National income computation

1. Output approach / product method

   This method adds all the sectors value of output in an economy or output approach measures the value of an economy at the source of production. It sums value of output from sector like mining, wildlife, and manufacturing etc.

   In output approach added by all firm in different stages of production can be added to get national income using output approach.

   Example: Suppose we have a maize producer who sells maize to a miller at TSH 1500 per kilogram. The miller changes the maize into flour and sells it to traders at TSH 1000. Traders sell to the final consumer at TSH 2100/=. To get the income using the value added method we add: Maize 1500 + Value of flour 400 + Value of traders 600 = 2100.

2. Expenditure approach

   This is a method where the value of spending on all final goods and service is added up to get the value of national income.

   $E = C + G + I + (X - M)$

   Where C – personal consumption expenditure G – expenditure by the government I – expenditure on investment X – expenditure on export by buyers M – expenditure on import

   Note: $(X - M)$ gives net export

   $GDP = C + I + G + (X - M)$ $GNP = GDP + \text{Net foreign income}$ $= C + I + G + (X - M) + NFI$

3. Income approach

   This method adds all incomes received by factor of production. They include wages, profit, interest, and rent.

   $GDP = \text{Wages} + \text{profit} + \text{rent} + \text{interest} + \text{operating surplus}$

Qn: what is circular flow of national income?

Given: a simple closed economy with mainly two sectors i.e. household and firm (business) the flow of income can be illustrated as follows.

In the above economy the following assumptions have been used:

1. It is a closed economy i.e. there is no foreign trade
2. There are no leakages, every income received must be spent, e.g.; Saving-taxes-import
3. The economy has two sector namely household and firm
4. The household provide factors of production to firm and spend all the income it receives in purchase of goods and services.
5. It assumes there are no injections i.e. there is no income arising from expenditure outside the economy. e.g. Investment-Government expenditure-Exports

Each time something is produced and sold its value is equal to the purchases expenditure. The purchaser expenditure will be received as income by those who produced. Hence $E = O = Y$. National expenditure is equivalent to national output equivalent to national income.

1. Availability of resources and their utilization

   National income largely depends on the availability and efficient use of resources. These resources include:

   • Natural resources (such as land, minerals, water bodies),
   • Man-made resources (like infrastructure and machinery), and
   • Human resources (skilled and unskilled labor).

   When these resources are fully and effectively utilized, a country can increase its production, leading to higher national income.

2. Political and social stability

   A stable political and social environment encourages both domestic and foreign investment. Stability reduces uncertainty and risk, allowing businesses to plan and operate efficiently, which in turn boosts production and national income.

3. Availability of entrepreneurial force in the economy

   Entrepreneurs play a vital role in identifying business opportunities, organizing production, and taking calculated risks. A strong entrepreneurial force promotes innovation and efficient resource use, contributing to a higher national income.

4. The size of capital accumulated by a country

   Capital goods such as machinery, factories, and tools are essential for production. The greater the capital stock, the more efficiently and on a larger scale goods and services can be produced, resulting in increased national income through higher investment.

5. The level of technology

   Advanced technology improves productivity by allowing more output with the same or fewer inputs. The adoption of modern techniques and innovation increases production efficiency and quality, directly raising national income.

   Advancement of technology leads to higher production leading to a higher national income

6. Government policy

   This is particularly in developing policy such as infrastructure policy and privatization, licensing etc. The more the government policy is complicated the lesser the entrepreneur the lesser the output and hence the lower the national income.

7. The efficient of labour force

   The more the labour is inefficient the lesser the quality and output affecting the size of National income.

1. Showing the growth rate of an economy

   National income statistics are essential for measuring economic growth annually. The government computes the national income for each year and compares it to previous years. By calculating the percentage growth rate, policymakers can assess whether the economy is expanding or contracting and make informed decisions accordingly.

2. Determining per capita income

   Per capita income is calculated by dividing the national income by the population. This statistic helps in understanding the average income of an individual within the country, which is important for assessing the overall standard of living and economic well-being of citizens.

3. Assessing the effectiveness of government in tax and revenue collection

   National income statistics are used to evaluate how effectively the government is collecting taxes and generating revenue. Ideally, the tax revenue collected should be proportional to the national income. This ensures that the government's fiscal policies are in line with the country's economic output.

