Market Economy : Concept, Features and Functions of Market Economy

Concept of Market Economy

The resources are limited in the society. Hence, throughout history, every society has faced the fundamental economic problem of deciding what to produce, and for whom. According to R.G. Lipsey and C. Harbury, "the term economic system refers to a distinctive set of social and institutional arrangements within which answers are provided by determining how resources are allocated."

In the 20th century, two competing economic systems were used for the solution of these problems: command economies directed by a centralized government and market economies based on private enterprise. The market economies are prevalent in North America, Western Europe and Japan. The command economies were prevalent in the former Soviet Union, Eastern Europe and parts of Asia over the past half-century.

At present in the last decade of 20th century, the command economy has been found to be a failure. It has "failed to sustain economic growth, to achieve a measure of prosperity, or even to provide economic security for its citizens."

The market economies are, by nature, decentralized, flexible, practical and changeable. The central fact about market economies is that there is no center. The 'invisible hand' works in the private market place. The market economies are based on the principle of individual freedom: freedom as a consumer to choose among competing products and services, freedom as a producer to start or expand business and share its risks and rewards, freedom to choose a job, join a labor union or change employers.

According to R.G. Lipsey and C. Harbury, "In a type of economic system all decisions about resource allocation are made without any central direction but, instead, as a result of innumerable independent decisions taken by individual producers and consumers: such a system is known as a market economy."

Functioning of Market Economy

The functioning of a market economy may be described as follows: 

Production

Decision in command economies the economic planners, production experts and political officials establish production levels of goods and designate which factories will produce them. The central planning committees establish the prices of the products and wages for the workers who produce them. It is the set of central decisions that determines the quantity, variety and prices of products. Due to this, there either shortages or surpluses of the products in the economy. The planning authorities are unable to make efficient decisions when number of people, products increase and the production technologies change rapidly.

The phenomenon of command economies does not happen in the market economy. In a market economy, government ministry, or planners do not decide the quantity, quality, and design of the products. Anyone individual or company, can decide and sell products. This leads to direct competition between different firms producing the products. Competition is the heart of market economies. Due to competition there are different products available to the consumers. 

Pricing Decision

Another key point about market economies is that the planning committee does not fix the prices of products. The sellers are free to raise or lower prices according to changing market conditions. When products become scarce, the price usually rises. The price increase accomplishes two things at the same time. 

The price rise makes the product more expensive compared to other products. Hence, some consumers will choose fewer of them. 

The higher price goes directly to the producers and sellers. Hence the higher price increases the profits of the firms enabling them to produce and sell more goods. Attracted by high price, other firms will also begin to make the popular product. 

Incentives

The higher prices give every consumer and producer incentive to respond. Because, they are allowed to reap the benefits of their own decisions while also bearing the associated risks and costs. For example, the consumers willing to pay the higher prices can get the popular product. But they have to give up more money and other goods and services to do so.

On the production side, the firms making popular products can sell them at competitive prices and earn profits. The producers who make unwanted products or produce inefficiently incur losses. Eventually, they must either learn to produce efficiently or will go out of business. In sum, the economic incentives work in a market economy. 

Efficient Resource Allocation

The consumers, producers and workers all work in their own self-interest in open and competitive markets. They use their economic resources in ways that have the greatest value to the national economy. They are useful in satisfying more of people's wants. The first person to point out this fact in a systematic way was the great classical economist Adam Smith. He published his famous book 'An Enquiry Into The Nature and Causes of Wealth of Nations,’ in 1776. He was first to describe how an economy based on a system of market could promote economic efficiency and individual freedom.

Smith described the feature of market economics in these words, "People are led as if by an invisible hand" to work and behave in ways that use resources efficiently, in terms of producing things that other people want and are willing to pay for, even though that may have been "no part of their original intentions". In market economies, with a decentralized system of private markets, resources are efficiently allocated to satisfy consumer demands.

Despite many benefits of market economy, it provides no magic solutions. "The market economies are by no means immune to issues such as inflation, unemployment, pollution, poverty and barriers to international trade". Hence, the government will have to play a critical role in helping correct problems that cannot be fully solved by a system of private markets.

