Effects of marketing, bank loan and credit debt on consumer’s spending. Mathematical models based on an engineering concept

Introduction to the study

The main objective of this study is to utilize an engineering concept in order to propose a mathematical model to correlate consumer spending, utility and income. The difference between the proposed model and the Keynesian consumption theory is explained by the fact that the Keynesian consumption theory takes into account the consumption of costumers with no income. The effects of marketing, bank loans and credit debt on consumer spending are also analyzed using the general equation of transport phenomena and mathematical models are presented for the first time. Based on a case study, marketing has increased the utility (driving force) by 61%. Taking into account the theory of consumption smoothing, bank loans also provide the consumer with additional spending power by decreasing the resistance for consumption. In case of excessive debt, customers might spend the money only to buy the “utility” in order to be able to repay the debt. In this situation, the effects of debt are described in the proposed engineering model as a decrease in income (extra resistance to spend money).

1. Dynamic Systems & their Universal Law

Everything in the universe is continuously in motion and the object can be as small as an atomic particle or as large as a planet. Gravitational and electromagnetic forces are responsible for large objects to be in motion while weak and strong nuclear forces are the driving factors for the quantum world to be in continuous motion. From an engineering perspective, flows take place in dynamic systems due to a driving force within the system and are controlled by a resistance located between two poles of the system. According to the second law of thermodynamics, this driving force is the difference in concentrations of energy between the two poles. For example, heat transfer in a piece of metal is transported from a higher temperature to a lower temperature and the speed of the flow of heat transfer is controlled by the resistance of the metal to heat transfer. The rain falls from the sky (higher altitude) to the land (lower altitude). Without the resistance of air to the gravitational force, rain drops will destroy all the trees and vegetation. This universal phenomena could therefore be described using the following generalized relationship for transport phenomena:

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In the field of electricity, the current I (flow of electrons) is motivated by a driving force (difference in potential = ΔU) and controlled by the electrical resistance (R) of the circuit. Ohm’s law is then obtained:

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In the study of Chemical Engineering, momentum, mass and heat transport also share a very similar framework. For example, Fourier’s law of heat conduction (Thermal Ohm’s law) is defined as:

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Where: Q = heat flow; ∆T= Difference in Temperature (driving force), ∆x= distance of heat conduction, A= Surface area of the metal, k= Heat conductivity of the metal; (∆x/kA) is therefore the resistance to heat flow by conduction.

Based on the same concept of transport phenomena, described in equation (1), people could be described as dynamic systems motivated to take roads and highways to go to schools for studying, to workplaces to make money and to markets to buy what is needed for their daily life. People have therefore a natural motivation (driving force) to spend their money on buying food, homes, furniture, electronic devices, etc. On the other hand, the amount of money spent by consumers is limited by their income (conductance). The main objective of this investigation is an attempt to find a mathematical model, based on an engineering concept, in order to: (1) propose a new mathematical model for consumer spending, (2) mathematically correlate the effects of marketing (increasing the driving force), bank loan (decreasing the resistance) and credit debt (increasing resistance) on consumer spending (flow of money).

2.Gross domestic product and consumer-based economy

The gross domestic product (GDP) is the indicator of national income and all outputs for a given country's economy. The GDP represents therefore the total expenditures for all final goods and services produced within the country in a stipulated period of time. As shown in Figure 1, the Gross Domestic Product (GDP) of the United States was worth 19390.60 billion US dollars in 2017¹

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Figure 1: Gross Domestic Product for the USA from 2008 to 2017¹.

The expenditures approach and the income approach are the two known methods to calculate the gross domestic product (GDP). Both of these approaches attempt to best approximate the monetary value of all final goods and services produced in an economy over a set period of time (normally one year). The major distinction between each approach is its starting point. The expenditure approach begins with the money spent on goods and services. Conversely, the income approach starts with the income earned (wages, rents, interest, profits) from the production of goods and services². For the income approach, the GDP is calculated by adding the following elements³:

GDP= TNI + ST + D+ NFFI(4)

Where TNI= Total National Income; ST= Sales Taxes; D= Depreciation and NFFI= Net Foreign Factor Income. TNI is equal to the sum of all wages plus rents plus interest and profits. Some economists challenge the notion of including sales taxes in the GDP formula on the basis that taxation is counterproductive. They think it should subtract from total output rather than add to it. However, most use the income approach that includes sales taxes.

