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Abstract :
The idea of the application of the GST on tax structure in an economy is not a new one though India has adopted this idea recently. There are several countries in the world have implemented the GST. But in case of India, the Union Finance Minister Arun Jaitly announced GST on July, 2017. It brings the all indirect taxes under one umbrella and the main motto is one nation one tax (except Jammu & Kashmir). It will applicable at every stage of value addition chain and also removes the cascading effects (i.e. tax on taxes) of taxation. VAT is the origin based tax and GST is the destination based tax. In a nutshell it could be a revolutionary change in the Indian Economy in regards to the indirect tax structure of India after independence. After demonetization the implementation of the tax reforms in the form of GST is a brave challenge for the present BJP led government. Implementation of the GST may be the next revolution of growth and prosperity after globalization. Any change is definitely never too easy. Whether the GST implementation has either positive or negative impact on Indian economy is a debatable one and also frequently changing the growth parameters. The running government is trying the best to make a simple road to GST. This paper concentrates on the nature, merits and demerits of GST on Indian economy at the grass root level.
Keywords : Demonetization, Goods and Service Tax, Information Technology, Value Added Tax
Introduction :
The idea of the GST is nothing new. France was the first country to implement GST in 1954. Since then Germany, Italy, the UK, South Korea, Japan, Canada and Australia and many other nations have implemented GST. China implemented GST in 1994 and Russia in 1991 where as Saudi Arabia plans to it in current year. Only Canada has implemented the dual (Centre-State) GST model. At present there are 160 countries around the globe that have implemented GST/VAT. Although in some countries VAT is the substitutes for GST. In India, the Union Finance Minister Arun Jaitly announced GST on July, 2017 and Indian tax reforms adopted the Canadian dual
model of GST. For Indian tax system it is nothing new but the old wine in a new bottle. Any change is definitely never too easy. Whether the GST implementation has either positive or negative impact on Indian economy is a debatable one and also frequently changing the growth parameters. The running government is trying the best to make a simple road to GST and we have to wait for future about its achievements. Prof. Kaushik Basu rightly said, “No country in the world has ever succeeded in providing full employment. The chance of India –with its poor quality of governance and high corruption-being the first is zero. Hence, granting people the right to employment is to devalue the meaning of right.”
In India, the Prime Minister, Narendra Modi announced demonetization on high value currency notes on midnight 8th November, 2016. Currency notes on Rs. 500 and Rs. 1000 worth Rs 15.4 trillion (about 86% of the money value in circulation). This was also a bold attempt by the government to reduce cash transaction, to control “black money” to make India a corruption free economy. It was estimated that the Indian black money lies between 23 to 26% of the GDP. It was also estimated that 68% of total transactions in India was cash based. The main objectives of both these issues were to make a digitalized cashless economy. Undoubtedly GST will be the complementary of demonetization to curb black money. The evil effects of demonetization was mainly in rural areas where various problems faced by the common people. The real impact of demonetization on states tax revenue has mixed impact though the final computation is yet to be made.
What is GST ?
GST stands for “Goods and Service Tax” which aimed at creating a single and unified market that will benefit both the corporate and the economy. It brings the all indirect taxes under one umbrella and the main motto is one nation one tax. It is simply an indirect tax that leads to the abolition of other taxes like central sales tax, state level sales tax, excise duty, service tax and so called VAT. It is basically a single destination based tax on final consumption. It will applicable at every stage of
A Critical Analysis for the Implementation of the GST in IndiaDr. Ramsundar Bairagya, Asst. Prof., (Economics), SambhuNath College, Birbhum, West Bengal
value addition chain and also removes the cascading effects of taxation. VAT is the origin based tax and GST is the destination based tax. In a nutshell it could be a revolutionary change in the Indian Economy in regards to the indirect tax structure of India after independence. GST offers benefits for the government, industry as well as the common and it is expected that the price of the products reduce and internationally competitive.
The concept of Supply of IGST :
The nature of supply of IGST covers inter-state supply and intra-state supply. To determine which tax will be impose the i.e. CGST, SGST or IGST the location and place of supply is very important. The various states, UT and the coastal border are also considered and follow the section 15 of the IGST Act 2017. The location of the supplier and the place of supply together determine the nature of transactions. The place of supply of goods at the time of delivery to the recipient is very important for the export-import goods. For movements of goods on board a conveyance such as aircraft, vessel, and motor-cycle the place of supply shall be the location at which such goods are taken on board. In case of imported into India the location of the importer and exported from India shall be the location outside India. The place of supply includes the billing address of the final recipient. The place of final destination of goods is also very important for mail or courier services of the products.
GST will have two components namely Central GST (CGST) which is levied and collected by the central Government and State GST (SGST) is levied and collected by the state Government. There are some cases where dual taxation is applicable. For inter-state supply of goods and services the centre would levy and collect the Integrated GST (IGST). All goods and services likely to be covered under GST except :
(a) Alcohol for human consumption-State Excise plus VAT.
(b) Electricity-Electricity Bill.
(c) Real-Estate-Stamp Duty plus Property Taxes.
(d) Five Petroleum products.