4. Indicating resource utilization

   National income statistics help to gauge how well resources are being utilized. The greater the national income, the more effectively a country's resources (such as labor, capital, and natural resources) are being employed in the production process, signaling efficient economic activity.

5. International comparison of economic growth and performance

   These statistics are used to compare the economic performance of different countries. By examining national income, it becomes easier to understand how well a country is performing economically in comparison to others, which is crucial for global competitiveness and attracting investments.

6. Attracting foreign donors

   International organizations, foreign governments, and donors often rely on national income statistics to determine the economic status of a country. A higher national income or evidence of growth can make a country more attractive for foreign aid or investment.

7. Assisting in government decisions on resource allocation

   National income statistics help the government decide how to allocate resources across different sectors of the economy. By evaluating which sectors contribute most to national income, the government can prioritize investments in the most productive areas to enhance overall economic performance.

8. Informing government policies

   The government uses national income statistics to shape and implement various policies, such as employment policies, social welfare programs, and economic stimulus plans. Understanding trends in national income helps in crafting effective policies aimed at promoting growth, reducing inequality, or addressing unemployment.

1. Inaccurate data:

   It is difficult to obtain an accurate national income figure due to incomplete or incorrect data sources. Inaccurate reporting or incomplete records can cause distortions in the final figures. For example, if businesses or individuals fail to report their full income or expenses, the calculated national income may be significantly understated or overstated. This issue is particularly pronounced in less developed countries with weak data collection systems.

2. Transfer payments:

   Transfer payments refer to income transfers that do not correspond to the production of goods and services, such as government subsidies or gifts. These are included when calculating personal income, but estimating their exact value can be difficult. For example, the value of a gift or an informal transaction is hard to measure accurately, which makes it challenging to include these payments in national income calculations without overestimating or underestimating personal income.

3. Double counting:

   Double counting happens when the same value is counted multiple times during the process of compiling national income statistics. For instance, work in progress or intermediate goods may be included both in the value of final goods and as part of the production process. This inflation of the national income figure can lead to misleading results, as it does not accurately represent the total value of final goods and services.

4. Shortage of qualified personnel:

   The lack of skilled personnel in statistical data collection and national income calculation is a significant barrier in many countries. Without trained statisticians and economists, the data compiled may lack consistency or suffer from human error. This leads to misrepresentation in national accounts, as the compilation of accurate data requires expertise in both statistical methods and economic theory.

5. Subsistence economy:

   In countries where a large portion of the population is involved in subsistence farming or non-monetary activities, it is difficult to estimate national income accurately. These activities, such as growing food for personal use, are not part of the formal economy and do not involve monetary transactions, which means they are often excluded from official national income statistics. As a result, national income figures may be underreported in regions where subsistence economies are prevalent.

6. Illegal activities (black market, social evils):

   National income statistics typically exclude illegal activities, such as the black market, drug trade, and other informal or criminal sectors. Since these activities are hidden and not formally recorded, it is extremely difficult to estimate their value and include them in national income figures. Consequently, the real size of the economy may be understated, especially in economies with high levels of informal and illegal transactions.

7. Estimation of income from abroad:

   Estimating income received from abroad, such as remittances or foreign investment returns, poses a challenge. Often, these income sources are not officially recorded, or are underreported, leading to inaccurate national income figures. Without reliable data on cross-border economic activities, it becomes hard to calculate the total income a nation generates from external sources.

8. Data from self-employment activities:

   Gathering accurate data on income from self-employment is difficult because many individuals in this sector do not report their earnings fully. For example, small business owners, freelancers, or informal workers may not keep proper records, or may deliberately underreport their income to avoid taxes. As a result, this sector is often underrepresented in national income statistics.

According to Keynes national income equilibrium is determined at the intersection of demand and supply. In this argument he stated the following assumptions.

1. National income equilibrium determined by the intersection of demand and supply:

   According to Keynes, the equilibrium level of national income is achieved when the total demand for goods and services (aggregate demand) equals the total supply of goods and services (aggregate supply). At this point, the economy is in balance, and there is no tendency for national income to rise or fall. The equilibrium level is where the production decisions of firms align with the spending decisions of households, firms, and the economy as a whole.

