PRODUCTION ANALYSIS

SESSION OBJECTIVES

• PRODUCTION FUNCTION• CONCEPTS OF PRODUCTION• 3 STAGES OF PRODUCTION• SHORT RUN vs LONG RUN• RETURNS TO SCALE• ISOQUANTS AND ISOCOSTS• EXPANSION PATH

• We will see how firms can organize their production efficiently and how their costs of production change as input prices and the level of output changes. The physical relationship that describes how inputs are transformed into outputs are focused upon.

• Production refers to conversion of input to output. But in economics production means creating utility.

Production Function• The relation between input and output of a firm is termed as the

“ production function”.• Production function deals with the maximum output that can be

produced with a limited and given quantity of inputs. For example, the production function of a steel firm takes into consideration, various inputs like labor, raw material, power consumption, cost of land, etc. It also takes into account the quantity of output that is being produced, using all the above fixed and variable inputs. Thus, production function deals with input as well as output. A production function can be expressed as an equation, table, or a graph.

• If a firm uses inputs like labor (L) and capital (K), then the production function can be formed asQ = f (K, L)

• Production function is a simple numerical relationship between inputs and outputs

Concepts of Product

• There are three types of product concepts that are crucial to the production function. Total product, marginal product and average product.

• Total product is the total physical product or the total amount of output produced by all inputs put together.

• Marginal product is the additional output generated by one additional unit of input.

• Average product is productivity per unit of input.

Total Product, Average Product and Marginal Product

No of Labour units Total Product Marginal Product Average Product

1 2000 2000 2000

2 3000 1000 1500

3 3500 500 1167

4 3800 300 950

5 3900 100 780

6 3700 -200 617

Total Product and Marginal Product

The Three Stages of Production

• Cassels suggested that there are three stages of production for any firm. In the first stage, the average returns are increasing. Marginal product also increases up to a certain point, thereafter it starts declining.

• It can be observed from the graph that in the first stage, the marginal product is greater than average product. As there is increasing returns in this stage of production, it is known as stage of increasing returns.

• In the second stage of production, both average product and marginal product are decreasing. Though marginal product is decreasing, it remains positive in this stage. In this stage there is less than proportionate increase in the output, as a result of the change in the variable input. In this stage, the entrepreneur would like to make maximum utilization of the fixed assets. This stage is known as stage of decreasing returns.

• In the third stage of production, total product is diminishing, and the marginal product shows negative growth. Therefore, this stage is known as stage of negative returns. It can be observed from the graph that the third stage is the mirror image of the first stage.

3 stages of productionNo. of Labour Total Product Marginal

ProductAverage Product

stage

0 0 0 0 Ist stageIncreasing returns1 10 10 10

2 25 15 12.5

3 45 20 15

4 60 15 15 2nd stageDiminishing returns5 70 10 14

6 70 0 11.7

7 60 -10 8.5 3rd stageNegative returns8 45 -15 5.6

• Short Run and Long Run:• In the production process, there are various types of inputs that go into the

production process. In production process, two different time periods are discussed, short run and long run. In short run a firm can change its variable inputs like labor, raw material, etc. While in the long run, all factors of production including capital can be changed to alter the production levels.

• The difference between short run and the long run can be illustrated through examples.

• If a farmer wants to increase the productivity, he can hire additional labor, or can increase the quantity of seeds and fertilizers. Changes in these variable inputs can be made at any moment of time, and requires not much effort and resources. On the contrary, if the farmer wishes to change the crop, it takes considerable time and investment as well. This change cannot be made in the midst of a season. In the given case the decision of the farmer to increase the variable inputs like labor is a short run decision, and making change in the crop is a long run decision.

• An automobile company has installed capacity of producing 100 cars per week, and currently producing 70 cars per week. If the demand increases, it can increase the production by increasing the labor and raw material. If the demand persists and increases drastically, rising to 200 cars per week, then the firm cannot increase the production overnight. If it wants to install an additional plant, it requires huge investments and time as well. Therefore, in this case the decision to increase the labor is a short run decision, whereas decision to install a new plant or relocate the plant is a long run decision. Thus, in the long run all the factors are variable.

Technological Change

• Improvements in technology help increase in production and raises standard of living. Technological change leads to

• Process innovation• Product innovation• Process innovation: When improvements in the technology results in

improvements in the production methods, it is known as process innovation.

• Example: The introduction of optical fiber technology has transformed the whole telecommunication industry. This has resulted in minimization of costs for the companies offering telecom services. As the benefits are passed on to the customers, it is resulting in lower telecom tariffs.