The concept of Supply of IGST :
The nature of supply of IGST covers inter-state supply and intra-state supply. To determine
which tax will be impose the i.e. CGST, SGST or IGST the location and place of supply is very important. The various states, UT and the coastal border are also considered and follow the section 15 of the IGST Act 2017. The location of the supplier and the place of supply together determine the nature of transactions. The place of supply of goods at the time of delivery to the recipient is very important for the export-import goods. For movements of goods on board a conveyance such as aircraft, vessel, and motor-cycle the place of supply shall be the location at which such goods are taken on board. In case of imported into India the location of the importer and exported from India shall be the location outside India. The place of supply includes the billing address of the final recipient. The place of final destination of goods is also very important for mail or courier services of the products.
Different Slabs of the GST :
For the common man :
Cheaper items - Movie tickets, dining in restaurant, two-wheeler, television, washing machines, stoves, small cars etc.
Costlier items - Mobile bills, premium for LICI, residential rent, health-care, courier services, cigarettes and tobacco products, school fees, metro or rail fare etc.
There are several slabs for the implementation of the GST-
No Tax :
Goods – No taxes will be levied on mainly necessary goods like sanitary napkins, deities made of stone, marbles or wood, gold, silver, raw material used in brooms, saal leaves and fortified milk, fruits, vegetables, bread, salt, bindi, curd, sindoor, natural honey, bangles, handloom, besan, flour, eggs, stamps, printed books, judicial papers, and newspapers.
Services – All hotels and lodges who carry a tariff below Rs.1,000 are exempted from taxes under GST.
GST Tax Slab on 5%
Goods – The goods which will attract a taxation of 5% under GST include skimmed milk powder, fish fillet, frozen vegetables, coffee, coal, fertilizers, tea, spices, pizza bread, kerosene, ayurvedic medicines, agarbatti, sliced dry
mango, braids, insulin, cashew nuts, lifeboats, handmade carpets and other textile floor coverings etc.
Services – Small restaurants along with transport services like railways and airways, Standalone ACs non-ACs Restaurants and those which serve liquor, Takeaway Food, Restaurants in hotels with a room tariff less than Rs.7,500 will come under this category.
GST Tax Slab on 12% :
Goods – Items coming are the tax slab of 12% include frozen meat products, butter, cheese, ghee, pickles, sausage, fruit juices, tooth powder, medicine, umbrella, instant food mix, cell phones, sewing machine, man-made yarn, handbags, jewellery box, wooden frames for painting, photographs, mirrors etc.
Services – Business class air tickets will attract a tax of 12% under GST.
GST Tax Slab on 18% :
Goods – Some of the items are flavoured refined sugar, cornflakes, pasta, pastries and cakes, detergents, washing and cleaning preparations, safety glass, mirror, glassware, sheets, pumps, compressors, fans, light fitting, chocolate, preserved vegetables, tractors, ice cream, sauces, soups, mineral water, deodorants, suitcase, brief case, vanity case, oil powder, chewing gum, hair shampoo, preparation for facial make-up, shaving and after-shave items, washing powder, refrigerators, water heaters, washing machines, televisions (up to 68 cm), vacuum cleaners, paints, hair shavers, curlers, dryers, scent sprays, lithium-ion batteries, detergent, stones used in flooring, marble & granite, sanitary ware, leather clothing, wrist watches, cookers, stoves, cutlery, telescope, goggles, binoculars, oil powder, cocoa butter, fat, artificial fruits, artificial flowers, follage, physical exercise equipment, musical instruments and their parts, stationery items like clips, some diesel engine parts, some parts of pumps, electrical boards, panels, wires, razor and razor blades, furniture, mattress, cartridges, multi-functional printers, door, windows, aluminium frames etc.
Services – Restaurants located inside hotels with tariffs of ?7,500 and above, outdoor catering (input tax credit to be available), actual bill of hotel stay below ? 7,500, IT and telecom services and financial services along with branded
garments will be part of this tax slab.
GST Tax Slab on 28% :
Goods – Over 200 goods will be taxes at a rate of 28%. The goods which will be part of this category under GST are sunscreen, pan masala, dishwasher, weighing machine, paint, cement, vacuum cleaner. Other i tems include automobiles, hair clippers, and motorcycles.
Services – Five-star hotels, whose actual bill of hotel stay above ?7,500, racing, movie tickets and betting on casinos and racing will come under this category.
For export the GST is 0% because it earns foreign currency to boost up the economy. In case of imported products the GST depends upon the nature of the commodities. GST returns compromises of two types of returns-periodic and annual return. Periodic returns are monthly or quarterly basis for reporting transactions on month or quarter while annual return is for reporting the summary of periodic returns filled up at the end of the financial year and thus it has special significance and there is no provision for revise i.e. once it is filed cannot be revised latter.
Merits & Demerits of the GST :
Any government reform bound to have certain merits and demerits. Though GST is considered to be a historical tax reforms in India but the implementation of the GST has some advantages and disadvantages.