Features of Market Economy

Two major types of economic system are command and market economies. In command economies, resources are allocated by decisions taken by central planners. In market economies, the allocation of resources is determined by decentralized decisions coordinated through the price mechanism.

The basic features of market economy are as follows:

1. Decentralized decision-taking: In a market economy, decisions relating to basic economic issues are decentralized. But they are coordinated. The main coordinating device is the set of market-determined prices. 
2. Freedom of enterprise: People are free to choose nay occupation or take up any business according to self-interest. 
3. Profit motive: The economic activities are undertaken with the aim of earning profit. People themselves borne the risk and return of business. 
4. Consumer's sovereignty: The consumer is the king in the sense that they have complete freedom in making choice of the products. 
5. Price mechanism: The price mechanism guides producers and consumers in making production and consumption decisions. The price system is the coordinator of decisions. Every day millions of people independently make millions of decisions relating to consumption and production. Most of these decisions are not motivated by a desire to contribute to the social good, but by the consideration of self-interest. The price system coordinates these decentralized decisions. Due to this the whole system is sensitive to whishes of the individuals who compose it. Price is a signaling device, which give signals about scarcities and surpluses. 
6. Perfect competition: There is perfect competition in the market between producers, consumers and consumers and producers. 
7. Specialization in production: There is specialization in production. It is accompanied by freedom to exchange what is produced among individuals. 
8. Market-determined prices: The most remarkable feature of the market economy is that it requires no planning authority to allocate resources. The key to the whole process is to be found in the role of prices. The prices perform the crucial function of providing signals that help to determine the allocation of resources. 
9. Lack of conscious direction: The market economy fulfills its function of coordinating decisions without any one having to understand how it works. For example, a farmer need not know how many people eat rice and where they live. He needs to know only the cost of production and price of rice. By responding to such public signals as the costs and prices of what he buys and sells, the farmer helps the whole economy fit together, to produce what people want, and to provide it where and when they want it. 
10. Laissez-faire: There is what is called laissez-faire in the market economy. This French expression describes the belief that the market economy would perform most efficiently if left free from government intervention. Adam Smith opined that the 'hidden hand' of market forces should be allowed to govern the economy.

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Effects of Inflation in the Economy | Effects on Production | Effects on Consumption | Effects on Distribution

• Inflation has serious social and economic effects. Some economists have named it legal dacoits. It invisibly imbalance economic factors and delay the speed of economic growth. The following are the main effects of inflation.

Effects on Production

1. Decrease in the quality of goods: The demand for goods increase due to inflation. So, any type of goods can be sold. As a result, the profit seekers lessen the quality of goods to increase the profit.
2. Reduces saving: Due to inflation, most of the income is spent on consumption. So the saving reduces. As a result, there is less capital investment.
3. Encourages holding and speculation: The producers start to store the necessary goods. Due to this, the goods become even scarce; the businessmen hide the goods and create artificial scarcity, for black marketing.
4. Reduction in productivity: In the time of inflation, there is less capital formation. As a result, it is difficult to make available factors of production. It brings uncertainties in the economy, and entrepreneurs become discouraged in the production.
5. Devaluation of money and loss in faith: People have less trust of money due to the devaluation of money and its decreasing purchasing power. Foreign investors also can return their investment due to the loss of faith.

Effects on Consumption

1. Change in consumption pattern: In the time of inflation, the demand for quantity decrease as the price of the quantity increases. Those who have various sources of income buy luxury goods, foreign goods and goods of comfort but those who have limited source of income start to buy only essential goods. Most of the consumers start to consume artificial goods than natural ones.
2. Debt instead of saving: In the time of inflation, the consumer surplus slowly decreases because he has to pay more than he wants to pay. If there is high inflation, he will get loan.
3. Unequal consumption and lifestyle: In the time of inflation, the lifestyles of rich and poor will become more polarized. Those who have only limited income, is compelled to buy only the essential goods. Due to this, life becomes more difficult. But those, who have various sources of income feel opposite of that.

