Weebly - The Theory of Productionsmsecon.weebly.com/.../the_theory_of_production.docx · Web viewTo illustrate how this law underlies short-run production let us take the simplest

The Theory of Production

In this section, we will be examining the theory of production. The main objective is to explain the concepts underlying production decisions in the short and long run and the relationship between costs and production.

Profit and the aims of a firm

The traditional theory of supply, or theory of the firm, assumes that firms aim to maximise profit; this is a realistic assumption in any cases. In some circumstances, however, firms may not seek to maximise profits. Instead they may seek to maximise sales, or the rate of growth of sales. Alternatively, they may have no single aim, but rather a series of potentially conflicting aims held by different managers in different departments of the firm. Sometimes there may be a conflict between the owners of the firm and those running it. Not surprisingly, a firm’s behaviour will depend on just what its aims are.

The Production Function

Resources are used in producing goods and services. These resources are called factors of production. The basic factors include land, labor and capital.

The costs of production are measured as the costs of those resources. To asses these costs, we should know that given an amount of the resources, what is the best way of producing a product? Or that’s the maximum amount attainable from a given quantity of resources?

The answer to these questions is reflected in the production function. Thus this function defines a relation between maximum amount of output for given amount of inputs, holding technology constant. In this case, the production function represents maximum technical efficiency.

Short-Run Production Function:

The short run production is defined as the period of time which the inputs of some factors of production, called fixed factors, factors that do not vary with output. The factor that is fixed in the short run is usually an element of capital (such as plant and equipment), but it might be land, or the supply of labour that is on a long term contract. What matters about the short run is that at least one factor is fixed. The inputs that can vary in the short run are called variable factors.

`These handouts were adapted from

Sloman, J., Wride, A. (2009). Economics (7th ed.). England: Pearson Education Limited.

It is important to note that the short run is not the same duration in all industries. In the electric power industry, it may take two or three years to build a new power station. At the other end of the scale, a mechanic workshop may acquire new equipment in a few weeks, and thus the short run is correspondingly short

The law of diminishing returns

Production in the short run is subject to diminishing returns. You may well have heard of ‘the law of diminishing returns’: it is one of the most famous of all ‘laws’ of economics.

To illustrate how this law underlies short-run production let us take the simplest possible case where there are just two factors: one fixed and one variable. Take the case of a farm. Assume the fixed factor is land and the variable factor is labour. Since the land is fixed in supply, output per period of time can be increased only by increasing the amount of workers employed. But imagine what would happen as more and more workers crowd on to a fixed area of land. The land cannot go on yielding more and more output indefinitely. After a point the additions to output from each extra worker will begin to diminish.

Total Physical Product (TPP)

This is the total quantity of some output produced during a given time by all the factors of production that the firm employs.

Average Physical Product (APP)

This is output (TPP) per unit of the variable factor (Qv). In the case of the farm, it is the output of wheat per worker.

APP TPP/Qv

Marginal Physical Product

This is the extra output (Δ TPP) produced by employing one more unit of the variable factor. In symbols, marginal physical product is given by

= Δ TPP / ΔQv



Table below helps to illustrate these concepts.

Table 5.1 Total, Average and Marginal Physical Product in the Short Run

Average product is shown in column three in Table 5.1. Notice that as more of the variable factor is used, APP first rises then falls. The point where the APP reaches its maximum is call the point of diminishing average returns. This occurs at the 4th worker where maximum APP is 9.

The MPP is shown in column 4 in table above. Notice that it reached a maximum at point (b) and there after it declines. The level of output where the MPP reaches a maximum is called the point of diminishing marginal returns.



Figure 5.1 below plots the TPP. A simple illustration of the a TPP.

Figure 5.1 TPP of wheat

As the first farm workers are taken on, wheat output initially rises more and more rapidly. The assumption behind this is that with only one or two workers efficiency is low, since the workers are spread too thinly. With more workers, however, they can work together –each, perhaps, doing some specialist job – and thus they can use the land more efficiently. In Table 5.1, output rises more and more rapidly up to the employment of the third worker (point b). In Figure 5.1 the TPP curve gets steeper up to point b.

After point b, however, diminishing marginal returns set in: output rises less and less rapidly, and the TPP curve correspondingly becomes less steeply sloped. When point d is reached, wheat output is at a maximum: the land is yielding as much as it can. Any more workers employed after that are likely to get in each other’s way. Thus beyond point d, output is likely to fall again: eight workers produce less than seven workers.



Figure 5.2 below show the corresponding APP and MPP.