2. Assumption of two sectors (household and firm):

   Keynes simplified his model by assuming that there are only two sectors in the economy: households and firms. Households provide labor to firms in exchange for wages, and they use their income to consume goods and services. Firms produce goods and services and sell them to households. By limiting the model to these two sectors, Keynes focused on the core interactions between consumption and production, without complicating factors like government or foreign trade.

3. Constant prices of products:

   In Keynes's model, he assumes that the prices of goods and services are constant in the short run. This means that the economy is not experiencing inflation or deflation, and businesses do not change prices in response to changes in demand or supply. This assumption simplifies the analysis by focusing on the volume of production and income rather than price fluctuations, which can complicate the equilibrium determination.

4. No government expenditure:

   Another assumption made by Keynes is that there is no government expenditure in his basic model of national income determination. This means that the government does not engage in any fiscal policy actions like spending on infrastructure, education, or welfare programs. In the absence of government involvement, the model focuses solely on the interaction between households and firms, simplifying the determination of national income equilibrium.

5. Constant supply of labor:

   Keynes assumed that the supply of labor is constant, meaning that the total number of workers available in the economy does not change in the short run. This assumption implies that there is no significant change in the size of the labor force due to migration, population growth, or other factors. By holding the labor supply constant, Keynes could focus on how changes in aggregate demand and supply affect national income without the complication of shifting labor market conditions.

Demand: according to Keynes is the total expenditure by the society, it is obtained from consumption and investment i.e. total demand is equal to total expenditure = $C + I$

Hence $Y = C + I$

Supply: is the total goods and services produced in a country within a year. According to Keynes supply = consumption + saving because when goods and services are sold the income received is spent on consumption and saving.

Hence total supply = $C + S$

$DD = SS$ $Y = C + I \quad Y = C + S$ $C + I = C + S$ $I = S$

Hence; according to Keynes equilibrium in the national income is obtain when investment (I) is equal to saving (S).

Consumption: is the total expenditure by household which gives a satisfaction.

Consumption function: is a mathematical relationship between consumption and the level of disposable income. It is denoted by

$C = a + bY$

Where; $C$ is consumption $a$ is autonomous consumption. This is consumption that does not depend on income. It comes from past saving and borrowing. $b$ is induced consumption i.e. consumption that depends on income i.e. changes with change in income. This is the proportional of the income spent on consumption, it is also called marginal propensity to consume (MPC). It is a slope of consumption function.

The consumption function can be illustrated graphically as follows.

Average propensity to consume (APC)

This is consumption per unit of income i.e. it is total consumption divide by total income.

Marginal propensity to consume (MPC)

Is the additional consumption resulting from additional income.

1. Level of income (disposable income):

   Disposable income refers to the amount of income available to households after taxes and other necessary deductions. The higher the disposable income, the more people can afford to consume goods and services. When individuals have more disposable income, they are able to spend more, increasing overall consumption levels in the economy.

2. Government expenditure:

   Government spending plays a significant role in determining consumption levels. When the government increases its expenditure on infrastructure, welfare programs, education, and other public services, it can boost income levels and purchasing power for individuals. As a result, higher government expenditure generally leads to an increase in consumption, as people have more resources to spend.

3. Taxes:

   Taxes directly influence the amount of income available for consumption. The higher the taxes imposed on individuals and businesses, the less disposable income people have to spend on goods and services. Higher taxes reduce consumption because they lower the effective income of households, while lower taxes typically increase the available income, promoting higher consumption.

4. Prices of goods and services:

   The price level of goods and services plays a crucial role in consumption decisions. When the prices of goods and services increase (inflation), consumers may find it harder to afford the same quantity of goods, leading to a reduction in consumption. Conversely, when prices fall, consumers may increase their spending, as they can afford more with the same amount of income. Thus, inflationary pressures tend to decrease consumption, while deflation can encourage it.

5. Amount of undistributed profits:

   Undistributed profits are the portion of a company's earnings that are not paid out as dividends but are retained within the business for reinvestment or future growth. The higher the amount of undistributed profits, the lower the income available to shareholders or employees. As a result, less disposable income is available for consumption, and consumption levels may decrease. On the other hand, if companies distribute more profits as dividends, individuals may have more income to spend.