Effects on Distribution

1. Fixed income groups: Government officials, pensioners and those depend on post savings are the fixed income group. In the time of inflation, general price increases, so the expenditure on living increases and the life becomes harder.
2. Creditors and debtors: In the time of inflation, creditors are in loss and debtors are in profit because of the decrements in the purchasing power of money. As the creditor give the money having more purchasing power and get it back when it has less purchasing power. Therefore, they get in loss.
3. Salary and wage earners’ group: This group will be in hard time as the expenditure of living increases where as wage and salary do not increase.
4. Merchants and industrialists benefited: In the time of inflation, merchants and industrialists get sudden profit. The price of assets (stock) increase but the cost of current capital does not increase so much, so merchants and industrialists get extra profit.
5. Effect on Balance of Payment: Inflation has negative effect on balance of payment. Indigenous goods happen to be more expensive than foreign goods. So the farmer cannot compete with foreign goods. As a result, import increase and export decrease. Thus, balance of payment becomes negative. In the long run, it creates scarcity in the foreign exchange.

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Externalities in the Economy | Economic effects that occur from the production or the use of goods

Externalities are pervasive and significant phenomena in modern societies. The term externalities refer to the economic effects which occur from the production or the use of goods to other parties or economic units. It is said that public goods and externalities are not un-related. In other words, public goods and externalities are related. Externalities may affect a large number of people in a uniform manner, in which case the externality is essentially a public good (or public “bad”).

For example, education increases the skills and general welfare of the person being educated and may in addition, make the person better citizen. That is, the person’s behavior in political process may be more wise and informed, and an informed may make better political decisions. Since, such decisions affect every one, the education of each person produces an external benefit that accrues to the members of the community and the nation in which person reside.

This external benefit is a public good that is jointly produced along with the private goods (marketable skills) resulting from education.

Similarly, air pollution generated by an iron mill’s smoke and the exhaust of automobiles are public bads that are produced jointly with private goods (iron mills and private transportation). Again, the railways using a lot of coal in firing steam locomotives put the residential and other areas near the railway loco sheds to a lot of suffering on account of the smoke nuisance. These are the cost to the society but not to the individual undertaking.

In the above examples, public goods, i.e., benefits and public bads that are produced with private goods are known as externalities. These are the cost to the society but not the individual undertaking. This causes divergence between private cost (internal cost) and social marginal cost or external cost of benefit, of the goods in question. Market takes into account of internal costs and not the social marginal cost or external cost (or benefit) of the goods in question. Consumers reveal their preferences for the benefits which are wholly internalized (rival) but not for the external benefits, i.e., purification of air (non-rival). Thus, market fails to achieve efficient allocation of resources when externalities are present.

To be more clear, let the production of a commodity, say iron generates air pollution that adversely affects the welfare of the people in the surrounding community. The cost of iron, thus, have two components: (i) the cost of the labor, machines, iron ore, coal and other inputs directly required to produce the iron; and (ii) the costs borne by the members of the community in the form of air pollution damages. Market takes into account first component of the above costs but not the second. This is the cause of divergence between private cost (internal cost) and the social marginal cost (external bads). Hence, markets fail to achieve efficient allocation of resources when externalities, i.e., external costs or benefits are present.

Thus, externalities can take many forms. For example, external benefits from education: children gain from having educated parents; society benefits in so far as education reduces crime, social un-rest, unemployment and welfare costs; society benefits from an educational system that inculcates acceptable social values, improves communication and strengthen democratic institutions, on the (external bads) side are many forms of pollution and other disseminates such as congestion and noise etc.

i) Externalities in the form of external benefits

Problems of social goods-type arise not only in the budgetary context but also wherever private consumption or production activities generate external benefits. Suppose, for instance, that A derives benefits being inoculated against polio but this also benefits others, since the number of potential carriers and hence the danger of infection, is reduced. Similarly, by getting educated, A not only derives personal benefits but also makes it possible for others to enjoy association with a more educated community. Since, large number of other consumers may be affected, market does not work and a budgetary process is needed to secure preference revelation. But budgetary intervention in this case will not involve full budgetary provision rather, it will take the form of subsidy to private purchases.