• Product innovation: Product innovation takes place, when new and improved products are introduced in the market. Electronic goods industry is witnessing rapid changes in the products. Product innovation has helped in raising the standard of living. Many organizations rely heavily on the product innovation, and have made it as a part of the strategy. The advantages of the product innovation are difficult to quantify.

• Example: Intel the computer processor manufacturer launches a new improved processor after a given period of time.

Returns to Scale

• Returns to scale show the responsiveness of total product when all the inputs are increased proportionately. Returns to scale is a factor that is studied in the long run. Returns to scale can be constant, increasing or decreasing.

• Constant returns to scale:• In this case, the change in inputs results in proportional change in output. • For example, if a firm is using three factors of production, land, labor and capital, and

if it doubles all these inputs, output should also be doubled.• Increasing returns to scale:• When rise in inputs result in more than proportional increase in the output, it is

known as increasing returns to scale. • For example, if a plant is producing 100 units of the product using 10 units of labor

and 100 units of capital. If the labor is doubled to 20 units and capital is also doubled to 200 units, and the output generated is 250 units, then the firm is operating at increasing returns to scale level.

• Decreasing returns to scale:• When increase in all the inputs result in less than proportional increase in output,

then it is known as decreasing returns to scale. • For example, if a firm increases all its inputs by 20 percent and the resulting increase

in the output is just 15 percent, then it is the case of decreasing returns to scale.

Diminishing Marginal Returns

• There are two ways in which a firm can approach the optimal production function. First, a firm can keep the input rate of one factor constant. In the second approach both the inputs are allowed to vary. If any of the input is fixed for a particular period of time, it is known as short run. In the short run, atleast one input is fixed, whereas in the long run all the inputs can be varied. A firm can add variable inputs in the short run to meet the immediate requirements, but in the long run it needs to put in more capital. Thus, it can be said that firms operate in the short run but plan in the long run.

• According to the law of diminishing returns, we get less and less extra output with the addition of an input, holding other inputs constant. It means that the marginal product of each unit of input declines, as the input increases.

• The law of diminishing returns is not only applicable to industry, it is equally applicable to agriculture as well. Suppose a farmer has a fixed area of land, his marginal productivity will increase to a certain point, beyond which the additional labor yields negative returns.

• It helps in allocating scarce resources. Suppose a firm feels that it has surplus labor in any of the plant, it can divert those labors to any other unit, or can make use of them for some other purpose. It also helps in determining the input combination that yields maximum output.

Example for Diminishing marginal returns

• A firm producing readymade shirts has a limited shop floor area and has 25 machines and 25 workers. Using these resources, firm could produce 100 shirts per day. To increase production, the firm hired 2 additional workers. This resulted in marginal increase in the production. To increase the production further, the firm hired three additional workers. This has declined the production of shirts to 90 shirts per day, instead of increase in production of shirts. This happened because workers were not feeling convenient while working because of lack of working space and less number of machines. Though, the number of workers was increased, but the area of shop floor remained unchanged. This has resulted in deterioration of the working conditions, leading to decline in production. Hence, law of diminishing marginal returns was into play.

The Production Isoquant

• If a firm is having two variable inputs, the approach to determine the optimal input rates is completely different. In this scenario, the problem of efficient resource allocation can be solved in two ways.

• Maximize the production, utilizing the available resources. These two problems are known as constrained optimization problems. The problem of resource allocation can also be solved by producing the profit maximizing output.

• Isoquants also known as production-indifference curves, represent the combinations of inputs that produce same quantity of output. This can be explained with the help of an example,

PRODUCTION ISOQUANT

Factor Combination Labour capital

A 2 24

B 4 16

C 6 10

D 8 6

E 10 4

PRODUCTION ISOQUANT• It is assumed that the there are two factors

of production - labor and capital. In the given example, the factor combination A consists of 2 units of labor and 24 units of capital producing the required output of 100 units. Various combinations of the factors labor and capital for the isoquant are shown in the figure. Each isoquant curve represents the specified level of production.

PRODUCTION ISOQUANT

Marginal Rate of Technical substitution

• MRTS can be defined as the number of units of one input that can be replaced by one unit of another input, keeping the level of output constant. If labor and capital are two inputs, MRTS of labor would be the number of units of capital that can be replaced by one unit of labor.

• In the given case, when we move from combination A to combination B, 4 units of capital are replaced by one unit of labor. The marginal rate of technical substitution on a point on an isoquant is the slope of the isoquant at that point.

