Accumulation of capital The change in the capital stock per worker (known as capital deepening) is equal to per worker gross investment minus depreciation: Dk = i - dk. Ignore government for present purposes, so that investment is equal to private sector saving: i = S/L = s Y/L = sy.
What is the formula to calculate capital stock per worker?
Δk = i – (δ + n)k … (20) Equation (20) shows that new investment (i) increases k, while depreciation (δ k) and population growth (n) decrease k. These factors thus, together, determine capital stock per worker. The term (δ + n)k may be treated as the break-even level of investment Which is necessary to keep per capita capital stock constant.
What are the factors that affect capital stock per worker?
Equation (20) shows that new investment (i) increases k, while depreciation (δ k) and population growth (n) decrease k. These factors thus, together, determine capital stock per worker. The term (δ + n)k may be treated as the break-even level of investment Which is necessary to keep per capita capital stock constant.
What is the amount of capital stock?
The amount of capital stock is the maximum amount of shares that a company can ever have outstanding. Issuing capital stock allows a company to raise money without incurring debt. The drawbacks of issuing capital stock are that the company relinquishes more control and dilutes the value of outstanding shares.
How does technology affect the stock of capital per worker?
If two countries share the same technology (A) and the same production function, then over time these two countries will eventually have the same stock of capital per worker.
How do you calculate capital stock per worker?
The change in the capital stock per worker (known as capital deepening) is equal to per worker gross investment minus depreciation: ∆k = i - δk. Ignore government for present purposes, so that investment is equal to private sector saving: i = S/L = s Y/L = sy.
What is capital per effective worker?
Capital per effective worker is how much capital is there for a worker who can use technology. With more technology, every worker can produce more.
What is the difference between capital per worker and output per worker?
The economy accumulates capital through saving, but the amount of capital per worker falls when capital depreciates physically or when the number of workers rises. Output per worker increases with the level of technology and the saving rate and decreases with population growth and physical depreciation.
How do you calculate capital per worker Solow model?
Solving the Solow Growth ModelIn our analysis, we assume that the production function takes the following form: Y = aKbL1-b where 0 < b < 1. ... Therefore, output per worker is given through the following equation: y = akb where y = Y/L (output per worker and k = K/L (capital stock per worker)More items...
What is the golden rule level of capital per worker?
The Golden Rule capital stock is the level at which MPK = δ, so that the marginal product of capital equals the depreciation rate.
Why does capital per effective worker increase?
Increasing the rate of saving increases the level of investment, and as the capital stock grows, so too does the amount of capital per effective worker.
What is the meaning of capital stock?
Capital stock is the amount of common and preferred shares that a company is authorized to issue—recorded on the balance sheet under shareholders' equity. The amount of capital stock is the maximum amount of shares that a company can ever have outstanding.
Which country has the highest TFP?
A comparison of average productivities in each region shows that Moldova, Nicaragua, Ethiopia and Indonesia have the highest values among the countries surveyed. This note also discusses separate estimates of TFP values obtained at the industry level.
How do you find NX in economics?
The net exports formula subtracts total exports from total imports (NX = Exports − Imports). The goods and services that an economy makes that are exported to other countries, less the imports that are purchased by domestic consumers, represent a country's net exports.
Why is it important to sell capital stock?
The biggest advantage to selling capital stock is that a company does not need to take out debt in order to finance new projects. If a company needs more money to grow, instead of taking out a loan that they will have to pay back with interest, they can sell capital stock.
What is share trading?
Share trading is the process of buying and selling shares within a company. It is a process that only goes on between shareholders and has no impact on accounting or bookkeeping unless the company actually buys them back (then they become treasury stock).
What is outstanding stock?
Outstanding shares are shares that have been issued to investors and are not owned by the company. To figure out your company's outstanding shares, simply subtract the number of treasury shares from the total number of issued shares.
What happens to preferred stockholders when a company goes bankrupt?
If a company liquidates (whether it is bought or goes bankrupt), the preferred stockholders will receive a payout before the common stockholders. They also receive different dividends than common stockholders, usually more.
