC or the TVC curve.

MC Curve

In the above diagram, from the first unit of output to Q0, the firm is experiencing increasingmarginal returns. The slope of the TC curve is decreasing and hence the MC curve is

falling. At Q0, the slope of the TC curve is the smallest and hence the MC curve is at its

minimum. After Q0, the firm is experiencing diminishing marginal returns. The slope ofthe TC curve is increasing and hence the MC curve is rising.

2.4 Average cost

Average cost (AC) is the cost per unit of output.

Mathematically,

TC

AC -------Q

Therefore, average cost is the slope of the line from the origin to the TC curve.


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AC Curve

In the above diagram, from the first unit of output to Q2, since the slope of the line from the

origin to the TC curve is decreasing, the AC curve is falling. At Q2, the slope of the line

from the origin to the TC curve is smallest and hence the AC curve is at its minimum. AfterQ2, since the slope of the line from the origin to the TC curve is increasing, the AC curve is

rising.

Average variable cost (AVC) is the variable cost per unit of output.

Mathematically,

TVC

AVC --------Q

Therefore, average variable cost is the slope of the line from the origin to the TVC curve.


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AVC Curve

In the above diagram, from the first unit of output to Q1, since the slope of the line from the

origin to the TVC curve is decreasing, the AVC curve is falling. At Q1, the slope of line

from the origin to the TVC curve is smallest and hence the AVC curve is at its minimum.After Q1, since the slope of the line from the origin to the TVC curve is increasing, the

AVC curve is rising.

Average fixed cost (AFC) is the fixed cost per unit of output.

Mathematically,

TFC

AFC --------Q

Therefore, average fixed cost is the slope of the line from the origin to the TFC curve.


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AFC Curve

In the above diagram, from the first unit of output, since the slope of the line from the

origin to the TFC curve is decreasing, the AFC curve is falling.

2.5 Relationship between marginal cost and average cost

In the above diagram, from the first unit of output to Q0, the MC curve is falling, and is

rising thereafter. From the first unit of output to Q1, the MC curve is lower than the AC andthe AVC curves and hence the AC and the AVC curves are falling. After Q1, the MC curve

is higher than the AVC curve and hence the AVC curve is rising. After Q2, the MC curve is

higher than the AC curve and hence the AC curve is rising. Therefore, the MC curve cutsthe AVC and the AC curves at the minimum points.


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Since AC is the sum of AVC and AFC, the vertical distance between the AVC and the AC

curves is equal to AFC. Since the AFC curve is falling, the vertical distance between the

AVC and the AC curves narrows as the output level increases.

2.6 Optimum capacity

If a firm produces the output level that corresponds to the lowest point on the average cost

curve, it is producing at optimum capacity.

In the above diagram, if the firm produces Q0, it is producing at optimum capacity. If the

firm produces an output level lower than Q0, such as Q

1, it is producing under capacity or

with excess capacity. If the firm produces an output level higher than Q0, such as Q2, it is

producing over capacity.


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3 LONG-RUN THEORY OF COST

3.1 Cost minimisation in the long run

Since there are no fixed factor inputs in the long run, a firm will choose the quantity of

fixed factor inputs that achieves the lowest average cost of producing any output level.Suppose that a firm can choose among three quantities of fixed factor inputs: smallquantity, medium quantity and large quantity.

In the above diagram, the average cost curves that correspond to the three quantities of

fixed factor inputs are AC0, AC1 and AC2, where AC0 corresponds to the small quantity,

AC1

corresponds the medium quantity and AC2

corresponds to the large quantity.

If the firm wants to produce Q0, average cost will be lowest if it produces on AC0 and hence

it will choose the small quantity of fixed factor inputs. If the firm wants to produce Q 1,average cost will be lowest if it produces on AC1 and hence it will choose the medium

quantity of fixed factor inputs. If the firm wants to produce Q2, average cost will be lowest

if it produces on AC2 and hence it will choose the large quantity of fixed factor inputs.

3.2 Long-run average cost

The long-run average cost (LRAC) curve shows the lowest average cost of producing each

output level when all the factor inputs used in the production process are variable in the

long run. Each point on the LRAC curve is a point of tangency to the AC curve with the

lowest average cost of producing the corresponding output level.

In section 3.1, we assume that a firm can choose among three quantities of fixed factor

inputs. For an output level below Q, the lowest-average-cost quantity of fixed factorinputs is the small quantity of fixed factor inputs that corresponds to AC0. For an output


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level between Q and Q, the lowest-average-cost quantity of fixed factor inputs is the

medium quantity of fixed factor inputs that corresponds to AC1. For an output level above

Q, the lowest-average-cost quantity of fixed factor inputs is the large quantity of fixed

factor inputs that corresponds to AC2. Therefore, the LRAC curve is the bold curve in thebelow diagram.

However, if we assume that a firm can choose among an infinite number of quantities offixed factor inputs, we will get a U-shaped LRAC curve.

LRAC curve


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3.3 Productive efficiency

From a firms perspective, it isproductively efficient when it produces on its LRAC curve

and this occurs when it is x-efficient and uses the least-cost combination of factor inputs toproduce any amount of output. As we discussed earlier, the least-cost condition is met

when the last dollar of each factor input employed produces the same additional output. If afirm employs two factor inputs, labour (L) and capital (K), the least-cost condition can beexpressed mathematically as MPL/PL = MPK/PK, where MP denotes marginal product and

P denotes price. A firm is x-efficient when it is not lax in cost control. In other words, it is

not overstaffed, it does not lack the incentive to use the most efficient productiontechnology, etc. Since the least-cost condition will be met, in the long run, if not in the

short run, whether a firm is productively efficient depends on whether it is x-efficient. In

other words, if a firm is x-efficient, it will also be productively efficient. The converse is

also true.

From societys perspective, a firm is productively efficient when it produces on the lowest

point on its LRAC curve.

chapter 6_the theory of cost

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