Defining the term Y t= N t and kt-1 in which plays the role of standing or rather representing the output in a given economy. The output is measured in terms of per capita; per capita income is the income per head of a given country A, The national income is divided by the total population in that particular country. The Per capital income= Income divided by the N t population.
Y=f (K, L)
Y=KaL1-a
Small a represents the returns to the overall factor input in the given economy, hence the function is k own as Douglas type of function this formula multiplies two together in order to obtain the best results in the sum. “(Samuel,2016) said that the exponents are added to give the maximum sum and obtainable results which is one and thus shows the constant returns to the scale of the given country’s production”.
If the sum of two inputs put together results two is greater than the value of one then the country is deemed to be experiencing the typical increase in the returns as compared the scale of production and scope of production. Therefore there is a decreasing return to the given scale of operation and production function thus this happens if and only the sum is less than one. Numbers have been incorporated instead of using variables in the following manner Y=K1/2L1/2
And
Y=K1/3L2/3
Y=KaL1-a
Use labor to divide both sides by the value of it r, or L:
Y/L= (KaL1-a)/L
y=ka
Assuming the law of motion for the stock of the given stock I am going to format the equation in consideration of the per capita capital stock. Stock= Kt- (1-d) Kt-1-It.
It represents the aggregate investment in a particular country at certain particular time t.
The term per capita in this equation represents the income per person from the investments hence the observances made in statistical approach are considered detrimental.
The economy of this country will be determined whether is strong or weak by calculating the per capita income as follow. The purchasing power is put into consideration using the GVI or rather the gross national investment y= Stock= (K t- (1-d) Kt-1-It.) divided by the population in this aspect of the perspective the population will be taken as the investment in time t. thus (K t- (1-d) Kt-1-It.) t.
Income of the country is denoted by y and N in many equations of economic nature and in this equation the t represents the time of the growth for h t per capita of the citizens per head. I have used the indicators that portray economic perspective and they include the gross domestic product known as the GDP and the gross national product known as the GNP. Per capita basis of these numbers s formulate d in y popular economists who undertake the initiative of the entire computation pertaining to the income per head.
This is a determinant of the steady state value of the given per capital, K and it is going to be represented as the function of a, d, n and s.
Let’s take the value of K to represent the income per head thus K = per capita
Therefore it is correct to generalize and say K= (a +d+ n +s)
I am the evaluator of investment in this country at time t which is the period of growth and development.
Value of K is used as a measurement of per capita in the population P. hence the equation can also be converted to represent eh number of citizens who receive the income from the operation sand undertakings in the economy. (a +d+ n +s)
Where P represents the total number of individuals who are residing in a particular country and are earning a living from their hard work and the contribution g to the gross national product GNP and thus it is through the consumption of the local commodities that the variables a, d, n and s are deemed to be increasing in the returns production. K is constant as long as there are no fluctuations in the variables hence it is inversely proportional to the value of d, n, s, a. The suitable equation which shows dependence nature of income per head of individuals on the factors such as the economy and national product as well as the investment levels is as shown: Kα A, D, N,S K is inversely proportional to the factors such as the level of technology in the country, trade activities d n foreign income that contributes to increase in the overall capital structure of the country.
Determination of the golden rule of the capital and the per capita in a country considering the aspect of the A, kgr as the given function of these a, d, n and s.
Y t=F(K t; Lt; At)
The above is production function under consideration wills results to the capital return in terms of scale that is measurable in this context.
The golden rule prevails where the society accumulates the savings rate and thus the s is the value or rather the amount of savings that a country accumulates as a result of depreciating the consumption of C. Therefore the Y t iα S
Where Y t is income and product in the perspective of economic generation or rather the Consumption function which is as follows, the consumption levels depend on the amount of income that the person has or individuals, OIN the entire country it will be regarded as the income per head.
It α C
Where C is consumption
In this case I am going to assume the country is known as A has growth of population that adds up to null or zero, 0 Therefore there is no population growth in this country A. the depreciation of capital takes place each and every year to the levels of 5% . Savings function is represented by denoting savings as S and then proceeding with r=the computations as follows S of Output = Y t
Y t is the amount of product that is produced in particular period taking time into consideration and thus there is determination of the steady state level of the given per capita k and y as follows
K= Yt – S(savings)o.5%?( d)
( Kgr + Cgr +Ygr) 0.5
The depreciation is charged on the product Y t which is the overall investments plus all the other savings S less consumption
The country has experienced war in the recent times because of the political upheavals, There is detrimental destruction in the composition of the capital including the oil extracting, equipment, structures and the vehicles depreciation as well.