ii) Externalities in the form of external costs or bads

Let us now consider a case of a commodity which generates external costs or bads. Suppose, the production of iron generates air pollution that adversely affects the welfare of the people in the surrounding community. The cost of iron, thus, has two components: (i) the cost of the labor, machines, iron ore, coal and other inputs directly required to produce the iron, and (ii) the costs borne by member of community in the form of air pollution damages. However, the second component of cost is not taken into account by the market. In fact, private activities, whether in production or consumption frequently give rise to external costs which are not accounted for by the market. Hence, public (Government) intervention is needed to get this part of the cost to be internalized.

iii) Efficiency and equity problems

In the first place, failure to account for external costs leads to an over supply of production question (i.e., here iron) and an under supply of the benefits (i.e., clean air) which are reduced by pollution. This is the efficiency problem. If the damage cost of pollution were internalized, resource use would become more efficient. The price of iron would be higher, less iron would be produced and the air quality would be improved.

Second, the existence of pollution poses distributional or equity problems. Through, the loss of environmental quality, consumers of air are forced to subsidize consumers of iron, much as they would if a tax were imposed on them (consumers of air) and transferred to the latter (i.e., consumers of iron). Moreover, the incidence of pollution damage may fall with different weight upon low income and high income families, and this affects the distribution of real income. The same goes for the cost of pollution prevention and the net gains to be derived there from.

iv) Efficient solution

It should, however, be noted that air is a public property, it is a social good. The principle of exclusion does not apply. Hence, market fail to take into account external costs or the damages caused by air pollution. The benefits of this good are shared by all those who are damaged by pollution.

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Law of Returns to Scale in Production | Increasing Returns to Scale | Constance Returns to Scale | Decreasing Returns to Scale

Returns to scale describe the change in output when all inputs are changed / increased by the same proportion. This means that returns to scale explains production activities over the long run. Over the long run, a firm can increase all inputs by equal proportion or by unequal proportion. Returns to scale is based on the assumption that over the long run all inputs of production are increased by equal proportion.

According to A. Koutsoyiannis, “The term returns to scale refers to the changes in output as all factors change by the same proportion.” This law of returns can also be defined as, “Returns to scale related to the behavior of total output as all inputs are varied and is a long run concept.”

When each of the inputs of production are increased proportionately, output may increases more than proportionately or less than proportionately or equi-proportionatly. If it increases more than the percentage increase in inputs, it is called increasing returns to scale (IRS); if output increases by less than the percentage increase in inputs it is called decreasing returns to scale (DRS); and if output increase by equal proportion to the increase in inputs, it is called constant returns to scale (CRS). The concept of returns to scale is summarized in table.

Table: Returns to Scale

Increase in the Quantity  of Factors/inputs	Increase in Output	Type of Returns  to Scale
10%	20%	Increasing
10%	10%	Constant
10%	5%	Decreasing

Increasing returns to scale occur when the economies of scale operate. Diminishing returns to scale occur when the diseconomies of scale operate. Constant returns to scale are an intermediary situation, when certain advantages of large scale production are counterbalanced by certain disadvantages.

The law of returns of scale can be explained with the help of Isoquants for a single output with the use of two inputs.

i) Increasing Returns to Scale (IRS)

When a certain proportionate change in both the inputs K and L, leads to a more than proportionate change / increase in output, it exhibits increasing return to scale. For instance, if quantities of both the inputs, K and L are successively doubled and the corresponding output is more than doubled, the return to scale is to be increasing return. It is illustrated with the help of figure.

Increasing Returns to Scale

The movement from point A to B as the line / ray OR should mean doubling the inputs K and L. In above figure, input combination increases from 1K + 1L to 2K + 2L. As a result of doubling the inputs, output is more than doubled. Similarly, the movement from point A to B, B to C, C to D indicates increase in inputs as a result of which the output increases more than the increase in inputs. Along the ray OR, the gap between AB, BC and CD is decreasing, that is OA > AB > BC > CD.

Increasing returns to scale (IRS) means the reduction in average cost of production with the expansion in the scale of the firm and increase in the size of output. That is, increasing returns to scale is another name of decreasing average cost of production with increase in the size of production.