6. Changes in interest rates:

   Interest rates influence consumption through their impact on borrowing and saving behavior. When interest rates are low, borrowing is cheaper, making it easier for households to take out loans for large purchases (e.g., homes, cars, etc.). Additionally, low interest rates can reduce the incentive to save, encouraging people to spend more. Conversely, high interest rates make borrowing more expensive and saving more attractive, which generally reduces consumption as people tend to save more and borrow less.

7. Population size:

   The size of the population directly affects the overall level of consumption. As the population grows, the total demand for goods and services increases, leading to higher consumption. Larger populations lead to greater consumption levels due to the higher number of people who need goods and services. Conversely, in smaller populations, consumption tends to be lower. Therefore, changes in population size can have a significant impact on the consumption pattern within an economy.

Saving: refers to that part of income which is not spent in the current period.

Saving function: is a mathematical relationship between saving and income.

$\text{Given: } Y = C + S \quad \text{(i)}$

$C = a + bY \quad \text{(ii)}$

Substitute equation (ii) into (i):

$Y = a + bY + S$

Make $S$ the subject:

$S = Y - a - bY$ $S = -a - bY + Y$ $S = a + Y - bY$ $S = a + Y(1 - b)$

The saving function can be illustrated as follows:

Average Propensity to Save (APS)

This refers to saving per unit income

$APS = S/Y$

Marginal propensity to save (MPS)

Is additional saving resulting from additional income

$MPS = \Delta S / \Delta Y$

QN: show that MPS + MPC = 1 where MPS is marginal propensity to save and MPC is marginal propensity to consume.

Soln:

$Y = C + S$

Assume there is a change in income bringing a change in consumption and savings.

$\text{MPC} = \frac{\Delta C}{\Delta Y} \quad \text{and} \quad \text{MPS} = \frac{\Delta S}{\Delta Y}$

Divide throughout by change in income:

$\frac{\Delta Y}{\Delta Y} = \frac{\Delta C}{\Delta Y} + \frac{\Delta S}{\Delta Y}$

$1 = \text{MPC} + \text{MPS}$

Why is MPS + MPC = 1

1. Level of income:

   The level of income is a primary determinant of savings. As income increases, individuals have more disposable income available, which can be saved. Higher-income earners generally have more capacity to save a portion of their income compared to lower-income individuals. However, individuals with lower incomes may struggle to save due to their limited resources. Thus, the higher the income, the greater the potential for savings.

2. Amount spent on consumption:

   The amount spent on consumption directly impacts the level of savings. If individuals or households allocate a significant portion of their income to consumption (purchasing goods and services), they will have less available to save. Conversely, the less people spend on consumption, the more they can save. A higher consumption-to-income ratio reduces savings, while a lower ratio increases savings potential.

3. Rate of interest on savings:

   The rate of interest offered on savings accounts or other savings instruments can influence the level of savings. A higher interest rate makes saving more attractive, as individuals can earn more from the money they save. On the other hand, if interest rates are low, individuals may not find saving appealing, as the returns on savings will be minimal. Therefore, higher interest rates generally encourage people to save more, while lower rates may reduce the incentive to save.

4. Price of commodities:

   The prices of goods and services can affect savings behavior. When prices of commodities rise (inflation), people may find it more difficult to save, as they need to spend more on essentials. In times of inflation, the real value of savings can erode, discouraging individuals from saving. Conversely, when prices are stable or decreasing, people may have more disposable income and be more inclined to save, as they are not spending as much on rising costs.

5. Government expenditure:

   Government expenditure can influence savings indirectly. If the government increases spending on public services, welfare programs, or infrastructure, it may increase the overall income levels of households, which could lead to higher savings. However, if the government borrows heavily to fund its spending, it might lead to higher taxes or inflation, which could reduce disposable income and discourage savings. In a stable economy with productive government spending, savings levels may rise as income increases.

6. Level of taxes:

   Taxes play a crucial role in determining the level of savings. High taxes reduce the disposable income available to individuals, leaving them with less money to save. On the other hand, lower taxes increase the amount of income that individuals can allocate towards savings. Tax incentives, such as tax-free savings accounts or deductions for retirement savings, can encourage individuals to save more by reducing the tax burden on savings.

