EC210 LT Flashcards
GDP Definitions
Gross domestic product (GDP) is the most common measure of the ‘size’ of an economy
Definition: Value of all goods and services produced in a country in a period of time
Gross = opposite of net, not accounting for depreciation
Domestic = covers the geographical area of a country (irrespective of ownership or nationality)
Product = based on the amount of goods newly produced (irrespective of what is being sold)
Only final goos counted: excludes intermediate goods - those entirely used up producing other goods in the same time period
GDP is a flow, measured in a time period
Three Approaches
1) Production approach: sum of value added over all industries producing goods and services -> Value added: Value of output produced minus value of intermediate goods used in production (avoids double counting), not possible for many services provided by gov: use cost of production instead
2) Expenditure approach: sum of all expenditure on final goods and services -> C+I+G+(N-X), capital goods included but intermediated goods excluded
3) Income approach: sum of all incomes derived from producing goods and services (wages, rents, net interest paid by firms, profits, plus indirect taxes)
Other Measures in National Income
Gross national product (GNP) = GDP + Net international income (Foreign income received by domestic residents - domestic income received by foreigners)
Net national product (NNP) = GNP - Depreciation
NNP at basic prices = NNP - Indirect taxes
Problems in Measuring GDP
Difficult to obtain timely GDP data: Initial estimates of GDP based on very limited data, often large revisions made to GDP
Difficult to obtain comprehensive data on all economic activity: Informal/underground economy, tax evasion, criminal activity
Difficulties in measuring the output of particular sectors of the economy: owner occupied housing, financial services
Issues of Interpretation of GDP
Often used as measure of success buts it really a good measure of welfare/living standards
If market prices reflect the value of different foods and services, adding up value of all output should give a fair representation of benefit to consumers
Adjustments need to be made to measure welfare -> Adjust for prices differences (real, not nominal), divide by population (per capita)
This does not represent inequalities/distribution
GDP as a Measure of Welfare
Provision of public services valued at a cost??
Exclusion of non-market activities (home production)
Total benefit derived from goods greater than price (e.g. google search)
Costs of production not reflected in price (e.g. pollution)
Value of leisure (labour require effort)
Increase in GDP might be due to more spending to deal with ‘bads’ (crime, policing)
Depreciation of capital (should be treated like intermediate goods if capital used up in future)
More to happiness than economic success
Extra GDP Context Definitions
Value added is computed by deducting the value of intermediate inputs consumed in production from the value of output
Inventories are unsold in production so treated as if bought by firm themselves, retained for the future as a for, of investment
Profit is defined as sum of revenues minus cost. Retained earnings count towards profits. Anything not used up in production is included as profit
Profits equal output minus intermediate consumption minus wages
Real v Nominal
Nominal: variables expressed in units of money
Real: variable adjusted for changes in the value of money (aim to capture quantities only, remove effects of inflation)
Real GDP at Constant Prices
In the past, the most common approach to calculating real GDP used the year-1 constant prices approach
Concern this was leading to overestimates of real growth (e.g. large output of computers combined with large falls of relative prices)??
Solution: frequent rebasing of the real GDP measure i.e. every five years, recalculate the real GDP series with an updated set of fixed prices
But: Year-1 fixed prices overstate real growth, year-2 prices understate real growth
Rebasing also leads to continual revisions of the historical real GDP time series
Choice of Base Year
It is possible that the increase in the relative price of good x1 led consumers to substitute towards good x2 and this is why consumption of good x1 fell
In general, substitution effects in demand mean that goods whose relative price increases tend to have low production growth
When taking year 1 prices as our base these goods are multiplied with their initial low price and their low growth receives little weight (calculated real GDP growth is high)
When taking year 2 prices as our base, they are multiplied with a high price, their low growth receives a substantial weight and calculated real GDP growth is low
Different between the two growth rebates can lead to very different policy decisions (could be either growing or contracting depending on which measure is chosen)
Chain-weighted Real GDP
Take average over-estimate and under-estimate of real growth: this should be more reliable, no need for rebasing
Measurement of Inflation
CPI: price index based on computing cost of buying a basket of goods based on past consumption patterns
GDP deflator: price index based on difference between nominal and real GDP
CPI is cost of purchasing the basket of goods that was consumed in year 1
Use of the consumption basket from year 1 is arbitrary, could use year 2
Substitution Bias
The CPI is calculated using a past basket of goods
CPI ignores the tendency of consumers to substitute away from goods that become relatively expensive towards food that become relatively cheaper, therefore overstates inflation
But using the year-2 basket of goods would probably understate inflation
There we use fisher’s ideal index to average between the two years
GDP Deflator
Ratio between normal and real gdp -> GDPDEF = NGDP/RGDP
GDP Deflator vs CPI
There are other differences between the CPI measure of inflation and the GDP deflator in addition to the issue of the substitution bias
Substitution bias -> substitution away from goods that have become relatively more expensive