The income per head will decline due to the reduction of the economic performance and the national product Y t at the time t is also very poor. The aggregate income available is not sufficient enough to meet the expenditure as the country is war torn. The capital available is depleted in buying ammunitions and repairing the destroyed parts of the country in the restoration of peace. The next five years will be tough time for country A because of the diminishing returns to scale. The declining output is the result of low income per individual per citizen thus the citizens will compete for the few opportunities that are scarce and thus increasing the consumption function as deducing the savings s. The capital per capita will be affected in the manner that will affect the investment s that has been erected in the nation that gains revenue and income. “(Harrison, 2016) said the operations are haltered and thus the population that has a dire need for the resources s such as oil is depleted and explored without any funds”. There is increasing inflation which are prices of commodities will increase and this creates an inflationary gap because of the recession. The recession period is associated with the difficulty to raise capital per capita
The effect is the destruction of oil wells and vehicles will reduce the gross national product and lower the national output to insignificant levels and thus creating unemployment. The individuals who depend on the income from the sources and resources that a=have been destroyed will suffer from the declining returns to scale of the economic growth , The business undertaking s or rather the commerce of the country is haltered and currency losses value as result of the wrangles. There is increase in expenditure in the budget thus s the consumption function will tend to increase at an increasing return with declining output or the product y.
There is less economies to scale and divesture in to the companies and industries that are in operation in country A due to the fear of losses, in the next five years the revenue authority will record low income form the revenue collections and this will be transferred the effect on to the burden of the citizens individually who will be charged a higher tax to compensate. There is compensation strategy in place for the existing people in country A in order to counter the raising inflation and the weakening of the economy as well as the devaluation that is taking =g place due to the destruction of investments and property. The capital is set aside is spread over the period of 5 years to amend the bills and the complications into eh development of projects which had already commenced and failed to attain completion because of the war and political upheavals.
The growth rate will be affected in wide perspective in that the perceptual income is dependent on the national income NI. Ni denotes the national income or rather the national product can be used in place of the national income in order to facilitate computation according to the keys theory of speculator motive where they are speculation some I regards to the current situation of the economy. The diminishing returns will slower the rate of economic growth and thus under performance of the capital that has been injected. The flow of investment funds is directed to consumption function in the long run to ascertain the future of entities to ensure that will be promising into the times to come. The Rate of per capita growth will be declining at an increasing rate due to the depletion of the returns to scale of the production and at the end the individuals residing in this country will be competing for the few goods with few money in circulation in the economy and poor economic performance due to the failure to manage the balance of trade. “(Barnet, 2014) said the trade is balanced when the exports equal the imports or rather the imports are eliminated”. In order to give way for the gross domestic product sources such as ell =s for oil which are initially destroyed. The government will borrow abroad the injections in the economy in order to boost current economy of the country A which is underperforming. The increasing returns will be experienced after the 5 YEAR period due to the maintenance of the capital per head of each and every citizen.
Supposed the investment form investors are permitted or rather allowed in the country, the recovery will shut up and the country will stabilize. The investment from these investors acts as injections which assists the expenditure to the country best settled without complications. The budgetary controls will be initiated in order to deal with the rising external sources of funds such as the investment from the foreigners. The recovery will also be strong and occur faster than expected due to the increase in national output of the country by utilizing the capital injected in terms of the investment from eh investors who are operating the business into the country of residence A which was previously war torn. In the lingerie of the investors will be of great benefit to the country thus enable to incur and settle all in the debts and faults that had preceded the economic times and lowering the economic growth rate. “(George, 2013) said the permission will be allowed and thus the recovery boosted to higher levels” The strengthening of the currency will be witnessed from the exports and increasing returns to scale of production.
References
George, P. (2015). The permission will be allowed and thus the recovery boosted to higher levels. Harvey press, Britain.
Barnet, G. (2014). The trade is balanced when the exports equal the imports or rather the imports are eliminated. Marconi press. Australia.
Harrison, N. (2012). The operations are haltered and thus the population that has a dire need for the resources s such as oil is depleted and explored without any funds”. Napes press, Berlin.
Samuel, C. (2016). The exponents are added to give the maximum sum and obtainable results which is one and thus shows the constant returns to the scale of the given country’s production. Herman press, Hungary.
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