Figure 5.2 TPP, APP, MPP Curves for wheat

Relationship between TPP, APP and MPP

•The MPP between two points is equal to the slope of the TPP curve between those two points• MPP rises at first: the slope of the TPP curve gets steeper.

• MPP reaches a maximum at point b. At that point the slope of the TPP curve is at its steepest.

• After point b, diminishing returns set in. MPP falls. TPP becomes less steep.

• APP rises at first. It continues rising as long as the addition to output from the last worker (MPP) is greater than the average output (APP): the MPP pulls the APP up. This continues beyond point b. Even though MPP is now falling, the APP goes on rising as long as the MPP is still above the APP. Thus APP goes on rising to point c.



• Beyond point c, MPP is below APP. New workers add less to output than the average. This pulls the average down: APP falls.

• As long as MPP is greater than zero, TPP will go on rising: new workers add to total output.

• At point d, TPP is at a maximum (its slope is zero). An additional worker will add nothing to output: MPP is zero.

• Beyond point d, TPP falls. MPP is negative.

Long-Run Production Function:

In the long run, all factors of production are variable. There is time for the firm to build a new factory (maybe in a different part of the country), to install new machines, to use different techniques of production, and in general to combine its inputs in whatever proportion and in whatever quantities it chooses.

In the long run, then, there are several decisions that a firm has to make: decisions about the scale and location of its operations and what techniques of production it should use. These decisions affect the costs of production. It is important, therefore, to get them right.

The scale of production

If a firm were to double all of its inputs – something it could do in the long run – would it double its output? Or will output more than double or less than double? We can distinguish three possible situations:

Constant returns to scale. This is where a given percentage increase in inputs will lead to the same percentage increase in output.

Increasing returns to scale. This is where a given percentage increase in inputs will lead to a larger percentage increase in output.



Decreasing returns to scale. This is where a given percentage increase in inputs will lead to a smaller percentage increase in output.

Notice the terminology here. The words ‘to scale’ mean that all inputs increase by the same proportion. Decreasing returns to scale are therefore quite different from diminishing marginal returns (where only the variable factor increases). The differences between marginal returns to a variable factor and returns to scale are illustrated in Table 5.2.

Table 5.2 Short run and Long run illustration

In the short run, input 1 is assumed to be fixed in supply (at 3 units). Output can be increased only by using more of the variable factor (input 2). In the long run, however, both input 1 and input 2 are variable.

Economies of scale

The concept of increasing returns to scale is closely linked to that of economies of scale. A firm experiences economies of scale if costs per unit of output fall as the scale of production increases. Clearly, if a firm is getting increasing returns to scale from its factors of production, then as it produces more it will be using smaller and smaller amounts of factors per unit of output. Other things being equal, this means that it will be producing at a lower unit cost.

There are several reasons why firms are likely to experience economies of scale. Some are due to increasing returns to scale; some are not.



Specialisation and division of labour. In large-scale plants workers can do more simple, repetitive jobs. With this specialisation and division of labour less training is needed; workers can become highly efficient in their particular job, especially with long production runs; there is less time lost in workers switching from one operation to another; and supervision is easier. Workers and managers can be employed who have specific skills in specific areas.

Greater efficiency of large machines. Large machines may be more efficient in the sense that more output can be gained for a given amount of inputs. For example, only one worker may be required to operate a machine whether it be large or small. Also, a large machine may make more efficient use of raw materials.

By-products. With production on a large scale, there may be sufficient waste products to enable some by-product or by-products to be made.

Multi-stage production. A large factory may be able to take a product through several stages in its manufacture. This saves time and cost in moving the semi-finished product from one firm or factory to another. For example, a large cardboard-manufacturing firm may be able to convert trees or waste paper into cardboard and then into cardboard boxes in a continuous sequence.

Organisational economies. With a large firm, individual plants can specialise in particular functions. There can also be centralised administration of the firm; for example, one human resources department could administer all the wages. Often, after a merger between two firms, savings can be made by rationalising their activities in this way.

Financial economies. Large firms are often able to obtain finance at lower interest rates than small firms. They may be able to obtain certain inputs cheaper by buying in bulk.

Economies of scope. Often a firm is large because it produces a range of products. This can result in each individual product being produced more cheaply than if it was produced in a single-product firm. The reason for these economies of scope is that various overhead costs and financial and organisational economies can be shared among the products. For example, a firm that produces a whole range of CD players, amplifiers and tuners can benefit from shared marketing and distribution costs and the bulk purchase of electronic components.

Diseconomies of scale

When firms get beyond a certain size, costs per unit of output may start to increase. There are several reasons for such diseconomies of scale:



• Management problems of co-ordination may increase as the firm becomes larger and more complex, and as lines of communication get longer. There may be a lack of personal involvement by management.