For the expenditure approach, the formula utilized to calculate the GDP is⁴:

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1. “C” (consumption) is normally the largest GDP component in the economy, consisting of private expenditures (household final consumption expenditure) in the economy.
2. “I” (investment) includes, for instance, business investment in equipment and spending by households (not government) on new houses is also included in Investment.
3. “G” (government spending) is the sum of government expenditures on final goods and services
4. “X” (exports) represents gross exports. GDP captures the amount a country produces, including goods and services produced for other nations’ consumption.
5. “M” (imports) represents gross imports. Imports are subtracted since imported goods will be included in the terms “G”, “I”, or “C”, and must be deducted to avoid counting foreign supply as domestic.

A consumer economy is defined as an economy driven by consumer spending as a percentage of its GDP (Gross Domestic Product). Keynesian economic theory proposes that governments should stimulate spending to end a recession. Supply-side economists recommend the opposite. They believe that governments should cut business taxes to create jobs. However companies won't increase production if the demand is not there⁵. Consumers are, therefore, very important to businesses. The more money consumers spend with a given company, the better that company tends to perform. For this reason, it is unsurprising that most investors and businesses pay a great amount of attention to consumer spending figures and patterns⁶.

3. Proposed engineering model for consumer spending

Contemporary measures of consumer spending include all private purchases of durable goods, nondurables and services. Consumer spending (CS) is the demand side of “supply and demand"; production is the supply. Without consumer spending, there is therefore no motivation to produce goods. Goods are generally divided into two categories: durable goods, like autos, furniture or any item that has a useful life of three years or more. The second is non-durable goods, such as fuel, food, and clothing. In 2017, the consumer spending in the USA made up to 70% of GDP ($12.6 trillion) ³, ⁴. Consumer spending is therefore the main driving force of the economic system in the USA. Nearly two-thirds of consumer spending is on services, like real estate and healthcare. The remaining one-third of personal consumption expenditure is on goods. These include so-called durable goods, such as washing machines, automobiles, and furniture. More frequently, people buy non-durable goods, such as gasoline, groceries, and clothing. The consumption of these goods is the result of economic activity. This is because individuals ultimately use these goods to satisfy their own needs and wants; economists refer to this satisfaction as “utility⁴.

The consumption function, or Keynesian consumption function, is an economic formula that represents the functional relationship between total consumption and gross national income. It was introduced by British economist John Maynard Keynes, who argued the function could be used to track and predict total aggregate consumption expenditures⁷. The relationship between consumption and income is based on the fundamental psychological law of consumption which states that when income increases consumption expenditure also increases but by a smaller amount⁸.

Abbildung in dieser Leseprobe nicht enthalten Figure 2: Consumption Function⁸

Based on Figure2, the Keynesian consumption function is linear⁸:

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(6)

Where a is the intercept (a constant which measures consumption at a zero level of disposal income), b is the marginal propensity to consume (MPC) and Y is the disposable income. The MPC is the proportion of an aggregate raise in pay that a consumer spends on the consumption of goods and services, as opposed to saving it. Y is total personal income minus personal current taxes. The above formula describing consumption as a function of current disposable income whether linear or non-linear is called the absolute income hypothesis. This consumption function has the following properties⁸:

1. As income increases, average propensity to consume (APC = C / Y) falls.
2. The marginal propensity to consume MPC is positive but less than unity (0 < b < 1) so that higher income leads to higher consumption.
3. The consumption expenditure increases or decreases with increase or decrease in income but non-proportionally. This non-proportional consumption function implies that in the short run average and marginal propensities do not coincide (APC > MPC).
4. This consumption function is stable both in the short run and the long run.

In this investigation, consumer’s spending (CS) taken as the money people spend to buy the goods during one month will be defined. Considering an analogy with equation (1), people have a motivation (driving force) to spend their money to buy goods, defined as utility⁴. On the other hand, the amount of money spent depends on personal income. The income effect relates to how a consumer spends money based on an increase or decrease in income. An increase in income results in demanding more services and goods, thus spending more money. A decrease in income results in the exact opposite. In general, when income is lower, less spending occurs⁹. In the proposed model, the income is considered as the conductance for spending money and the inverse (1/income) is therefore its resistance. Following the general equation (1) of transport phenomena, consumer’s spending (CS) is defined in this investigation as:

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Equation (7) could be reorganized as:

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The proposed equation (8) indicates that consumer spending increases proportionally with the utility, as the driving force, and the personal income of the buyer as the conductance (1/resistance) for buying. In this concept of dynamic systems, it is assumed that people buy only what they need. As a consequence, without this driving force, the consumer spending is equal to zero. This concept is also based on the fact that people with no income are not able to spend money to buy what they need. In comparison with the Keynesian consumption function, the proposed equation (8) could be rewritten as:

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