Merits :
i) After the implementation of the GST the revenue collection is increasing slowly for the month wise collected data and it shows a positive trend.
ii) By means of GST both the small scale and large scale industries expand as well as both the regional and foreign trade boost up.
iii) For inter-state supply the online registration must be required.
iv) For the government taxation is the main source of revenue collection. Through GST revenue collection must be raised and also enhance the GDP growth.
v) GST eliminates the cascading effects of taxation (i.e. tax on tax) as the whole supply chain will get an-inclusive input tax credit
mechanism.
vi) GST is a transparent and corruption free tax administration and there will be no hidden taxes. It brings in one standard rate for all products across states means transparency to the taxpayers.
vii) Inflation rate did not rise but the recent spike in consumer inflation due to high food and fuel price and is unrelated to GST.
viii) It is a transparent tax system which does not require registration fees.
ix) It is backed by the GSTN which is fully an integrated tax platform to deal with all aspects of GST.
x) It is easy to collect and reduce the manpower.
xi) On-line registration must be applied if yearly turn-over is above ? 20 lakhs except Jammu and Kashmir and Chandigarh the same limit is ? 10 lakhs.
xii) The process is simple and uniform for refund, payment and registration through e-commerce taxation. Since technologies are used to drive GST taxpayers will have common portal (GSTN) also the on-line process is automated and simplified.
xiii) Through the operation of GST the cost of production and hence price will be lower which finally increased consumption. The common people are benefitted as they get their essential baskets at lower price due to fair competition among the various manufacturers. It also creates more job opportunities for the unemployed youth.
Demerits :
i) After the implementation of the GST some products are expensive which create burden for the common people.
ii) Agricultural growth is also lower from 4.9% in the previous year to 2.1% in the current financial year. There is a policy logjam or policy paralysis for the present government.
iii) For the up gradation of business software will require skilled and professional trained employees which create an extra burden for the small scale industries.
iv) GDP growth is decreasing to a four year low of 6.5% in 2017-18 against 7.1% in 2016-17.
It is the lowest growth rate of the BJP-led government due to the adverse impact of the GST and demonetization.
v) GST is not applicable liquor for human consumption which is not socially acceptable.
vi) In the new tax system switching from pen and paper invoice, registration and e-filling might be tough for some small scale industries and hence the SMES are the higher tax burden.
vii) Inflation is common phenomenon for this type of taxation.
viii) Multiple registrations are also a burden for operation of the GST.
ix) Since petroleum products are not included in the GST the states will collect levy without no input credit for the industry and related ones.
x) Suppose a person has Rs. 100 in hands. Now he has to spend this amount of money in the following options. For secure return if he save this amount in saving bank account he can earns Rs. 4 (@ 4% per annum) at the end of the year. Now if he borrows the same amount from a nationalized bank he has to pay Rs. 13 (@ 13% per annum). Again if he purchases various commodities from the market he has to pay Rs. 18 for GST. As a result if he borrows the same amount from the bank and purchase from the market he has to pay the sum of Rs. 31 (i.e. Rs. 13+ Rs. 18). The evil side of the situation is worsen if is a salaried person he has to pay the income tax also. In this case though he has to pay the income tax he has to pay the GST. This simply results that he cannot avoid the negative impact of GST. The situation is more worsen from the welfare point of view if there is negative externality in the economy.
xi) The operational costs are hike.
xii) Though GST has certainly various merits for the taxpayers. But at the same time there are several disadvantages of this type of taxation. GST is imposed in the middle of the year and as consequences this creates a lot of problems to follow the parallel two types of taxation.
Role of IT :
In the present day context, IT solutions for providing doorstep facilities hold the key to enlarging the implementation of the GST. This Pilot projects have been initiated by online registration, billing, tax payments and e-filing returns would be done through online system through the technology upgradation except pen and paper work. The same delivery channel can be used to provide other financial services like low cost remittances and insurance. IT can reduce cost and time in processing of applications, maintaining and reconciliation of accounts and enable taxpayers to use their staffs at branches for making the critical minimum effort in sustaining relationship especially with new account holders. In rural areas customers cannot be expected to come to branches in view of opportunity cost and time and hence banks will have to reach out through a variety of devices such as weekly banking, mobile banking, satellite offices, rural ATMs and use of post offices. In urban and even in rural areas while mobile phones have penetrated, banks could mobile technology for facilitating banking transaction. There are more than one crore mobile users today. The number of mobile phones currently is more than the number of borrowers from the banking system. Mobile phones are used to transfer funds real time from and to bank accounts and to make remittances and payments at very low cost. Once the data base and track record are established, a multiple of financing services can be offered including saving remittance, receipt of salaries, pensions, and payments for utilities, loan insurance and mutual fund products. There are a number of such organizations and delivery channels-including retired bankers and school teachers-who can be used for such credit enhancements in the form of reliable information.
Conclusion :
Any change is definitely never too easy. Whether the GST implementation has either positive or negative impact on Indian economy is a debatable one and also frequently changing the growth parameters. The running government is trying the best to make a simple road to GST. We have to learn about the countries who implemented the GST and how they overcome the difficulties. Though it is a new system for all the tax payers there must be a regular training programme
through radio, television, daily news, through mobile messages and may it be included in the course curriculum. After demonetization the implementation of the tax reforms in the form of GST is a brave challenge for the present government. We have already passed one year of the implementation of the GST. We have certainly got some pros and cons and some positive and negative impacts on Indian economy. From the historical aspects we saw that the countries adopted the GST model definitely gain at least in its growth aspects of the economy. For Indian economy it must require some change in its policy level for the common people living in the rural areas. If we follow the systematic reforms of GST as a strategy for the next FYPs we hope India to shine rather than suffer. For the government it requires capacity building digitalized economy from shifting a pen-and-paper economy. A massive amount of investment is required at the initial stage both from the government and the industry. To “Make in India” initiative the GST has been a long-term impact on the country’s GDP growth, doing business and expansion of trade and industry. For the overall success of the coming plan our states should adopts “National best practice” and not “Global best practice”. There may be some difficulties in its primary stage but we can assume that it will overcome all these difficulties in the near future and make the Indian economy stronger in the long-run and we have to go many miles to reach the ultimate goal.