• Workers may feel ‘alienated’ if their jobs are boring and repetitive, and if they feel that they are an insignificantly small part of a large organisation. Small- to medium-sized companies often report that workers feel they ‘make a difference’; this may be lost in a large firm and as a consequence lower motivation may lead to shoddy work.

• Industrial relations may deteriorate as a result of these factors and also as a result of the more complex interrelationships between different categories of worker. More levels of ‘people management’ may therefore be required.

• Production-line processes and the complex interdependencies of mass production can lead to great disruption if there are hold-ups in any one part of the firm.

Whether firms experience economies or diseconomies of scale will depend on the conditions applying in each individual firm.



Costs in the Short Run and Long Run

We have seen how output changes as inputs are varied in the short run. We now use this information to show how costs vary with the amount a firm produces. Obviously, before deciding how much to produce, it has to know the precise level of costs for each level of output. But first we must be clear on just what we mean by the word ‘costs’. The term is used differently by economists and accountants.

Measuring costs of production

When measuring costs, economists always use the concept of opportunity cost. Remember from Chapter 1 how we defined opportunity cost. It is the cost of any activity measured in terms of the sacrifice made in doing it: in other words, the cost measured in terms of the opportunities forgone. How do we apply this principle of opportunity cost to a firm? First we must discover what factors of production it is using. Then we must measure the sacrifice involved. To do this it is necessary to put factors into two categories.

Factors not owned by the firm: explicit costs

The opportunity cost of using factors not already owned by the firm is simply the price that the firm has to pay for them. Thus if the firm uses £100 worth of electricity, the opportunity cost is £100. The firm has sacrificed £100 which could have been spent on something else. These costs are called explicit costs because they involve direct payment of money by firms.

Factors already owned by the firm: implicit costs

When the firm already owns factors (e.g. machinery), it does not as a rule have to pay out money to use them. Their opportunity costs are thus implicit costs. They are equal to what the factors could earn for the firm in some alternative use, either within the firm or hired out to some other firm.

Here are some examples of implicit costs:

• A firm owns some buildings. The opportunity cost of using them is the rent it could have received by letting them out to another firm.

• A firm draws £100 000 from the bank out of its savings in order to invest in new plant and equipment. The opportunity cost of this investment is not just the £100 000 (an explicit cost), but also the interest it thereby forgoes (an implicit cost).



• The owner of the firm could have earned £20 000 per annum by working for someone else. This £20 000 is then the opportunity cost of the owner’s time. If there is no alternative use for a factor of production, as in the case of a machine designed to produce a specific product, and if it has no scrap value, the opportunity cost of using it is zero. In such a case, if the output from the machine is worth more than the cost of all the other inputs involved, the firm might as well use the machine rather than let it stand idle.

What the firm paid for the machine – its historic cost – is irrelevant. Not using the machine will not bring that money back. It has been spent. These are sometimes referred to as ‘sunk costs’.

Costs and inputs

A firm’s costs of production will depend on the factors of production it uses. The more factors it uses, the greater will its costs be. More precisely, this relationship depends on two elements:

• The productivity of the factors. The greater their physical productivity, the smaller will be the quantity of them required to produce a given level of output, and hence the lower will be the cost of that output. In other words, there is a direct link between TPP, APP and MPP and the costs of production.

• The price of the factors. The higher their price, the higher will be the costs of production. In the short run, some factors are fixed in supply. Their total costs, therefore, are fixed, in the sense that they do not vary with output. Rent on land is a fixed cost. It is the same whether the firm produces a lot or a little. The total cost of using variable factors, however, does vary with output. The cost of raw materials is a variable cost. The more that is produced, the more raw materials are used and therefore the higher is their total cost.

Total cost

The total cost (TC) of production is the sum of the total variable costs (TVC) and the total fixed costs (TFC) of production:

TC = TVC + TFC



Figure 5.3 – Illustration of Total Cost curves.

Figure 5.4 Diminishing returns on total cost curves

Consider the above diagrams.



In our example in Figure 5.3, total fixed cost is assumed to be £12. Since this does not vary with output, it is shown by a horizontal straight line.

The shape of the TVC curve follows from the law of diminishing returns. Initially, before diminishing returns set in, TVC rises less and less rapidly as more variable factors are added. Take the case of a factory with a fixed supply of machinery: initially as more workers are taken on the workers can do increasingly specialist tasks and make a fuller use of the capital equipment. This corresponds to the portion of the TPP curve that rises more rapidly (up to point b in Figure 5.1).