• The following are the properties of isoquants:• They slope downward towards right indicating that if the utilization of one

factor increases the utilization of another decrease.• The higher isoquants represent higher output. If one factor is kept constant,

and the other factor is increased, the output level also increases.• As there is no common point on the two isoquant curves, they cannot intersect.• Isoquants are convex to the origin because it becomes more difficult to

substitute one factor of production by other as we move along isoquant and increase the use of one factor to substitute the other factor.

Production Isocost

• Isocost line provides various combinations of inputs that can be employed at a given level of cost. Isocost lines give information regarding costs. Suppose a firm is using two inputs, labor and capital, isocost lines provide various combinations of labor and capital that a firm can hire at a given level of cost.

• Since isocost is concerned with the prices, they are also known as price lines. Isocost helps in determining the combination of inputs that gives maximum output. It helps a firm to minimize the costs, and thereby increase the profits.

• The slope of the isocost line shows the ratio of the price of labor to the price of capital or price of capital / price of labor.

Isocost Line

Least Cost Combination

• Any rationale firm would like to maximize its output with the least cost. In order to attain this, a firm should have a least cost combination. Least cost combination is attained at a point where the isoquant touches the isocost line. Thus, the least cost input combination is that combination where the slope of the isoquant is equal to the slope of the isocost. Thus, the least cost combination depends upon both isoquants as well as isocost.

• The least cost combination can be explained with the help of the given figure . It can be seen that the Y axis of the curve represents capital and labor is represented by X axis. In the given case, producer wants to produce 500 units of output. Producer has the option of using various combinations of labor and capital on the isoquant curve R, S, E, T, and J.

• It can be observed from the figure that cost will be minimum at point E where the isocost line CD is tangent to the isoquant Q, whereas all other points R, S, T, and J on isoquant Q are on higher isocost lines when compare to CD. At these points, higher costs are incurred in producing the given output. The factor combination E is the optimum combination under the given conditions. Therefore, the tangency point of an isoquant with an isocost line represents the least cost combination of factors for producing a given output.

Least cost combination

Isocost Line

Expansion Path

• Expansion path can be defined as the locus of different equilibrium points where there is an increase in the expenditure of the firm, with no change in the price of the inputs. Expansion path reveals the change in the factor combinations when output and expenditure changes, with no change in the input prices.

• If there is an increase in the firm’s expenditure without increase in the price of input, there will be a parallel shift in isocost line. In this case, each isocost line gives a new tangency point and new equilibrium point. It can be observed in the given figure that after joining all equilibrium points the expansion path (P) is arrived at.

Expansion path

Economies and diseconomies of scale

Types of economies

• Internal economies• External economies

External Economies

• Internal – advantages that arise as a result of the growth of the firm– Technical– Commercial– Financial– Managerial– Risk Bearing

How do unit or average costs fall as the scale of production increases? 1

• Technical economies – using large scale productive equipment. Whilst this equipment is expensive the large output leads to reduced unit costs. To acquire such equipment requires that the business has the finance and the demand.

• Marketing economies – selling in bulk reduces admin / transport costs. Also large scale selling can be supported with a marketing budget that does not need to increase with the sales revenue generated. Eg a television advert costing $1m can support $4m sales a day or $8m sales a day.

• Financial economies – larger businesses are simply less likely to go bankrupt and they have sizable assets they can use as collateral. They can negotiate the interest they pay on loans and even issue their own debt (commercial bonds).

How do unit or average costs fall as the scale of production increases? 2

• Managerial economies – as businesses expand they employ specialist managers. The boss with a eye on each business function becomes departments staffed by specialists.Whilst this increases the managerial salary bill these managers are experts.

Human resource managers now recruit better suited candidates who fit with the organisation’s needs and culture. Employees stay longer, are more motivated and more productive.

Production managers can re-arrange production so that it is more efficient and they have better knowledge regarding what equipment to purchase.

• Purchasing economies – bulk buying discounts

External Economies• External economies are the advantages firms can gain as a

result of the growth of the industry – normally associated with a particular area

• Supply of skilled labour• Reputation• Local knowledge and skills• Infrastructure• Training facilities

External economies• These occur when an industry develops in a certain

area:• Pool of trained workers• Ancillary services – marketing, accountancy to

cleaning• Co-operation between businesses eg on research and

development• Development of specialist suppliers of components

and raw materials

Diseconomies of Scale

• The disadvantages of large scale production that can lead to increasing average costs– Problems of management– Maintaining effective communication– Co-ordinating activities – often across

the globe!– De-motivation and alienation of staff– Divorce of ownership and control