Showing posts with label ECONOMY. Show all posts
Showing posts with label ECONOMY. Show all posts

The Overview of Linear Programming

Linear Programming is a mathematical device developed by the mathematician George Dantzig in 1947 for planning the diversified activities of the US Air Force connected with the problem of supplies to the forces. Linear or mathematical programming, also known as activity analysis, has been further developed in its application to the firm, managerial economics and finally to development planning. It is a mathematical technique for the analysis of optimum decisions, subject to certain constraints in the form of linear inequalities.

Mathematically speaking, it applies to those problems which require the solution of maximization or minimization problems subject to a system of linear inequalities stated in terms of certain variables.
The problems of maximization and minimization are also called optimization problems. When cost and price per unit change with the size of output, the problem is non – linear and if they do not change with output, the problem is linear. Linear programming may thus be defined as a method to decide the optimum combination of factors to produce a given output or the optimum combination of products to be produced by given plan and equipment. It is also used to decide between a variety of techniques to produce a commodity. The technique involved in linear programming is similar to the one adopted in input – output analysis for the industry.
Conditions And Generalisations Of Linear Programming
You should know that for any principle to hold in any situation, certain conditions and generalizations has to be satisfied. The application of linear programming (LP) technique to any problem rests on certain conditions and generalizations.
First, there is a definite objective. It may be the maximization of profits or national income or employment of the minimization of costs. It is known as the objective function or the criterion function. If a quantity is maximized, its negative quantity is minimized. Every maximization problem has its dual problem, that of minimization. The original problem is the primal problem which always has its dual. If the primal problem pertains to maximization, the dual involves minimization and vice versa.
Secondly there should be alternative production processes for achieving the objective. The concept of process or activity is the most important in linear programming. A process is a specific method of performing an economic task. It is some physical operation, e.g consuming something, storing something, selling something, throwing something away, as well as manufacturing something in a particular manner. The LP technique enables the planning authority to choose the most efficient and economical process in attaining the objectives.
Thirdly, there must be certain constraints or restraints of the problem. They are the limitations or restrictions pertaining to certain conditions of the problems, as to what cannot be done and what has to be done. They are also known as inequalities. They may be limitations of resources such as land, labour or capital.
Fourthly, there are the choice variables, the various production processes or activities so as to maximize or minimize the objective function and to satify all the restraints.
Lastly, there are the feasible and optimal solutions. Given the income of the consumer and the prices of goods, feasible solutions are all possible combinations of the goods he can feasibly buy. Feasible solutions of two goods for the consumer are all combinations that lie on and to the left of the budget line. Whereas, on an isocost line, they are the combinations that lie on and to right of it. We may put it differently that a feasible solution is one which satisfies all the restraints.
The optimal solution is the best of the feasible solutions. If a feasible solution maximizes or minimizes the objective function, it is an optimal solution. The best available procedure for finding out the optimal solution out of the possible feasible solutions is the simplex method. It is a highly mathematical and technical method involved in linear programming.
However, the main aim of linear programming is to find out optimal solutions and study their characteristics.
Assumptions Of Linear Programming Technique
The linear programming analysis is based upon the following assumptions;
i. The decision-making body is faced with certain constraints or resource restrictions. They may be credit, raw material and space constraints on its activities. The type of constraints in fact depend upon the nature of problem. Mostly, they are fixed factors in they production process.
ii. It assumes a limited number of alternative production processes.
iii. It assumes linear relations among the different variables which implies constant proportionality between inputs and outputs within a process.
iv. Input – output prices and coefficients are given and constant. They are known with certainty.
v. The assumption of additivity also underlies linear programming techniques which means that the total resources used by all firms must equal the sum of resources used by each individual firm.
vi. The LP technique assumes continuity and divisibility in produces and factors.
vii. Institutional factors are also assumed to be constan