What is par value in stock?
It is important to note that par value is a set dollar amount assigned to each common share. Any amount paid by investors above the par value is noted in the accounting books under additional paid in capital. The amount of capital stock can never be more than the amount of' authorized stock.
What happens when a company repurchases stock?
Once a stock is repurchased the company can either cancel it, reissue it, or hold onto it. What is a share? A share is a word used to describe a single capital stock. When a share is issued, it is identified by a share certificate or stock certificate that can be traded by the shareholder.
What is corporate charter?
A corporate charter, also known as a "charter" or as "articles of incorporation ," is a legal document that is used to start a corporation. It is filed with the state government of whatever state the company incorporates in.
Solving the Solow Growth Model
1. In our analysis, we assume that the production function takes the following form: Y = aK b L 1-b where 0 < b < 1. The production function is known as the Cobb-Douglas Production function, which is the most widely used neoclassical production function.
Implications of the Solow Growth Model
There is no growth in the long term. If countries have the same g (population growth rate), s (savings rate), and d (capital depreciation rate), then they have the same steady state, so they will converge, i.e., the Solow Growth Model predicts conditional convergence. Along this convergence path, a poorer country grows faster.
Additional Resources
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16.18 The Solow Growth Model
The analysis in Chapter 6 "Global Prosperity and Global Poverty" is (implicitly) based on a theory of economic growth known as the Solow growth model. Here we present two formal versions of the mathematics of the model. The first takes as its focus the capital accumulation equation and explains how the capital stock evolves in the economy.
Presentation 1
There are three components of this presentation of the model: technology, capital accumulation, and saving. The first component of the Solow growth model is the specification of technology and comes from the aggregate production function. We express output per worker ( y) as a function of capital per worker ( k) and technology ( A ).
Presentation 2
In this presentation, we explain the balanced-growth path of the economy and prove some of the claims made in the text. The model takes as given (exogenous) the investment rate; the depreciation rate; and the growth rates of the workforce, human capital, and technology. The endogenous variables are output and physical capital stock.
The Production Function
The production function we use is the Cobb-Douglas production function:
Growth Accounting
If we apply the rules of growth rates to Equation 16.1, we get the following expression:
Balanced Growth
The condition for balanced growth is that gY = gK. When we impose this condition on our equation for the growth rate of output ( Equation 16.2 ), we get
Capital Accumulation
The second piece of our model is the capital accumulation equation. The growth rate of the capital stock is given by
C.1 The Solow Growth Model with Exogenous Growth
Consider the Solow growth model we saw in class, with however two small changes. Assume that the production function is given by: F (Kt,Lt) = AtKα t L1−α t, F ( K t, L t) = A t K t α L t 1 − α, where productivity At A t grows exogenously at rate g g and A0 = 1 A 0 = 1 : At = (1 +g)t. A t = ( 1 + g) t.
C.3 An increase in the depreciation rate (Homework material)
Continuing with the logic from the previous problem, suppose that the economy’s production function is given by Y = KαL1−α Y = K α L 1 − α with α = 1/3 α = 1 / 3 and that both the saving rate, s s, and the depreciation rate, δ δ are equal to 0.10 0.10.
C.4 Deficits and the capital stock
Suppose that the production function is given by: Y = KαL1−α Y = K α L 1 − α with α = 1/3 α = 1 / 3.
C.5 U.S. saving and government deficits
This question continues the logic of the previous question, to explore the implications of the U.S. government budget deficit for the long-run capital stock.
Solving The Solow Growth Model
Implications of The Solow Growth Model
- There is no growth in the long term. If countries have the same g (population growth rate), s (savings rate), and d (capital depreciation rate), then they have the same steady state, so they will converge, i.e., the Solow Growth Model predicts conditional convergence. Along this convergence path, a poorer country grows faster. Countries with different saving rates have different steady s…
Additional Resources
- Thank you for reading CFI’s guide on Solow Growth Model. To keep learning and advancing your career, the following resources will be helpful: 1. Economic Indicators 2. Gini Coefficient 3. Human Development Index 4. Marginal Propensity to Consume