Saving, investment and
Saving, capital formation and comparative economic growth - Saving, investment and economic growth o Saving, investment and the income account identity § Both saving and investment represent resources that are withheld from current consumption • Used to generate future benefits § National income accounting identity • 𝑦 = 𝑐 + 𝑖 + 𝑔 • 𝑦 = 𝑐 + 𝑠 + 𝑡 • 𝑠 + 𝑡 − 𝑔 = 𝑖 o Left hand side is national saving § In a closed economy national saving is equivalently the same as investment - The Solow-‐Swan model of economic growth o Also called the neo-‐classical growth model § Predicts the existence of a positive relation between a country’s preparedness to put aside current resources for the purposes of saving and investment and its long-‐run level of per capital GDP o Interpreting the production function in per capita income § If the production function is 𝑦 = 𝐴𝑓(𝑘, 𝑙) § Divide the primary factors of production and output by the size of the labour force gives • •
o o
o
! ! !
! !
,
= 𝐴𝑓
! ! !
= 𝐴𝑓
!
Level of per capital GDP will depend on • Total factor productivity • The amount of capital relative to the size of the labour force Capital labour ratio § Diminishing marginal productivity • Increases in the capital-‐labour ratio increase per capital GDP at a decreasing rate Left hand side can also be interpreted as the level of per capita income that will be earned in the economy at each level of the capital-‐labour ratio The steady state § A situation in which the per capita capital stock is neither growing nor shrinking and per capital income is unchanging Investment § Two types of investment • Replacement investment o Involves purchases of new plant and equipment that is either to replace worn-‐out depreciated capital or to provide new capital for a growing population o Keeps the capital-‐labour ratio constant • Net investment o Investment that adds to the size of the per capita capital stock • Investment per capita can be written as §
o
!
o
!
!
=
!" !
+
!" !
§
Because net investment only changes the capital-‐labour ratio, !
!"
!
!
𝛥 = • §
! !
=
!" !
! !
Replacement investment • Assumptions o Capital stock depreciates at a constant rate over time, 𝑑 o Population grows at a constant rate of 𝑛 o Constant returns to scale • Therefore, in order to keep the capital-‐labour ratio constant, replacement investment must grow at the combined rate of depreciation and population growth o
§
+𝛥
!" ! !
= 𝑑+𝑛
!
!
!
!"
o = 𝑑 + 𝑛 + ! ! ! Investment per worker • Because 𝑠 + 𝑡 − 𝑔 = 𝑖, (savings equals investment) investment per worker can be understood as the proportion of total income devoted to saving o o
• •
𝜃
! !
!
!
= 𝜃 ! Where 𝜃 is the savings rate !
= 𝑑+𝑛
! !
+𝛥
Rearranging gives 𝛥
! !
! !
=𝜃
! !
− 𝑑+𝑛
! !
The capital-‐labour ratio will grow only if the total saving in the economy exceeds replacement investment Diagrammatic representation § See diagram § Economy has an automatic tendency to reach steady state o
o
•
!
If operating where = 500, then total saving equals $800 ! and replacement investment equals $600 o Total investment exceeds replacement investment by $200 !
§
§
o Per capita capital stock will increase until = 1000 ! Growth in per capita income occurs only when the economy has an existing capital-‐labour ratio that is below its steady state • As the capital-‐labour ratio increases, diminishing marginal returns set in o Means that subsequent increases in the capital-‐ labour ratio has less and less of an impact on per capita income Increase in population growth • If the level of investment required grows, then this will push the savings rate upwards o Capital is required to fund investment – increase in demand for capital will push up interest rates, encouraging people to save more (higher return on loans)
o
o
Implications § Ceteris paribus, the model predicts an end to growth in per capita income • Countries that are poor will grow at a relatively faster rate than those that are rich o Convergence hypothesis § Per capita income in poor countries will grow at a faster rate than in rich countries, as long as both groups of countries have the same long-‐run steady state Evidence § Comparative economic growth • The name given to the study of different cournties’ growth experiences § Negative regression line can be fitted to OECD economies when average annual growth rate since 1970 is regressed on per capita GDP in the base period in 1970 • Economies have the same characteristics and are likely to have the same steady state § On small subsets of economies with similar characteristics, the convergence hypothesis holds • Conditional convergence
o o
o
! ! !
! !
,
= 𝐴𝑓
! ! !
= 𝐴𝑓
!
Level of per capital GDP will depend on • Total factor productivity • The amount of capital relative to the size of the labour force Capital labour ratio § Diminishing marginal productivity • Increases in the capital-‐labour ratio increase per capital GDP at a decreasing rate Left hand side can also be interpreted as the level of per capita income that will be earned in the economy at each level of the capital-‐labour ratio The steady state § A situation in which the per capita capital stock is neither growing nor shrinking and per capital income is unchanging Investment § Two types of investment • Replacement investment o Involves purchases of new plant and equipment that is either to replace worn-‐out depreciated capital or to provide new capital for a growing population o Keeps the capital-‐labour ratio constant • Net investment o Investment that adds to the size of the per capita capital stock • Investment per capita can be written as §
o
!
o
!
!
=
!" !
+
!" !
§
Because net investment only changes the capital-‐labour ratio, !
!"
!
!
𝛥 = • §
! !
=
!" !
! !
Replacement investment • Assumptions o Capital stock depreciates at a constant rate over time, 𝑑 o Population grows at a constant rate of 𝑛 o Constant returns to scale • Therefore, in order to keep the capital-‐labour ratio constant, replacement investment must grow at the combined rate of depreciation and population growth o
§
+𝛥
!" ! !
= 𝑑+𝑛
!
!
!
!"
o = 𝑑 + 𝑛 + ! ! ! Investment per worker • Because 𝑠 + 𝑡 − 𝑔 = 𝑖, (savings equals investment) investment per worker can be understood as the proportion of total income devoted to saving o o
• •
𝜃
! !
!
!
= 𝜃 ! Where 𝜃 is the savings rate !
= 𝑑+𝑛
! !
+𝛥
Rearranging gives 𝛥
! !
! !
=𝜃
! !
− 𝑑+𝑛
! !
The capital-‐labour ratio will grow only if the total saving in the economy exceeds replacement investment Diagrammatic representation § See diagram § Economy has an automatic tendency to reach steady state o
o
•
!
If operating where = 500, then total saving equals $800 ! and replacement investment equals $600 o Total investment exceeds replacement investment by $200 !
§
§
o Per capita capital stock will increase until = 1000 ! Growth in per capita income occurs only when the economy has an existing capital-‐labour ratio that is below its steady state • As the capital-‐labour ratio increases, diminishing marginal returns set in o Means that subsequent increases in the capital-‐ labour ratio has less and less of an impact on per capita income Increase in population growth • If the level of investment required grows, then this will push the savings rate upwards o Capital is required to fund investment – increase in demand for capital will push up interest rates, encouraging people to save more (higher return on loans)
o
o
Implications § Ceteris paribus, the model predicts an end to growth in per capita income • Countries that are poor will grow at a relatively faster rate than those that are rich o Convergence hypothesis § Per capita income in poor countries will grow at a faster rate than in rich countries, as long as both groups of countries have the same long-‐run steady state Evidence § Comparative economic growth • The name given to the study of different cournties’ growth experiences § Negative regression line can be fitted to OECD economies when average annual growth rate since 1970 is regressed on per capita GDP in the base period in 1970 • Economies have the same characteristics and are likely to have the same steady state § On small subsets of economies with similar characteristics, the convergence hypothesis holds • Conditional convergence