References :
i. Agarwal S. & Malhotra S. (2018). “Goods and Service Tax Laws, Concepts & Impacts of Selective Industries”, Bloomsbury India.
ii. Datt R. and Sundharam K.P.M. (2018). Indian Economy, S. Chand and Co. New-Delhi.
iii. GST Acts & Rules, (2017). Directorate of Commercial Taxes, Government of West Bengal, 14, Beliaghata Road, Kolkata-700015.
iv. WGST Rules, (2017). GST Policy Planning Unit, Directorate of Commercial Taxes, Government of West Bengal, 14, Beliaghata Road, Kolkata-700015.
At a recent AICD luncheon, I was speaking with a group of people about what we do at Insight to Influence. One individual chimed in and said, "so, you are a training organisation"? My immediate response was unusually defensive, and a tad semantic, yet I felt compelled to differentiate that we are in the business of 'learning' not training.
It later struck me how the distinction between training and learning is incredibly important. Organisations invest buckets of money based on an expectation that training will enable their people to do something new or differently - yet only learning can achieve this.
The dilemma is: training works and learning works, but which is needed to get the right outcomes? By definition, training gives information or knowledge in a manner that instructs the trainee whereas learning is the re-creation of self in terms of our capacity to apply new knowledge, skills and behaviours in a variety
of contexts.
It is important to recognise that training and learning satisfy different business needs and that there are various types of training determined by the learning objectives and participant outcomes that the organisation requires. This then dictates the facilitators role, focus, methods and how actively engaged the participants need to be. However, I can't help wonder...
"Are organisations overly dependent on one-off training events to equip their people with the necessary skills to perform their role?"
When thinking about what is going to meet your organisational need, it is vital to check your expectations, manage any assumptions and get crystal clear on the purpose and desired outcomes so that the learning methods are suitably matched. For example, the following outlines some key distinctions and variation that exists in the field of training.
Training and Learning : Why it's Important to know the Difference
Nicole Barrett (Psychologist), Managing Director Insight to Influence, Australia
Not distinguishing between the various levels of participant engagement and required skill level is a huge risk that organisations unconsciously take, often setting themselves up for failure. For example, when undertaking evaluations on the effectiveness of training as a learning method, we frequently discover less than desirable results in terms of sustainability and the participant's ability to apply their new-found knowledge and skills in the business context. Consider these not so uncommon scenarios:
• The introduction of a new enterprise ICT management system required training of all employees yet the training was deployed months before implementation, the method was instructional and the participants had few opportunities to practice using relevant examples on the computer. On 'go live' day, very few employees reported feeling competent in their ability to use the new system and organisational anxiety and chaos ensued.
• An organisation invested in a training program to develop the capability of their people leaders. The training method was level 2 with some elements of level 3. Self-awareness was raised yet, there were limited opportunities to practice with others and zero links with the immediate day-to-day requirements of their role. On evaluation, it was found that the participants had no real understanding of why they had been selected to attend. Nor did their managers overtly connect the training with the expected c o m p e t e n c i e s a n d p e r f o r m a n c e improvement outcomes. As a result, there was little motivation or accountability to make any substantial changes to their management practices and the program failed to have any meaningful impact on the business.
"Learning is hard - if it is not difficult then you are probably not learning"
The brain and Learning :
Understanding how the brain functions has been extremely influential for adult learning theory
yet, too often, training programs neglect to adhere to the basic principles. Neurologist Donald Hebb pioneered that we learn through repetition and recognition, "when neurons fire together, they wire together" yet we continue to deliver one-off training events and expect a different result. There is also truth in the old cliché "if you don't use it you lose it", highlighting the need for training to be directly linked with the immediate needs of a person's role.
Whilst counter intuitive, unless our lives depend on it (and even then), our brains have habits and a preference to protect the status quo which inhibits learning. When a change, such as a new task or new behaviour is required, the need to shift gears to learning mode increases brain activity and creates stress which we are inherently motivated to move away from. Filling people up with consecutive days of training is exhausting for the brain. The brain filters information and returns to the default mode (i.e. no change) at every opportunity.
There is an art to designing training programs and getting the balance right between being light and engaging, and the need to push people to an uncomfortable learning edge. It can be tricky because, when it starts to feel hard, the brains natural defence mechanism is to resist learning and look for a way out.
What else gets in the way of learning and the ability to change ?
Aside from the quality of the training, matching the type with the desired outcomes and physical environment, other impediments to learning that are often overlooked include:
• Individual capacity - not only can an individual's aptitude for learning be limiting, a motivation to learn must exist. Also, the participant's past experiences and mental models around learning can present as a barrier if the participants hold an expectation that the 'teacher' is going to give them what they need with very little effort on their part.