Causes of Increasing Returns to Scale

a) Specialization

Each worker can acquire specialization in the performance of simple repetitive task rather than many different tasks. As a result, labor productivity registers a rise.

b) Dimensional relation

Increasing returns to scale is a matter of dimensional relation. For example, when the size of cloths (10m x 20m = 200 sq. m) is doubled to 20m x 40m = 800 sq. m., the size of the cloth is more than doubled, 800 sq. m. is 4 times of 200 sq. m. Following this relationship, when labor and capital are doubled, output is more than doubled over initial level of output.

c) Use of specialized machinery

In addition, a large scale of operation permits the use of more productive specialized machinery, which was not possible at a smaller scale of operation.

d) Effect of research and development

Conduction of research and development (R & D) works modifies methods of production. Research and development bring efficiency, economy and effectiveness in the production process. Hence, more spending on research and development is possible only in firms of large size.

e) Use of indivisibilities

Capital equipment of a given capacity and entrepreneur skill are the indivisible factors. They cannot be sub-divided into parts. Hence, as output increases, there is better and effective utilization of these factors. Therefore, as a results of the effect of all these factors, a given proportionate increase in the amount of all inputs leads to more than proportionate increase in output.

ii) Constant Returns to Scale (CRS)

When the change in output is proportional to the change in inputs, it exhibits constant return to scale (CRS). In other words, if quantities of both inputs, K and L are doubled and output is also doubled, then returns to scale is said to be constant.

A production function showing constant returns to scale is often called ‘liner and homogenous’ or homogeneous of the first degree’. The case of CRS is illustrated by means of figure.

Constant Returns to Scale

In the figure, the movement from point A to B, B to C and C to D is assumed to indicate doubling of the inputs. When inputs are doubled, output is also doubled. Similarly, the movement from A to C indicates trebling input, output also trebling. The gap between AB, BC and CD is same, that is OA = AB = BC = CD which means that the distance of successive isoquants is equal in case of CRS.

The main reason for the operation of constant returns to scale is that beyond a certain point, internal and external economies are neutralized by the growing internal and external diseconomies of production. When inputs of same efficiency are duplicated, output would increase by equal proportion.

iii) Decreasing Returns to Scale (DRS)

When output increases in a smaller proportion than the increase in all inputs, decreasing returns to scale (DRS) are said to operate. When a firm goes on expanding by increasing all its inputs / resources of production, eventually decreasing returns to scale will occur. For example, when inputs are doubled and output will be less than doubled. The decreasing return to scale (IRS) is illustrated with the help of figure.

Decreasing Returns to Scale

When the inputs K and L are doubled, that is, when capital-labor combination is increased from 1K + 1L to 2K + 2L, output also increases but by less than the proportionate increase in inputs. The movement from A to B, B to C and C to D indicates increase in the inputs. But the output increases by less than the increase in inputs. The gap between AB, BC and CD is increasing, that is AB < BC < CD. When decreasing returns to scales applies, the distance of successive isoquants along the ray through origin increases. Decreasing returns to scale also means increase in average cost of production with the expansion in the size and output of the firm.

Causes of Decreasing Returns to Scale

i) Managerial inefficiency

With the fast expansion of the scale of production, personal contacts and communication between (a) owners and management and (b) managers and labor, get rapidly reduced. Remote control and management replace close control and supervision. With the increase in managerial personnel / staff, decision-making becomes complex and delay in decision-making becomes inevitable. Implementation of decision is also delayed due to co-ordination problem between different sections and/or branches. As a result, output increases less than proportionately than the proportionate increase in inputs.

ii) Labor inefficiency

Another cause of decreasing returns to scale is over crowding of labor causing to loss of labor productivity and their accountability. On the other hand, increase in number of workers encourages labor union activities which mean simply the loss of output per unit of time.

iii) Exhaustible natural resources

The decreasing returns to scale may be found in the use of exhaustible natural resources. For example, if more and more fisherman used to fishing in a certain area of Trishuli river of Nepal, the catching of the fish will not increase in the same proportion.

iv) Fiscal diseconomies

With the expansion of the scale of production, the discount and concession that are available on bulk purchase of inputs come to end. As a result, output increases less proportion than the proportionate increase in all output.