Limitations Of Linear Programming
Linear programming has turned out to be a highly useful tool of analysis in development planning. But it has its limitations. As a matter of fact, actual planning problems cannot be solved directly by the LP technique due to a number of restraints.
Firstly, it is not easy to define a specific objective function.
Secondly, even if a specific objective function is laid down, it may not be so easy to find out the various social institutional, financial and other constraints which may be operative in pursuing the given objective.
Thirdly, given a specific objective and a set of constraints, it is possible that the constraints may not be directly expressible as linear inequalities.
Fourthly, even if the above problems are surmounted, a major problem is one of estimating relevant value of the various constant co-efficients that enter into an LP problem, i.e. population, prices, etc.
Fifthly, one of the defects of this technique is that it is based on the assumption of linear relations between inputs and outputs. This implies that inputs and outputs are additive, multiplicative and divisible. But the relations between inputs and outputs are not always
linear. In real life, most of the relations are non-linear.
Sixth, this technique assumes perfect competition in product and factor markets. But perfect competition is not a reality.
Seventh, the LP technique is based on the assumption of constant returns in the economy. In reality, there are either diminishing or increasing returns.
To further buttress this point, it is a highly mathematical and complicated technique. The solution of a problem with linear programming requires the maximization or minimization of a clearly specified variable. The solution of a linear programming problem is also arrived at with the Simplex method which involves a large number of mathematical calculations.
It requires a special computational technique, an electric computer or desk calculator. Such computers are not only costly, but also require experts to operate them. Mostly, the LP models present trial-and-error solutions and it is difficult to find out really optimal solutions to the various economic problems.
Uses Of Linear Programming In Planning
Linear programming as a tool of economic development is more realistic than the input￾output approach. In input-output analysis only one method is adopted to produce a commodity. It does not take into consideration the bottlenecks (constraints) which a development project has to face in underdeveloped countries. But in linear programming a definite objective is set to maximize income or minimize costs.
All possible processes or techniques are taken into account for achieving the desired objective. This necessitates even the substitution of one factor for another till the most efficient and economical process is evolved. So projects and techniques which are too uneconomical to implement are not undertaken.
By assuming certain constraints, linear programming as a tool of development planning is superior to the input-output technique. In underdeveloped countries, the planning agencies are faced with such constraints as the lack of sufficient capital and machinery, growing populations, etc. Resources exist that cannot be used properly for want of the co operant factors. Linear programming takes to due note of
these constraints and helps in evolving an optimum plan for attaining the objectives within a specified period of time. Thus the LP technique has been used for constructing theoretical multi- sector planning models for countries like India. Such models extend the consistency models of the input-output type to optimization of income or employment or any other quantifiable plan objective under the constraints of limited resources and technological conditions of production.
In practice, however, the LP technique is being used in solving a limited number of economic problems in developing countries. This is due to the lack of proper personnel for working out mathematical equations and for operating highly mechanical computers.
Mostly the LP technique has been found to be extremely useful for sectoral planning in developing countries, for example, in selecting optimum alternatives in respect of location and technologies in industries, transport, and power or in farm management.This technique is being used in farm management for determining the optimum combination of different crops e.g Livestock and crops. The objective function used in such studies is either the minimization of costs or the maximization of income.
The constraints are set by pre-determined levels of demand or the availability of resources such as raw materials or capacity. Besides, this technique is being used for the solution of diet problem where the aim is to minimize costs, given the values of minimum nutrients of the diet and the prices of products as constraints. It is also with the LP technique that the transport problems is being solved by the railways, airways and transport companies with regard to the selection of routes, transportation of goods, allocation of the means of transport ( i.e. railway, wagons, aircrafts,trucks etc.depending on the type of transport under study).Again, this technique is used to assign jobs to the work force for maximum effectiveness and optimum results subject to constraints of wages and other costs.
Similarly, purchasing, assembling, production and marketing problems are being solved through the LP technique in order to minimize costs and maximize profits, given the various constraints in the case of each problem. However, for an extensive use of this technique for development planning, developing economies will have to depend upon larger resources of trained personnel, and finance.

You can also read;
The Evolution Of Money
Summary and Conclusion
From our discussion so far on the introduction to linear programming as a concept , we can deduce the following facts:
That Linear or mathematical programming, also known as activity analysis, has been further developed in its application to the firm, managerial economics and finally to development planning for the analysis of optimum decisions, subject to certain constraints in the form of linear inequalities. It also applies to those problems which require the solution of maximization or minimization problems subject to a system of linear inequalities stated in terms of certain variables which is also regarded as Optimisation problems. Mostly the LP technique has been found to be extremely useful for sectoral planning in developing countries, for example, in selecting optimum alternatives in respect of location and technologies in industries, transport, and power or in farm management.
Also, from the point of view of our discussion, you have learnt that the main aim of linear programming is to find out optimal solutions and study their characteristics.  Production capacity technique of LP, Limitations of linear programming technique and the uses of linear programming technique in planning. Also, from the point of view of our discussion, you have learnt that the main aim of linear programming is to find out optimal solutions to available constraints posed by available resources.