• Team capacity - returning to a team that has not 'read the same book' can be challenging
for individuals because we humans love to belong. The potential consequences of applying new behaviours in the team presents an unknown risk that could threaten relationships.
• Organisational capacity - the extent to which the organisation's culture, structure, systems and processes enable the practice and application of new skills in a given context is also vital. Learners often return from training with a new set of expectations only to find these are in direct conflict with the general status quo, unwritten rules and the 'way things work around here'.
Another factor that gets in the way of learning to the point where actual change is embedded can be found in poor problem definition and a tendency for organisations to wheel in trainers to address 'symptoms' rather than the root cause. By way of example, an HR department recently asked me to deliver emotional intelligence and conflict resolution training. Fortunately, I had some insight on this team's performance and knew that a one-off level 2 (or even 3) type training event would have little to no lasting impact on the team's system dynamics.
The importance of evaluating training effectiveness :
A final note around learning, and a particular objection of mine, is the lack of formal evaluation processes over and above filling in 'happy sheets'. These are nothing more than a tick-the-box exercise. For example, consider the potential consequences when sending people on emergency response training: the food was fantastic; the facilitator was awesome; and it was great to mix with other people in the organisation. There were relevant and interesting examples, a whole lot of detail about important procedures and the event generally left people feeling energised. 'Happy sheets' collected at the end of the day revealed the participants were happy, happy, happy on all counts - tick. Yet, did they actually learn? Will the participants recall and apply their learning in a real emergency when it matters most ?
Aside from the lack of connection with the persons role and failure to demonstrate that learning has been applied, 'happy sheets' are skewed and misleading. I should think the extent to which learning has occurred is far more important than whether the training event was enjoyable. Heaven forbid that we actually dare to learn and change as a result of a quality evaluation.
"Are organisations undertaking rigorous evaluations to verify that training has been effective or are they simply ticking the box ?"
Granted, establishing the baseline of current state can be time consuming where the business is required to ascertain both hard and soft metrics. Nevertheless, if there is a genuine commitment to l ea rn ing ou tcomes and pe r fo rmance improvements then rigorous evaluations are time well spent.
What can be done to capitalise on the learning cycle ?
A 'tick the box' mindset around training and learning comes with the potential for serious consequences in terms of safety, employee engagement, organisational performance and reputation. Some important considerations when choosing training or learning are:
• One-off training events are problematic for the reasons discussed herein. Learners need small bites and scaffolding to build on so that the learning is embedded. We recommend learning at periodic intervals so that the participants have an opportunity to practice new skills and reflect on their experience back in the learning environment which serves to strengthen and cement their skills.
• The training must be immediately relevant to the learner's role and business context. In this way, learners recognise the 'need' for change. In addition, making specific links between the training initiative and the specific competencies and expected performance improvement ou tcomes inc reases motivation and accountability.
• Experiential learning works best. Use current business and/or role challenges and provide as many opportunities to practice in a safe learning environment as possible.
• Send teams or groups of peers to learn together. Not only does this create ongoing support networks, the participants develop a deep appreciation of themselves, leverage diversity and sharpen inter-relational skills by navigating the group dynamics. A team that learns together grows together with greater levels of accountability and sponsorship.
• Undertake robust evaluations so that the business impact and return on investment can be measured, and the training or learning intervention continuously improved over time.
"A shift from one-off training events and conferences to regular peer learning interventions is a powerful competitive advantage that brings about sustainable improvements and highly valued outcomes.”
Abstract :
Convex functions are closely related to convex sets. Convex functions have many important properties that are very useful in the field of applied mathematics particularly inoptimization techniques in economics. For checking convexity various mathematical techniques are used. With the help of convexity preferences we can derive the consumer’s equilibrium and duality theorem in a linear programming problem. The uses of convex technologies and homothetic production functions have also an important role in optimum resource allocation. The convexity property is the heart of consumer preference theory and in production techniques. The present paper analyses the application of convexity property in consumer preference and in the theory of production regarding the optimum allocation of resources.
The mathematical property of convexity is commonly used in various fields of economics. The idea of convexity may use for optimum allocation of resources and thereby reduce deprivation. Without this property we cannot reach the consumer’s equilibrium point. Without this property the demand and supply functions are discontinuous and hence we cannot draw the market equilibrium point. We will not be possible to use the mathematical programming and duality in the absence of convexity (K C Roychowdhury 1991).In non-convex preferences the consumer prefers a glass of beer or a glass of champagne alone to any mixture of the two.The convex idea shows that all resources would not use to produce in a single commodity production simply because the one item cannot serve the all human wants. For an individual three basic essential things are required for his survival: food, clothing and shelter. In the primitive community when man lived in jungles he did not have clothing or even shelter. But he needed food to survive. Animals can live without clothing or shelter but also need
food. Plants also need food. While plants can make their own food man and other animals have to produce or collect food. Thus for all living beings food is the most essential component of life. It is necessary for getting energy which man needs for doing different works. Even when a man is sleeping his major organs like heart or lungs remain active. These are functioning from birth to death at a stretch.
2. Convex Set :
A set is called convex if any straight line (joining by two points from the set) entirely lie on the set. Suppose xÎA, y A, then the joining straight line,
(xy) = tx + (1-t) yÎA, tÎ [0, 1]
Now tx + (1-t)y is called the convex combination. When t = 0, yÎA and t = 1 xÎA. An intermediate values of t i.e. 0 < t < 1 gives us the weighted average of x & y.