As output is increased beyond the fourth point (b) in Figure 5.2, diminishing returns set in. Since extra workers (the extra variable factors) are producing less and less extra output, the extra units of output they do produce will cost more and more in terms of wage costs. Thus TVC rises more and more rapidly. The TVC curve gets steeper. This corresponds to the portion of the TPP curve that rises less rapidly (between points b and d in Figure 5.1).

Since TC = TVC + TFC, the TC curve is simply the TVC curve shifted vertically upwards by £12.

Average and marginal costs

Average cost (AC) is cost per unit of production:

AC = TC/Q

Thus if it cost a firm £2000 to produce 100 units of a product, the average cost would be £20 for each unit (£2000/100).

Like total cost, average cost can be divided into the two components, fixed and variable. In other words, average cost equals average fixed cost (AFC = TFC/Q) plus average variable cost (AVC = TVC/Q):

AC = AFC + AVC

Marginal cost (MC) is the extra cost of producing one more unit: that is, the rise in total cost per one unit rise in

output:

MC = change in TC/change Q



For example, assume that a firm is currently producing 1 000 000 boxes of matches a month. It now increases output by 1000 boxes (another batch): change in Q = 1000. As a result, its total costs rise by £30: change in TC = £30. What is the cost of producing one more box of matches?

30/1000 = .30

What will be the shapes of the MC, AFC, AVC and AC curves? These follow from the nature of the MPP and APPcurves that we looked at in section 5.1 above. You may recall that the typical shapes of the APP and MPP curves are like those illustrated in Figure 5.3.

Diagram A Diagram B

Figure 5.5 – Average and Marginal Cost Curves

Marginal cost (MC)

The shape of the MC curve follows directly from the law of diminishing returns. Initially, in Figure 5.4, as more of the variable factor is used, extra units of output cost less than previous units. MC falls. This corresponds to the rising portion of the MPP curve in Figure 5.5 Diagram B and the portion of the TVC curve in Figure 5.2 to the left of where diminishing returns sets in.

Beyond a certain level of output, diminishing returns set in. This is shown as point x in Figure 5.5 and corresponds to point b in Figure 5.2. Thereafter MC rises as MPP falls. Additional units of output cost more and more to produce, since they require ever increasing amounts of the variable factor.

Average fixed cost (AFC)



This falls continuously as output rises, since total fixed costs are being spread over a greater and greater output.

Average variable cost (AVC)

The shape of the AVC curve depends on the shape of the APP curve. As the average product of workers rises, the average labour cost per unit of output (the AVC) falls: as far as point y in Figure 5.5. Thereafter, as APP falls, AVC must rise.

Average (total) cost (AC)

This is simply the vertical sum of the AFC and AVC curves. Note that as AFC gets less, the gap between AVC and AC narrows.

The relationship between average cost and marginal cost

This is simply another illustration of the relationship that applies between all averages and marginals. As long as new units of output cost less than the average, their production must pull the average cost down. That is, if MC is less than AC, AC must be falling. Likewise, if new units cost more than the average, their production must drive the average up. That is, if MC is greater than AC, AC must be rising. Therefore, the MC crosses the AC at its minimum point (point z in Figure 5.5).

Since all marginal costs are variable, the same relationship holds between MC and AVC.

COSTS IN THE LONG RUN

We turn now to long-run cost curves. Since there are no fixed factors in the long run, there are no long-run fixed costs. For example, the firm may rent more land in order to expand its operations. Its rent bill therefore goes up as it expands its output. All costs, then, in the long run are variable costs.

Long-run average costs

Long-run average cost (LRAC) curves can take various shapes, but a typical one is shown in Figure 5.6.



Figure 5.6 Long Run Average Cost Curve



The relationship between long-run and short-run average cost curves

Take the case of a firm which has just one factory and faces a short-run average cost curve illustrated by SRAC1 in Figure 5.7.

In the long run, it can build more factories. If it thereby experiences economies of scale (due, say, to savings on administration), each successive factory will allow it to produce with a new lower SRAC curve. Thus with two factories it will face SRAC2, with three factories SRAC3, and so on. Each SRAC curve corresponds to a particular amount of the factor that is fixed in the short run: in this case, the factory. (There are many more SRAC curves that could be drawn between the ones shown, since factories of different sizes

could be built or existing ones could be expanded.) From this succession of short-run average cost curves we can construct a long-run average cost curve, as shown in Figure 5.7. This is known as the envelope curve, since it envelopes the short-run curves.





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Weebly - The Theory of Productionsmsecon.weebly.com/.../the_theory_of_production.docx · Web viewTo illustrate how this law underlies short-run production let us take the simplest