  • Jhingan M.L. (2007):- The Economics of development and planning, Vrinda publications India. (39th Edition).
  • Michael P. Todaro and Stephen C Smith (2011).Economic development, pearson education ltd, Edinburgh gate harlow, Essex, England.
  • Michael P.Todaro: Development planning, models and methods, Chapter 2-3.
  • Akosile I.O, Adesanya A.S Ajani A.O (2012):- Management of development ( A Nigeria per spective ) Olas Ventures, Mushin, Lagos.
  • Olajide O.T (2004):_ Theories of Economics development and planning, Lagos, Nigeria, Pumark Nigeria Ltd.
  • Otokiti S.O (1999):- Issnes and strategies in Economic Planning, Bitico publishers,Ibadan

The Evolution of Money

Before the evolution money, exchange was done on the basis of direct exchange of goods and services. This direct exchange is known as the barter system. Barter system involves the direct exchange of one good for some quantity of other goods, for instance, exchanging a horse for a cow.
Consequently, this exchange at a time become more difficult in that people finds it very difficult to get someone that can exchange what they have to what they want.
Apparently, this problem of search resulted to the problem of barter system. Consequently, in the quest to solving the problem of barter resulted to the means of exchange that requires no goods for goods rather money for goods, which is classified as monetary evolution of money .
To further understand the monetary evolution of money, we will have to discuss each of the Era in the evolution of money, down to the credit money era as follows;

China Intention of Expansion in Foreign Ports

China in 2015 announced its intention to build military facilities in Djibouti, citing reasons "to help the Navy and Army further participate in UN peacekeeping operations, carry out escort missions in the waters near Somalia and the Gulf of Aden and provide humanitarian assistance".

"China is expanding its access to foreign ports, such as in Gwadar, Pakistan, to pre-position the logistic framework necessary to support the PLA's growing presence abroad, including normalising and sustaining deployments into and beyond the Indian Ocean," the Pentagon said.

China is expanding its access to strategic foreign ports like Pakistan's Gwadar and Sri Lanka's Hambantota to pre-position the logistic framework necessary to support the growing presence of its military in the Indian Ocean and beyond, the Pentagon said.

The People's Liberation Army's efforts to obtain access to commercial ports in Africa, the Middle-East and South Asia would align with its future overseas logistic needs and meet its evolving naval requirements, said the Congressionally-mandated report on the increasing Chinese military power which was released by the US Department of Defence on Tuesday.

Needs For Planning In Less Developed Countries

One of the principal objectives of planning in underdeveloped or less developed countries is to increase the rate of economic development. As you know that LDC‘s are characterized with low level of savings, low level of income,  what is prevalence in such countries are poverty ridden people. This visions economic circle can only be broken by planned development. This can be achieves through importing capital from abroad know as foreign direct investment (FDI) and localized force saving to support the level of industrialization.