The solid triangle, circle, square, rectangle etc are the examples of convex set because any straight line drawn from taking any two points lies entirely on the set. A crescent shape or a star, or a hollow circle is not convex set. Straight line like (AB) does not lie entirely on the set.
3. Properties :
Any vector is an extreme point of a convex set if it cannot be expressed as a convex combination of two other vectors in the set i.e. an extreme point does not lie on the line segment between any other two vectors in the set. Any vector is a closed and bounded convex set with a finite number of extreme points can be expressed as a convex combination of the extreme point. The solution space of a set of simultaneous linear equations is a convex set having a finite number of extreme
Î
Application of Convexity in Consumer Preference and Production process
In consumer preference theory we assume that all consumers are rational and behave in accordance with a systematic consistent set of preference. Moreover in consumer choice theory we assume that each commodity is finely divisible so that any non-negative quantity can be purchased by the consumer. The consumption set can be written as:
C = {x =(x1, x2, x3, x4… xn), xi=0, "i = 1, 2, 3, ……, n.}
Now the set C is a closed, convex set.
Suppose a consumer is indifferent between two commodity bundles x and y in the set C i.e. xIy, x, yÎC. Now any weighted average of x & y always prefer to either alone. Thus if xIy, then
P tx + (1-t) y x or y"t, 0<t<1, x ¹ y
Now strict convexity implies that IC is convex towards the origin but it can contain straight line segments and a weak convex preference allows thick band IC (K C Roychowdhury 1991).
In economics, the commonly used budget set is closed and convex. D OAB is a convex set. Any point on this set is affordable by the consumer. At point O, the consumer does not buy either of any commodities. The other two extreme points i.e. at A, the consumer purchases only q2 and at B the consumer purchases only q1. This is the situation of monomania which is the corner or extreme point solution.
Suppose A & B are two convex sets. Then A intersection B is a convex set but A union B may or may not B a convex sets.
Suppose the consumption bundles of two individuals A & B are :
A = {rice, bread, fish, milk}
B = {rice, bread, meat, pepsi}
Let the equation of IC be U = f (q1, q2).
Along the IC, f1dq1+ f2dq2 = 0 or
dq2/dq1 = -f1/f2<0; f1 ,f2 > 0 Þ IC has negatively sloped.
\ MRS decreases along an IC. MRS decreases in absolute term iff
Preferences are strictly convex.
MRS is not always decreasing as q1 increases when the preferences are non-convex.
Any disjoint pair of convex sets can be separated by a hyper plane.
B q1
O
q2
A
q2
MRS= ( -) 1 MRS= (-) .5
IC
MRS= (-) 2
q1O
Any point in the region to the right of z is preferred.
4. Convex Function :
Convex functions are closely related to convex sets. If f(x) is convex, then for any constant, say k, it can give rise to a convex set, say S (AC Chiang 1984).
If S ={x|f(x) < K}then f(x) is convex.
If S ={x|f(x) > K}then f(x) is concave.
Suppose Y = f(x) be differentiable and second order derivative exist.
Then f(x) will be strictly convex iff f f ” (x) > 0 f (x) has a minimum value.
Then f(x) will be strictly concave iff f f ” (x) < 0 Þ f (x) has a maximum value.
Suppose Y = f(x) be differentiable and strictly convex and it has a minimum at point x = x0.
Then f ’ (x) < 0 for x < x0
f ’ (x) = 0 f or x = x0
f ’ (x) > 0 f or x > x0
f ’ (x) Changes sign from –ve to +ve at point x0
The situation will be reversed if the function is concave.
Let y = f(x) is concave iff any tangent drawn at point P lie entirely above or on the graph (C Birchenhall and P Grout 1987).
t(y) = r + f ’ (x) y. At the tangency point f(x) = t(x) and x = y
f(x) = r + f ’ (x)x ® r = f (x) - f ’ (x) x
\ t (y) = f (x) - f ’ (x) x + f ’ (x) y
Or t (y) = f (x) + f ’ (x) (y-x)
Now if Q lies below R then
Þ
f (y) < t (y) = f (x) + (y-x)
Thus y = f (x) is concave iff f (y) < f ‘ (x) + (y-x)
And y = f (x) is convex iff f (y) > f (x) + f ’ (x)(y-x)
5. Hessian-Determinant to Check Convexity :
Let multivariate function, z=f(x, y).
Then f(x, y) will be convex iff zxx > 0 and zxx.zy> 2
(zxy) .
And f(x, y) will be concave iff zxx < 0 and zxx.zy> 2
(zxy) .
A convenient or sufficient test or second order condition for convexity/concavity is the Hessian Determinant.
zxx zxy |H | =zyx zyy
When |H1| > o and |H2| > 0, the Hessian is called +ve definite and the function are convex and the function has a minimum value. When |H1 | < o and |H2| > 0, the Hessian is called -ve definite and the function are concave and the function has a maximum value (E T Dowling 1986).