GDP deflator includes all components of GDP, CPI only a hypothetical basket of consumer goods
GDPDEF covers all domestically produced goods and services
CPI covers goods and services consumed by domestic households, even if not imported
Our simple example economy includes only domestically produced consumption goods. More generally:
CPI is based only off the prices of consumer goods; the GDP deflator is based on the prices of all final goods
CPI includes prices of imported goods; the GDP deflator uses prices of domestically produced goods
Challenges in Measuring Inflation and Real GDP Correctly
Changes in quality of goods: if quality improves we do not account for it, we will overstate inflation and understate real growth
New products: if computers were a new product in year 2 then there would be no year 1 price available to use in the calculations, availability of new products leads to overstating inflation
Comparing GDP Across Countries
Need to use market exchange rates to convert values in different currency to those of a common currency
Law of one price (e.g. computers): traded good therefore the price is the same everywhere once expressed in therms of a common currency
Balassa-Samuelson effect
Purchasing power parity: compare the cost of the same basket of goods across two countries
Can use basket of goods for either country, therefore use a fisher ideal index
Why are Market Exchange Rates Misleading for International Comparison
Market exchange rates tend to equate prices of tradable across countries
Prices of non-tradables are usually cheaper in poorer countries, conversion of income by the market exchange rate undervalues the domestic purchasing power of poor countries’ currencies and overstates the relative income differences of poor and rich countries
GDP calculated by the PPP method relies on average international prices which are then used for evaluation of demotic goods
This method aims to remove the traded-sector bias in exchange rate valuations, yielding real income differentials which are substantially smaller than the income differentials of exchange rate comparisons
International Dollar
Carried out by means of PPP and not market exchange rates
Country’s nominal GDP multiplies by the PPP conversion rate relative to the US
By definition, GDP of the US in international dollars coincides with GDP in US dollars
One-Period Macroeconomic Model
A model takes exogenous variables and determines endogenous variables
Basic structure: decision makers (consumers and firms), objectives (consumers’ utility, firms’ profits), constraints (consumers’ budget constraints, firms’ production technologies)
Macro models emphasise “micro-foundations”: first derive optimal choices of firms and consumers given market prices and then derive the market prices using the market clearing conditions
Representative Consumer
Indifference curves represent the consumer’s preferences over consumption goods and leisure, its slope is the MRS between consumption and leisure
The representative consumer owns equal shares of firms in the economy
Pi-T is the after-tax non-wage income
In equilibrium pi = 0?
Any profits earned by firms, therefore, must be distributed to the representative consumer as income which we think of as dividend income (pi)
T is a lump-sum tax and it is independent of the consumer’s decisions
Consumer optimisation: increase in real wage
Substitution effect: the price of leisure rises, so the consumer substitutes from leisure to consumption
Income effect: since both consumption and leisure are normal goods, higher income implies both consumption and leisure increase
Conclusion: Consumption must rise, but leisure may rise or fall
If the substitution effect is larger than the income effect, then the labour supply curve is upward sloping
An increase in (Pi-T) induces a shift in the labour supply curve
Representative Firm
z is total factor productivity (TFP)
K is the quantity of capital input
Nd is quantity of labour input
A neoclassical production function satisfies: constant returns to scale, positive but diminishing marginal product of capital and labour and inada conditions
Inada conditions: MPK goes to infinity when K goes to zero, MPK goes to zero when K goes to infinity (similar for MPN)
When firm maximises profits (Pi), the marginal product of labour equals the real wage: MPN = w
Due to finishing marginal of labour, the labour demand curve is downward sloping
Competitive Equilibrium
Representative consumer optimises given market prices
Representative firm optimises given market prices
The labour market clears
The government budget constraint is satisfied or G = T
In equilibrium, the consumer and the firm face the same market real wage, and the marginal react of substitutions (from consumer’s preferences) is equal to the marginal rate of transformation (from production possibilities)
MRS = MRT = MPN -> competitive equilibrium and pareto optimum are identical in this model
First welfare theorem: under certain conditions, a competitive equilibrium is Pareto optimal
Second welfare theorem: under certain conditions, a Pareto optimum can be implemented as a competitive equilibrium
Taxation
Implications of a proportional labour income tax: Distortions (equilibrium is not Pareto optimal), Laffer curve (relationship between revenue raised and tax rate)
Pareto Optimum
A competitive equilibrium is Pareto optimal if there is no way to rearrange production or reallocate goods so that someone is made better off without making someone else worse off
The first fundamental theorem of welfare economics states that, under certain conditions, a competitive equilibrium is Pareto optimal
Allocation is Pareto efficient if it maximise the utility of households subject only to the physical constrains of an economy
All households identical, no trade off of making some better off without making others worse off
Pareto optimum requires MRS =MRT which is the marginal rate of substitution between consumption and leisure equated to the marginal rate of transformation which measures the technological possibility of converting one good into another