Therefore, the rationale and the need for planning arises in such countries to achieve he following;
1. Strengthen the market mechanism: The market mechanism works imperfectly in LDC‘ because of the ignorance and unfamiliarity with it. This is so because the production factor, money and capital markets are not organized properly, thus the price system fails to bring about adjustments between aggregate demand and supply of good and services. Therefore, to remove market imperfection, to mobilize and utilize efficiently the available resources, to determine the amount and composition of investment and to overcome structural rigidities, the market mechanism is required to be perfected in LDC‘s through planning Using a workable planning model.
2. The necessity of removing unemployment: Unemploymentis asituation where resources are not fully utilized. Capital is scarce and labour is in abundance thereby creating the problem of providing gainful employmentand resulting in absence of sufficient enterprises and initiatives. This required an urgent attention by the planning authority in LDC‘s immediately adopt a planning model that can salvage the situation.
3. The development of Agricultural sectors ad industrial sectors: Agricultural sector is known to produce food for household, rawmaterials for industries and foreign earnings to government when exported abroad. Industrial sector on the other hand utilizes the raw materials from the agricultural sector for the production of further finished goods that can be used for infrastructural development like roads, railways, power stations etc. Therefore there should be a conscious attempt by the LDC‘s planning authority to have a road map planning model towards the development of their agricultural and industrial sector.
4. The necessity of removing the nations poverty: The need for reducing inequalities income and wealth raising per-capital income, increasing employment opportunities, all round rapid development and national independence substance requires a careful ad conscious idea of planning targeted through a planning model that can achieve this. This was seen in the rapid development and transformation of USSR, a poor country at the time of October revolution.
Planning for economic development is undertaken presumably because the pace of direction of development taking place in the absence of external intervention is not considered to be satisfactory and because it is further held that appropriate external intervention will result in increasing considerable the pace of development and directly it properly.
The following are the usefulness of development models to economic planning;
  • It provides a framework for checking of consistency or the optimality of the official plan targets.
  • It provides a framework for the actual setting of targets.
  • It provides a framework for the evaluation and selection of projects.
  • It provides an insight into the structure of the economy and its dynamics to help better policy decisions.
  • It assists in budget and budgeting control.
  • It helps the preparation of feasible plan.
  • It helps the projection and forecasting of measurable changes.
  • It helps in adjusting competing participants within available time path
  • It helps the planning authorities to know their objectives, instrument variables and the functional relationship of the variables in the desired plan and low to achieve it.
  • It gives the planner a clear direction to follow on a projected economic plan.
Requirements For A Successful Planning
The formulation and success of a plan requires the following ;
1. Planning Commission: The first pre-requisite for a plan is the setting of a planning commission which should be organized in a proper way and should consist of experts like economist,statistician, mathematician, engineer etc to deal with various aspects of the economy. In Nigeria, it is called National Planning Statistical Data: A prerequisite for sound planning is a through survey of the existing potential resources of a country together with its resources. To have a successful planning in a country statistical data and information with regard to the available material, capital and human resource are needed.
3. Objectives: There must be a clear objective of what the plan aims at achieving. The objectives might be to increase national and per capital income, to expand employment opportunities, to reduce inequalities of income and wealth, to raise agricultural production or to industrialize the economy etc to mention but few.

4. Fixation of Targets and Priorities: One of the Major requirements for successful planning is to fix targets and priorities well for achieving the objectives laid down in the plan. These targets should be global and sectoral. Priorities should be laid down on the basis of the short and long terms need of the economy keeping in view the available resources.
5. Incorrupt and Efficient Administration: It should be known to you that an incorrupt and efficient administration is a strong determinant of successful planning. This however is lacking in most less developed countries. Competent administrative staff should be appointed into various ministries which should first prepare good feasibility reports of proposed projects before embarking on them.
Therefore the secret of successful planning lies more in sensible politics and good administration.

UN Reveals that Nigeria Needs $337bn to Implement SDGs from 2019-2022

The overarching goal of the Plan, targeting ten  countries as follows;
2.Burkina Faso

This is to scale up efforts to accelerate shared prosperity and lasting peace in the region.

The cost of implementing the SDGs in Nigeria, according to the plan is 80.65 billion dollars in 2019, 82.83 billion dollars in 2020, 85.07 billion dollars in 2021 and 87.37 billion dollars in 2022.

Nigeria needs nothing less than 337 billion dollars to implement the Sustainable Development Goals from 2019 to 2022, the UN Support Plan for the Sahel has estimated.

On the investment needs in the Sahel, the plan reported the cost of implementing the SDGs in the Sahel is projected to be between 140.25 billion dollars and 157.39 billion dollars per year between 2019 and 2022 in the 10 Sahelian countries.

The plan said the 10 countries under the UN Integrated Strategy for the Sahel needed an average of 148.7 billion dollars annually to implement the SDGs or 594.8 billion dollars from 2018 to 2022.


The table below shows the top 10 fastest growing economics in Africa in 2018

Top 10 Fastest Growing Economies In Africa In 2018 (World Bank, Imf....)
[1] Ghana
[2] Ethiopia
[3] Cote d'Ivoire
[4] Djibouti
[5] Senegal
[6] Tanzania
[7] Sierra Leone
[8] Benin Rep
[9] Rwanda
[10] Niger Rep

Nigeria was Number [1] in 2012, 2013, and 2014. In 2015 Nigeria was the 3rd Fastest growing Economy in the World but now, the 88th.

1. Nigeria - $38 (N18,000).
2. Algeria - $175 (N83,000).
3. Belgium - $1,738 (N810,000).
4. Cameroon - 36, 270CFA ($75) N38,000.
5. Chad - $120 (N60,000).
6. Denmark - $1,820 (N900,000).
7. Libya - $430 (N190,000).
8. Japan - $1000 (N450,000).
9. Cote D'ivoire -36,607CFA $72.
10. New Zealand -$3,187 (N1.4m).
11. Luxemburg - $2,500 (N1.1m).
12. Spain - $760. (N300,000).
13. Switzerland - $5,620 - N2.5m.
14. USA - $11 per hour.