The idea of convex sets and convex/concave functions has many important properties that are very useful techniques applied in economics particularly in various optimizing problems. Suppose f(x) is concave then - f(x) will be convex i.e. one is the mirror image of the other. Thus minimization of one will maximize the other and hence it is used in case of duality. As a result if we analyse the properties and applications of convexity the other is automatically done. To find global/local maximum/minimum and in duality the idea of convexity is very much helpful. The convexity property is the heart of consumer preference theory and in production techniques.
6. Convexity Property Under Uncertain Behaviour :
For the sake of simplicity here we assume that function can be measured the return on gambles on monitory terms, is strictly increasing and is continuous with first and second order derivatives exist. In this situation the consumer’s expected utility of a gamble:
E [W] =pW1+(1-p) W2 where Wi, "I = 1, 2 are different wealth levels and p is the probability of outcome of lottery (0<p<1) (J Henderson and R E Quandt 1987).
f ’ (x)
strictly convex and the consumer is risk lover.
7. Convexity and Production :
The convex production set similarly draw the CRS or DRS. In general equilibrium models only allow the non-convex production sets (or economics of scale) or non convex preferences. Production function is a purely technical relation which connects factor inputs and outputs (A Koutsoyiannis 1979). A method of production activity is a combination of factor inputs require for the production of one unit of output.
Suppose the producing firm has the following activity process:
P1 P2 P3
Labour 2 0 3
Capital 2 3 0
In the first process the firm is using a convex technology since here the combination of both the factors are used while in the other two cases only single output is used.
8. Minkowski Addition of Sets :2 2 2
Let Q = [0, 1] ,Q = [1, 2] ,Q = [1, 3]1 2 3
2 2 2Then Q = Q + Q3 1 2
From Minkowski addition of sets we get the sum 2 2of the squares Q and Q is the square of Q + Q 1 2 1 2
2 2 2i.e. Q + Q = (Q + Q )1 2 1 2
Suppose a firm has the following production process:
Lab. Cap. Lab. Cap. Lab. Cap.
Q1 [0, 1] [1, 2] [2, 3]
Q2 [1, 2] [2, 3] [3, 4]
Q3 [1, 3] [3, 5] [5, 7]
Utility
Income
U (W2)
U (W1)
O W1 P W2
A
Q
B
()()()Wr
WrWr
¢
¢¢-=
Now the person is risk neutral if the expected value of the lottery equals the expected utility of value of the lottery i.e.
U (pW1+ (1-p) W2) = p U (W1) + (1-p) U (W2)
In this situation expected utility function will be 450line i.e. he/she has no preference either in gambling or certainty.
Now if the consumer is risk averse then the expected utility function will be concave. If we take any two points A and B on the expected utility function then the chord must lie above the joining line (AB) (as shown in the following figure).
U (pW1+ (1-p) W2) > p U (W1) + (1-p) U (W2)
Thus we can say that concave utility function assured risk aversion. In this situation the consumer acceptance set A (W) must be convex (A (W) be the set of all gambles the consumer would accept at an initial wealth level W).
Now suppose the consumer is risk lover or plunger. Here his/her preference directly follows the Charbak principle i.e. his/her preference are such as that today’s pigeon is greater than tomorrow’s peacock. In this case the expected utility function will be convex. Then the chord must lie below the joining line AB. Here the utility of expected value is less than its expected utility i.e.
U (pW1+ (1-p) W2) < p U (W1) + (1-p) U (W2)
Arrow-Pratt used the following formula to measure the absolute risk aversion:
Now if r (W) < 0 implies the utility function is strictly concave and the consumer is risk averter. And if r (W) > 0 implies the utility function is
Q1
Q1+Q2
Q2
Y
O
X
Activity Q3 is derived from Q1 and Q2 i.e. simply adding Q1 and Q2.
2 2 2In production process Q L+K = QL + QK
Though the cost of productions in Q1 + Q2 is the same in Q3 it is better to use the activity Q3 to get the advantage of large scale production process. Here Q1 may be called small-scale production process, Q2 may be called medium-scale production process Q3 may be called large-scale production process. By means of the combination of Q1 and Q2, Q3 will be a possible and efficient method using increasing returns to scale.
The idea of convexity may be used in resource allocation in production process. Suppose we consider two production functions as :
Q1 = f1 (K1, L1) and Q2= f2 (K2, L2) which are non-decreasing, differentiable and concave.
Then the aggregate production functions can be written as :
Q = Q1 + Q2 = Ø (K, L)
Let aggregate capital= K and aggregate labour = L.
Then K1 + K2 < K & Then L1 + L2 < L
The aggregate production can be obtained as follows:
We know that the sum of two convex sets must be convex. Suppose f1 (K1, L1) and f2 (K2, L2) are homogenous and show constant return to scale (CRS). Then their convex combination must be convex and shows CRS.
Let Ø (K, L) = t f1 (K1, L1) + (1-t) f2 (K2, L2) "t, 0 < t < 1.
a b CQ1 = f1 (K1, L1) = K1 L1 and Q2= f2 (K2, L2) = K2
dL2
Now let Q11 = f1 (K1, L1) = log x and Q22 = f2 (K2, L2) = log y
‘Since f 1 (x) = 1 / x > 0 and = 2 1 / y > 0
\ Q11 and Q22 are homothetic function.
Suppose ? = Q11 + Q22 = Ø (K, L) = t x + (1-t) y
It should be noted that Ø (K, L) is not homogenous but homothetic.