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• Production of maximum output in the firm

Production of maximum output in the firm | Production of a given output at minimum cost | Production of maximum output with a given level of cost

Production of maximum output in the firm is possible in the given level of expenditure which can be studied with the help of Iso-cost curve and Iso-quant curve.

It is clear that any desired level of output can be produced by a number of different combinations of inputs. But the manager of the firm most make major decisions such as which input combination to be used, what the input, combination will be optimal.

The firm can choose from among different combinations of capital (K) and Labor (L) to produce a given level of output or faced with specified input prices, it can choose from among many combinations of K and L that would lead to fixed level of cost i.e. expenditure. Thus, the firm has to make either of two input choice decision.

1. Choose the input combination that yields the maximum level of output possible with a fixed output (i.e. output maximization subject to cost constraint).
2. Choose the input combination that leads to the lowest cost of producing a fixed level of output (i.e. cost minimization subject to output constraint).

The solution to any constrained maximization or minimization problem is obtained by choosing the level of each activity whereby the marginal benefits from each activity. Per dollar ($) spend are equal. Here the profit maximizing firm has to choose the input combination for which the marginal product divided by input price is the same for all inputs used. The implication is that for two input cases, a firm attains the highest level of output when,

MPL / PL = MPK / PK or MPL / w = MPK / r

Where, w and r are respectively the prices of labor (PL) and capital (PK). Thus, the MRTS = MPL / MPK equals the factor price ratio (wr).

Input Prices and Iso-costs

The Iso-quant shows the desire of the producer. Usually, a firm is supposed to have a fixed amount of money to buy resources. The Iso-cost line is the producer’s budget line. In determining the optimal input combination, a profit maximizing producing unit firm or producer has to pay attention to relative input prices, it is to minimize the cost of producing a given output or maximizing output for a given level of cost. Input prices are determined by the market forces.

The equation of total cost is C = rK + wL where all the terms have their usual meaning. Total cost is simply the sum of the cost of K units of capital at r $ per unit of L units of labor at w $ per units.

Suppose, capital costs $100 per month per unit (r = $100) and labor receives a wage of $200 per unit (w = S200). Then the firm’s total cost function is

C = 100 K + 200 L ……………………. (i)

Now, suppose that the firm decides to spend $2000 per month for capital and labor. Thus, equation becomes $2000 = $100 K + 200 L.

The process of solving this equation is

     2000 = 100 K + 200 L

or, K = 200 – 2 L

In a general situation, if a fixed amount Ḹ is to be spent, the firm can choose among the combinations given by

K = Ḹ/r – w/r . L

Production of a given Output at Minimum Cost

Whatever output a firm chooses to produce, the production manager is desirous of producing it at the lowest possible cost. To achieve this objective, the production process must not only to be technically efficient but economically efficient too. So, the production process has to organize in the most efficient manner.

For example, suppose that at given input prices r and w, a firm wishes to produce the output indicated by Iso-quant Q0 as shown in the figure.

In the figure, K1 L1, K2 L2 and K3 L3 are the three Iso-cost lines from which the producer can choose at the given factor prices. The firm will choose the lowest level of expenditure that enables output level Q0 = 200 to be produced. As shown in the figure, output level Q0 will be produced at the cost level Q0 will be produced at the cost represented by Iso-cost line K1 L1.

Any cost outlay below that such as represented by KL is not feasible since it is impossible to produce output Q0 with these factor combinations. Any factor combinations above that represented by K1L1 are not considered because the firm seeks to produce the desired output at least cost. If combination A or B is chosen at the cost outlay represented by K2L2, the producer can reduce costs by moving along Q0 to point E. Point E shows the optimal resource combination, K0 units of capital and L0 units of labor. This is known as the level of cost combination of inputs.

This Iso-quant shows the desired rate of factor substitution and the Iso-cost is the actual rate of factor substitution. A firm reaches equilibrium and thus minimizes cost when the Iso-quant is tangent to the lowest possible Iso-cost line. Thus, equilibrium is reached when the Iso-quant representing the chosen output is just tangent to an Iso-cost line. At this tangent the slopes of the two curves are equal, production at least cost requires that the MRTS (Marginal Rate of Technical Substitution) of capital for labor be equal to the ratio of the price of labor to the price of capital.