Ironically, Nigeria politicians earn the highest salaries in the whole world. In Luxemburg where minimum wage is $2,500, their lawmakers are paid $7,400. In Libya where minimum wage is $430, lawmakers earn $3000. In Nigeria where minimum wage is $38 (N18,000), lawmakers earn $65,000 (N29m).


Money is an important material resource. Which we use to purchase most of the goods and services we use. The amount of satisfaction we get from our money management is an organized process of allocating or using money to achieve specified goals (needs that are usually purchased with money. We cannot discuss money management without mentioning income, budgeting and savings. They are important aspects of money management.

Principles Of Money Management
The following principles should guide us in managing our money
  1. Expenditure must never exceed income. Ensure that your expenditure is within the limit of your income.
  2. Allowances should be made for emergencies that may come.
  3. Make a budget on how to use money available
  4. Separate your needs and goals in order of importance so that the most important should be given priority.
Guidelines Of Money Management
  1. Identify family goals e.g. providing education for the children, owning a house or buying a car, etc.
  2. Establish priorities. Here, the family should determine which objective or goal is most important or needs to be started early so as to yield interest as the family financial need increases.
  3. Estimates the cost of goals. The family should list goals, rank them, and tag the cost. For instance, if a person’s goal is to own a house that costs N60, 000 after five years of service, it means that the person should save at least at N1000 monthly for five years.
  4. Analyse the financial resources. The family should examine carefully all sources of family treasury for use in reaching family goals. For salaried workers with regular employment, money income is usually predictable over a lifetime. For those with irregular incomes and uncertain employment, planning is both more difficult and more necessary.
  5. Formulate a plan of action. Once the desired life style and goals of a family are established and current financial resources have been calculated the approach will need to be streamlined. In order words, a budget showing family need and the corresponding proportion of income to each need is made.
The budget could be monthly or yearly as the case may be.
  1. Organize all efforts. This involves taking decisions about who is to keep the records. What kind of checking account is to be used when banking, timing of purchases and what kinds of records to keep.
  2. Control activities: income should be channelled to planned objectives or goals and should not be wasted. For instance comparative buying should be used when making purchases to select durable and useful items for the family.
  3. Keep adequate records. All income and expenditure should be properly recorded. For instance, when properly or a home is purchased, cheques receipt and records relating to the property through the years should be kept until the property is sold. This practice could save money at tax returns.
  4. Evaluate regulatory families should check the effectiveness of their financial should be abandoned or revised. Expenditure should be adjusted to changes in income and goals.

Importance Of Budget
Family budget is important because of the following reasons:
  1. It serves as a guide in spending
  2. It helps to plan income within the limits of expenditure
  3. It helps to cater for the needs of every member of the family.
  4. It prevents unnecessary spending and promotes peace, security and stability in the family.
  5. It helps the family to see and access their spending patterns and to adjust properly.
  6. It helps to prevent the children and other members of the family on how to spend wisely.
  7. It helps to prevent impulse buying (buying things not planned for)
  8. It helps to accomplish a long term plan of difficult ventures.
  9. It helps to apportion the available income adequately to cater for both primary and secondary needs.
Factors That Influence Family Budget
The family budget is influenced by many factors such as the following:
  • Income
  • Occupation
  • Composition of family members
  • Locality
  • Family values
  • Season of the year
  • Inflation
  • Family future plans
A budget is the plan for the future expenditure of a given household or an individual. It is a useful devise that can help a family to achieve their goal. Budgeting is the first step in money management.
Steps In Making A Family Budget
According to Gross and Crandall (1963) the following steps are involved in making a budget.
  1. List all the commodities and services needed and wanted by family members throughout the proposed budget period.
  2. Estimate the cost of the needs or desired items
  3. Estimate the total expenditure for the planed period
  4. Bring expected income and expenditure
  5. Check the budget to ensure that it has a reasonable chance of success
Benefit Of Budgeting
  1. Budgeting enables the family to take an overview of the use of their income that is expenditure can be seen in perspective
  2. It can help avoid the use of limited family money for items to prevent impulsive buying
  3. A budget determines the use of other resources indirectly
  4. It enables the family to make decisions as to what to purchase