‘f (y)
tThus ? = t x + (1-t) y = t log x + (1-t) log y = log x
(1-t)y = log z, say.
1Now? = 1/z > 0 Thus again ? is homothetic.
Result :
The sum of the MPs of each times the level of use of that factor times the level of use of that factor is the convex combination of the share of input elasticities.
tProof : ? = t x + (1-t) y = t log x + (1-t) log y = log x (1-t) a b t C d (1-t)y = log (K1 L ) (K L )
= t log + (1-t) log ( )
\ K1 K1 + L L1 + K K2 + L2 KL2 = t a + t b + (1-t) c + (1-t) d
= t (a + b) + (1-t) (c + d)
Let a + b = r and c + d = ð
= t r + (1-t)
Hence the result QED.
Now we turn to our main objective function :
Ø (K, L) = max.{f1 (K , L ) + f (K , L ): K + K =K, L + L = L, L, K > 0 }
Substituting the values we get,a
Ø = t logK L + (1-t) log (K L ) + µ [L - (L1+ L + s )] + q [K - (K1+ K + s )] , where s & s are 2
dummy variables.
Here we apply the Kuhn-Tucker conditions as follows :
¶Ø/?K = bt / L - µ > 0 and L Ø / K = 0
\ L1 (bt/L1 -µ) = 0. But L1 ¹ 0 \ L1=bt / µ
lly, llyK1 = bt/q, L = (1-t)d/µ and K = (1-t) c / q
\ L* = L + L = 1 / µ (b t + (1-t) d)
K* = K + K = 1/q (a t + (1-t) c)
Now the Lagrangian constants ? and µ are shadow prices of that particular resource use in the production process.
Lemma : Optimum amount of a particular resource used is the per unit shadow price of the convex combination of the share of input elasticities.
Proof : We have already got,
1 2 2
a b c dK1 L1 K2 L2
? 1? 2? ?
\ K1 ?K1 + L1?L1 + K2?K2 + L2 ?KL2 ð
1 1 2 2 2 1
2 1 2
b c d1 1 2 2
2 2 1 21
1 1 1 ¶¶1
2 2
1 1
1 1
L^* = 1/µ(b t + (1-t) d) and K^*= 1/?(a t + (1-t) c).
which follows the result directly QED.
Result : Ø is strictly concave :2
Proof : Q = b/L and Q L L = -b / L
2Q = a/K and Q K K = -a/K
Q L = = 0
2 0, Q1 K K = -a/K < 0 and 2 2
Q L L . Q K2K - Q L Q K L > 0.
Here |H | > o and |H | > 0, the Hessian is called +ve definite and the function Ø is strictly convex
lly, lly Q is strictly concave.
Since Ø is derived by homothetic transformation (log transformation) Q & Q are strictly concave, therefore Ø is also strictly concave.
Hence the result QED.
Lemma: Ø is homothetic but not homogeneous.
Proof : By definition f = t x + (1-t) y = t log x + t 1-t
(1 - t) log y = log x y = log z, say.
Now / (z) = 1/z > 0
This directly implies ? is homothetic.
Result : If Q1 & Q2 follow CRS then also follows CRS.
Proof : Suppose f1 (K , L ) and f (K , L ) are homogenous and show constant return to scale (CRS). Then a + b = 1 and c + d =1 and their convex combination Ø (K,L) = t f (K , L ) + (1-t) f (K , L ) t, 0 < t < 1 follows CRS.
K1 + L + K + L = t a + t b + (1-t) c + (1-t) d
= t (a + b) + (1-t) (c + d) =1, substituting the values of (a + b) & (c + d).
Hence the result QED.
9. Conclusion :
The Lagrangian constants ? and µ are shadow prices of that particular resource use in the production process. The firm may take decision regarding optimum amount of a particular resource used is the per unit shadow price of the convex combination of the share of input elasticities. The main cause of deprivation is the over or under consumption and over or under
1 L 1 1 1 1 11
1K 1 1 2 2 11
1 1K1 Q1 K1L1
2\ Q1 L1L1 = b / L1 < 1
1 1 1 1 2 1 1K1 1 1 2
1 2
2
1 2
f
f
1 1 2 2 2
1 1 1
2 2 2 "
fK 1fL 2fK 2fKL1 1 2 2
production of any commodity or a particular resource. By choosing the value of parameters like a, b, c, d, q and µ we can simply allocate the resources for production and distribute the goods according to the common needs. This will lead to a better welfare state and obviously reduce the deprivation, hunger, poverty which is the common phenomena of the rural masses.
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7. Burra Neera (1998), Born Towork Child Labour in India. Oxford press Delhi.
8. Sadhu and Singh (1980), Child labour in India' in The Indian worker, 6 October
9. Singh, J. P., “Child labour as a challenge for urban sustainability: A case study of Azadpur mandi area, Delhi”, International Journal of Academic Research and Development, Vol. 2 (6) Nov. 2017: Pg. 944-949.
10. Singh, J. P., “Child Labour as a Social Problem with reference to India”, in Bal Shram evam Bal Apradh- Mudde evam Chunautiyan, by S.P.L. Srivastava, S. Yadav, S. and Namrata Prasad, Page - 305-314 : New Delhi, 2018 (ISBN: 9789382171690)
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