      MPL / PMK = w / r

or, MPL / w = MPK / r

where, MPL = Marginal production of labor

MPK = Marginal productivity of capital

        r = Price of capital

       w = Price of labor

Production of Maximum Output with a given Level of Cost

It is an alternative technique but more preferable way of presenting the optimization problem. It is to assume that the firm chooses a level of output and then select the factor combination that permits production of that output at least cost. This approach seems to be more practical than the previous one. It is assumed that the firm can spend only a fixed amount of money to spend and it seeks to attain the highest level of output consistent with that amount of outlay. It can be explained with the help of figure below:

The Iso-cost line KL shows all possible combination of the two inputs that can be purchased with a fixed market prices. Three Iso-quants are shown in the figure. At the given level of cost, output level Q2 is unattainable. Neither output level Q1 nor level Q2 would be chosen, since higher levels of output can be produced with the fixed cost outlay. The highest possible output with the given level of cost is produced by using OL0 amount of labor and OK0 amount of capital. At point E, the highest attainable Iso-quant (i.e. Q) is just tangent to the given Iso-cost (KL). Thus, in the case of constrained output maximization, the MRTS of capital for labor equal the input-price ratio (the price of labor to the price of capital).

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Determination of Optimal Employment of an Input

To see how the economic productivity of an input, as defined by its marginal revenue product, is related to the factor for productive purposes, one needs only consider the simple question. If the price of input X in the production system is $100, how many units of X would a firm use? If the marginal revenue products exceed the related cost, that level of such input number could be employed.

The relationship between resource productivity as measured by the marginal revenue product and optimal employment or factors use can be maximized. If marginal revenue exceeds marginal cost, profits most increase. In the context of production decisions, this means that if the marginal revenue product of an input, i.e., the marginal revenue generated by its employment in a production system exceeds its marginal cost, then profits are increased as input employment increases.

Similarly, when the marginal revenue product is less than the cost of the factor, marginal profit is negative, so the firm would reduce employment of that factor.

This concept of optimal resource employment can be clarified by examining a very simple production system in which a single variable input labor (L), is used to produce a single product, Q. Profit maximization requires that production be at a level such that marginal revenue equals marginal cost. Since the only available factor in the system is input L, the marginal cost of production can be expressed as:

MC = ∆C / ∆Q = PL / MPL …………….. (i)

That is dividing PL, the price of a marginal unit of L, by MPL, the number of units output gained by the employment of an added unit of L, provides a measure of the marginal cost of producing each additional unit of the product.

Since MR must equal MC at the profit maximizing output level, MR can be substituted for MC in equation (i), resulting in the expression,

MR = PL / MPL ……………………. (ii)

Equation (ii) must hold for profit maximization since it was demonstrated immediately above that the right-handed side of equation (ii) is just another expression for MC. Solving equation (ii) for PL results in PL = MR x MPL which is defined as the marginal revenue product of L.

PL = MRPL …………………….. (iii)

Equation (iii) states the general result that a profit maximizing firm will always employs an input up to the point where its MRP is equal to its cost. If the MRP exceeds the cost of the input, profits are increased by employing additional units of the factor.

Similarly, when the resources’ price is greater than its MRP, profit is increased by using less of the factors.

Only at the level of usage where MRP = P are profits maximized than the costs incurred (PL). Only at L where PL = MRPL, will total profits be maximized. If PL were higher, the quantity of L demanded would be reduced. Similarly, if PL were lower the quantity of L purchased would be greater.

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• Meaning of Market Failure | Ways of Correcting Marketing Failure | Utility Regulation

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Production Function | Linear Production Function | Quadratic Production Function | Cubic Production Function | Power Production Function

Production involves the transformation of inputs into outputs. Production involves the transformation of inputs into physical output. The output is thus, a function of factors which are also called inputs. The term ‘production function’ refers to the relationship between the inputs and outputs produced by them. The functional relationship between physical inputs and physical output of a firm is known as production function. Algebraically, production function can be expressed as,

Q = f ( Ld, L, K, M…. )

Where, 

Q stands for the quantity of output, Ld, L, K and M stand for the land, labor, capital and management respectively.