For consumers, optimality requires that MRS in equal to the net wage, in the case of an income tax; MRS = (1-t)w
For firms, optimality implies that MPn = w and therefore MRT = w
Therefore due to a labour income tax, competitive equilibrium means MRS and MRT do not equal and so Pareto optimality is not met
Consumers marginal product of labour would be higher than the after-tax wage the consumer receives
Socially optimal to supply more labour, but the promotional tax scheme doesn’t motivate workers to do so
Laffer Curve
Takes into account that higher proportional tax rates provide less incentives for households to work (assuming the substitution effect dominates the income effect of a change in the real wage)
Laffer Curve implies that there can be two different tax rates; low and high, both generate the same revenue
As tax rate increases, there is a positive mechanical effect on total revenue but at the same time labour supply will decrease because of the higher income taxes
If we are the wrong side of the Laffer curve, the incentive effect becomes the dominating factor: if the income tax rate falls, households will supply more labour such that the tax base increase outweighs the reduction in the tax rate and tax revenue will increase
Individual labour supply: the substitution effect (leisure relatively cheaper, therefore work less) dominates the income effect (your total income goes down and you want to work more). If there is a higher tax, you get a lower real wage, and you will work less. This can also be aggregated for the whole labor market.
For tax collection: There, the substitution effect is the effect described above: People substitute away from labor because their real wage is lower. The income effect is an income effect of tax collection: If you increase taxes, the units who still work will generate higher revenue.
Substitution effect explains why curve is humped: as tax rate increases, workers substitute away from labour
The tip of the curve shows where the income effect is offset by the substitution effect
The laffer curve increasing is due to the dominant income effect
Consumption = Output minus tax rate = Y - G (where G is gov spending which = T)
Welfare is consumer’s utility, if wage increases, utility increases
Labour Supply and Demand
Labour demand curve perfectly elastic at z where w=z and firms make zero profits regardless of how much labour is demanded (perfect competition expectancy)
Assume that substitution effect on wage changes is larger than the income effect (WHAT DOES THIS IMPLY?)
Equilibrium wage stays the same despite reduction in labour supply
Real wage (w) = MPN in in equilibrium, coincides with TFP (z)
Wage Increase
Opportunity cost of leisure increases -> l falls, c increases = N supply increases (Substitution effect) sub from leisure to consumption and go to work
Substitution effect: change in consumption patterns due to a change in the relative prices of goods
- Become more wealthy -> c increases, l can increase = N supply decreases (Income effect) - Income effect: change in consumption patterns due to a change in purchasing power - Conclusion: consumption must rise, but leisure may rise or fall - Assume sub effect is dominant - An increase in (pi-T) out of work earnings induces an inward shift in labour supply curve
The Effect of a Change in Total Factor Productivity in the Production Function
An increase in total factor productivity z has two important effects
First, because more output can be produced given capital and labour inputs when a increases, this shifts the production function up
Second, the marginal product of labour increases when z increases
This is reflected in the slope of production function (becomes steeper)
An increase in z arises from anything that permits more output to be produced for given inputs
Facts of Growth
Taking the natural logarithm of the raw data is a common way to plot data Measuring growth
Other important measures: life expectancy, infant mortality
Countries that have experienced growth in per capita output also experienced a long period of stagnation in output per capita
This stagnation is not because there was no growth in total output but because the increase in population offset the increase in output
Countries started to enter modern growth at different points in time, divergence
Will poor countries remain much poorer than rich countries or will they catch up, post WWII data seems to suggest convergence
Countries with lower levels of output per capita have typically grown faster
Conditional but not absolute convergence -> absolute = poor countries grow faster than rich/conditional = similar countries where the poorer countries grow faster than the richer
1) Before industrial revolution standards of living differed little across time and country -> population kept up with growth in aggregate income
2) Since the industrial revolution, per capita income has been sustained in the richest countries
3) There is a positive correlation between the rate of investment and out per worker across countries -> countries in which a relatively larger fraction of output is channelled into investment tend to have a relatively high standard of living
4) There is a negative correlation between the population growth rate and output per worker across countries -> Countries with high population growth rates tend to have low standards of living
5) Differences in per capita incomes increased dramatically among counties between 1800 and 1950 ->
6) There is essentially no correlation across countries between the level of output per capita in 1960 and the average rate of growth in output per capita for the years 1960-2007
7) Richer countries are much more alike in terms of rates of growth of real per capita income than are poor countries
Malthusian Model
Malthus argued that any advances in the technology for producing food would lead to further population growth
Higher population would ultimate reduce the average person to the subsistence level of consumption they had before the advance in technology