7. Government policy in establishing financial institutions and educating people on savings:

   Government policies that promote savings include the establishment of financial institutions, tax incentives, and public education campaigns. When governments create accessible and trustworthy financial institutions (e.g., banks, credit unions), individuals are more likely to save. Additionally, educating the public about the importance of savings, providing information about financial planning, and offering tools like pension schemes or savings bonds can encourage more people to save. Financial literacy and awareness programs are crucial for boosting savings behavior in the economy.

1. Is a change in equilibrium of net national products resulting from a change in investment.
2. Multiplier is the rate of change of national income resulting from changes in the determinant of the national income. It shows the number of times the investment has change to reach to a particular amount of national income.
3. It is denoted by letter $k$. $k$ multiplier is equal to change in income over change in investment.

Derivation of the multiplier

Suppose the equilibrium income is given by: $Y = C + I$

$Y_0 = C_0 + I_0 \quad \text{(i)}$

Assuming there is a change in investment leading to a new level of equilibrium:

$Y_1 = C_1 + I_1$

To obtain a change in income, subtract equation (i) from (ii):

$\Delta Y = \Delta C + \Delta I \quad \text{(iii)}$

The change in $I$ also leads to a change in $C$.

The change in consumption depends on the MPC, where:

$\text{MPC} = \frac{\Delta C}{\Delta Y}$

$\Delta C = \text{MPC} \times \Delta Y$

Substitute equation (IV) into (iii):

$\Delta Y = \Delta Y \cdot \text{MPC} + \Delta I$

Make the change in $I$ the subject:

$\Delta I = \Delta Y - \text{MPC} \times \Delta Y$ $\Delta I = \Delta Y (1 - \text{MPC})$

Divide throughout by $\Delta I$:

$\frac{\Delta I}{\Delta I} = \frac{\Delta Y}{\Delta I} (1 - \text{MPC})$

$1 = \frac{\Delta Y}{\Delta I} (1 - \text{MPC})$

Divide both sides by $(1 - \text{MPC})$:

$\frac{1}{(1 - \text{MPC})} = \frac{\Delta Y}{\Delta I}$

$K = \frac{\Delta Y}{\Delta I} = \frac{1}{(1 - \text{MPC})}$

$K = \frac{1}{(1 - \text{MPC})} \quad \text{or} \quad K = \frac{1}{\text{MPS}}$

QN1. Given that MPC = 0.2 find the multiplier.

Soln:

$K = \frac{1}{(1 - 0.2)} = \frac{1}{0.8} = 1.25$

Qn 2: Given that MPC = 0.8, find MPS.

Since: $\text{MPC} + \text{MPS} = 1$

$0.8 + \text{MPS} = 1$ $\text{MPS} = 1 - 0.8$ $\text{MPS} = 0.2$

Next, divide both sides by $(1 - \text{MPC})$:

$\frac{1}{(1 - \text{MPC})} = \frac{\Delta Y}{\Delta I}$

$K = \frac{\Delta Y}{\Delta I} = \frac{1}{(1 - \text{MPC})}$

$K = \frac{1}{(1 - \text{MPC})} \quad \text{or} \quad K = \frac{1}{\text{MPS}}$

Qn2. Given the MPC = 0.8 find MPS

$\text{MPC} + \text{MPS} = 1$ $0.8 + \text{MPS} = 1$ $\text{MPS} = 1 - 0.8$ $\text{MPS} = 0.2$

Qn3: Given $\Delta Y$ to be 100 which result from a $\Delta I$ of 20 find MPC.

$K = \frac{\Delta Y}{\Delta I} = \frac{100}{20} = 5$

$K = \frac{1}{1 - \text{MPC}} \Rightarrow 5 = \frac{1}{1 - \text{MPC}}$

$5(1 - \text{MPC}) = 1$ $5 - 5 \cdot \text{MPC} = 1$ $-5 \cdot \text{MPC} = 1 - 5 = -4$ $\text{MPC} = \frac{4}{5}$

Given: $Y = C + G + I + (X - M)$

$Y = 150 + 0.8Y + 50 + 30 + 0.05Y + (20 - 0.1Y)$ $Y = (150 + 50 + 30 + 20) + (0.8Y + 0.05Y - 0.1Y)$ $Y = 250 + 0.75Y$ $Y - 0.75Y = 250$ $0.25Y = 250$ $Y = \frac{250}{0.25} = 1000$