The above equation shows that the quantity (Q) of output produced depends upon the quantities of the factors used. Simply, production function expresses the relationship between the quantity of output and the quantities of the various inputs used for the production. More precisely, the production function states the maximum quantity of output that can be produced with by given quantities of various inputs.

In economic theory, there are two types of production functions on time basis. The production function when the quantities of some inputs such as capital and labor are kept constant and the quantity of one input such as labor is varied. This kind of production function [Q = f (K, L)] is known as short-run production function. The study of short-run production function is the subject-matter of the law of diminishing returns which is also called the law of variable proportion.

Secondly, we study production function (input – output relation) by varying all inputs, and this is called long-run production function and can be expressed as Q = f (Ld, L, K, M ). This form is the subject-matter of the law of returns to scale. Generally, the terms constant and increasing returns are used with reference to constant and increasing returns to scale.

Besides these, there are other production function, such as

1) Linear Production Function

A linear production function would take the form:

Total production Y = a + bx

From this, function for the managerial production will be,

= Y / X.a / x + b

The equation for the marginal product will be,

∆Y / ∆X = b

2) Power Function

A power function expresses output Y, as a function of input in the form:

y = AX^α

It contains certain properties:

a) The exponents are the elasticity of production. Thus, in the above function, the exponent α represents the elasticity of production.

b) The equation is linear in the logarithms, i.e., it can be expressed as, 

log Y = logA + αlogX

when the power function is expressed in logarithmic form as above, the coefficient α represents the elasticity of production.

c) If one input is increased while all others are held constant, marginal product will be decline.

3) Quadratic Production Function

The production function may be quadratic, taking the following form:

Y = a + bx – cx²

Where, the dependent variable Y shows total output and the independent variable X represents input. The small letters are parameters; their probable values are determined by a statistical analysis of the data.

Properties of quadratic function:

a) The minus sign in the last term denotes diminishing marginal returns.

b) The equation allows for decreasing marginal product but not for both increasing and decreasing marginal products.

c) The elasticity of production is not constant at all points along the curve as in a power function, but declines with input magnitude.

d) The equation never allows for an increasing marginal product.

4) Cubic Production Function

The cubic production function takes the following form:

Y = a + bx + cx² – dx³

Some important special properties of a cubic production function are:

a) It allows for both increasing and decreasing marginal productivity.

b) The elasticity of production varies at each point of the curve.

c) Marginal productivity decreases at an increasing rate in the later stages.

5) Power Production Function (Cobb-Douglas Function)

Power functions have been employed in a large number of empirical production studies, particularly since Charles W. Cobb and Paul H. Douglass’s pioneering work in the late 1920s. The impact of this work was so great that power production functions are now frequently referred to as Cobb-Douglas production functions.

Cobb-Douglas production function can be expressed as,

Q = AK^α L^β

Where, Q = total output

L = index of employment of labor in manufacturing

K = index of fixed capital in manufacturing

The exponents α and β are the elasticities of production i.e., α and β measure the percentage response of output to percentage changes in labor and capital respectively.

Properties of Power Function:

a) Power functions allow the marginal productivity of a given input to depend upon the levels of all inputs employed a condition that often holds in actual production systems.

b) They are linear in logarithms and thus can be easily analyzed using linear regression analysis.

log Q = log A + α log K + β log L

The least squares technique can be used to estimate the coefficients of equation and thereby the parameters of equation.

c) Power functions facilitate returns to scale estimation. Returns to scale are easily calculated by summing the exponents of the power function. If the sum of the exponent is less than one, (α + β < 1) diminishing returns are included. A sum greater than one (α + β > 1) indicates increasing returns. Finally, if the sum of the exponent is exactly one (α + β = 1), returns to scale are constant.

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• Law of Variable Proportions | Law of Diminishing Returns

• Law of Returns to Scale in Production | Increasing Returns to Scale | Constance Returns to Scale | Decreasing Returns to Scale

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• Derivation of Market Supply Curve and Shift in the Supply Curve

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• Elasticity of Demand: Types of Price Elasticity of Demand

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