Sholow Graph

macro

marginal product of capital

is the additional output generated by using one more unit of capital while keeping the amount of other inputs constant. It reflects the contribution of capital to the production process.

diminishing marginal product of capital

describes the phenomenon where the addition of capital results in progressively smaller increases in output. This occurs as more units of capital are employed, while other inputs remain fixed.

production function

is a mathematical relationship that describes how the quantity of inputs used in production corresponds to the quantity of output produced. It illustrates the efficiency and technology of production.

Yt=AtR(kt,Ht)

Solow growth model

mroe capital means more output, despite at a diminishing rate

where does capital come from? where

Relate Savings, Investement and output to the aggregate production function 

savings get channeled into investment

investment adds to the capital stock 

each period some capital wears out with use

the net increase in the capital stock ( a factor of production ) leads to increased output (GDP per capital)

solow model- main idea

if investment (saving) exceeds the amount of total depreciation, the capital stock will grow

since capital (a factor of production) is growing, this leads to an increase in output (real GDP per capital) 

eventually investment will equal total depreciation and the capital stock (and hence output ) will constant (steady state) 

steady state = ….

depreciation

solow model- savings

it is unrealisitc to assume that savings will always be channeled into productive investment without considering factors such as diminishing returns to capital and changes in technology.

production function

relationship between inputs and outputs in producing goods and services, typically representing how varying the quantity of inputs affects the level of output.

output (GDP) at time t depends on

the amount of physical capital at time t (Kt)

the amount of human capital t(Ht)

ideas- how efficiently the physical and human capital is used (At)

aspects of the solow model per capita

for capital stock to grow, investment must not only keep up with depreciation, but with population growth 

assume peopel save at a constant fraction of income

savings get channeled into investment

investment adds to the capital stock (it=syt=sf(kt))

resource constrain

assume that all income is spent either on consumption or investment

yt=ct+it

if your intial level of capital (Ko) is below the steady state, capital …. will …..

accumulate over time until it reaches the steady state.

if your intial level of capital is aboive the steady state, capital

will decrease until it aligns with the steady state.

capital growth=

investment- depreciation and pop growth

investment > depreciation and pop growth- the capital stock growth and output next period is bigger 

investment= depreciation and pop growth - the capital stock and output are constant ( the steady state)

investment < depreciation and pop growth- the capital stock shrinks and outout next period is smaller 

steady state 

is the point where capital per worker remains constant as investment equals depreciation and population growth, leading to stable output.

solow model predictons1

countries that have higher savings (investment ) rates over long periods fo time will tend to have higher levels of per capital GDP 

solow model predictions

countries that have higher population growth ratewill experience slower per capita income growth compared to those with lower population growth.