Malthusian theory predicts that technological growth will just increase population, with no long-run change in the standard of living, which is consistent with the data prior to the industrial revolution
Improvements in the production technology or increase in the quantity of land have no effect on the long-run standard if living
The factors of production are land and labour and there are constant returns to scale and diminishing marginal returns to each factor
Land labour ratio L/N, if it increases, output per worker is higher
Endogenous population growth, increasing function of consumption per worker, link between population growth and consumption per worker remains unchanged
We assume that we have a concave function of N
Concavity implies that there is a steady state in N towards which the economy converges
Key assumption is that land is fixed
Also: Population growth is an increasing function of consumption per worker: N’Ng(C/N)
All output is consumed: Y = C (no saving rate)
When population is low (below steady state), land per worker will be high leading to high output per worker
High output per work means workers are well-off but then will have more children and increases future population leading output per worker to decline
Lower output per worker leads to lower rate of population growth
These mechanisms mean there will be no population growth where N’/N, g(C/N) = 1
High population and low land per worker implies starvation so population will decline
Therefore there is a steady state standard of living which cannot increase in the LR
External interventions such as birth control or improvements in medicine may lead to greater life expectancy and can produced a sustained change in the standards of living
Increase in z
If z increases, the shifts up the per-worker production function
In the long run, the population increases to the point where per capita consumption returns to its initial level
There is no long run change in living standards
Transitional Dynamics
The economy does not move to the new steady instantaneously, as is takes time for the population to adjust according to N’=Ng(c.)
The transitional dynamics describe the changes in variable of the model (e.g. c and N) as the economy adjusts to the new steady state
The transitional dynamics caused by a higher z are: y increases/c increases/increases N’>N
Population Control
Reduces the population growth rate for each level of consumption
In LR, per capita consumption increases and living standards rise
Malthusian Model Shocks
After population falls (disease), consumption per worker increases at once as there is more land availability per worker and serving workers are able to produce more output per capita
Higher standards of living are present due to higher consumption per capita in SR and so population starts growing
MP of labour will eventually return to it’s LR point where c* = 1
Flaws of Malthusian Model
Model provides a good explanation for pre-1800 growth facts where production was mainly agricultural
However after industrial revolution there is sustained growth in GDP per capita, the model did not predict technological advances on fertility?? And the role of human capital
Also did not consider capital accumulation in growth
Malthusian Model and Technology Growth
Technological advances will just increase population with no long-run standard of living
In Malthus’ time, agriculture was the major production activity corresponding with the fact the model uses only labour and land as inputs of the production function
Steady state consumption per worker is constant and is is determined solely by population growth function N’/N = g(C/N) = 1 -> independent of TFP growth (B)
Growth in TFP(B) will only result in higher population, offsetting gains in productivity by decreasing land per worker with consumption per worker staying constant???
As all output is consumed, constant consumption per worker implies constant output per worker
Most of today’s bottom 5% of countries have not experienced growth in output per worker until recently
Therefore, differences in institutions or saving patters led some countries to switch from the Malthus technology into the Solow technology quicker than others
As these countries started to experience growth in output per worker earlier, it generated divergences in income levels in the 19th and 20th century
The Solow Model
Capital accumulation does not cause long term economic growth because it has diminishing returns and therefore output won’t increase continuously
Capital accumulation equation shows that change in capital stock is investment minus depreciation where investment equals savings and savings are a constant proportion of output
If saving rate (investment) > depreciation rate, incentive to accumulate more capital
If saving rate < depreciation rate, incentive not to accumulate more capital
Therefore, steady state where saving rate = depreciation
Increasing capital (moving along savings curve), increases depreciation
Increase capital per worker, increase output
Sustained rise in capital investment increases the growth rate only temporarily because ratio of capital to labour goes up
Marginal product of additional units of capital may decline and thus economy moves back to a long-term growth path, with real GDP growing at the same rate as the growth of the workforce plus a factor to reflect improving productivity
Steady-state growth path is reached when output, capital and labour are all growing at the same rate, so output per worker and capital per worker are constant
Assume population grows exogenously, growing population of consumers (workforce)
Basis for modern theory of economic growth
Steady state exists if two curves cross
It is unique if the two curves cross only once
Convergence if the saving curve is above the depreciation curve and if the saving curve is below the depreciation curve
There is no growth in the long run
If countries have the same n,s and d, then they have the same steady state so will converge, i.e. Solow Model predicts conditional convergence
Along this convergence path, a poorer country grows faster
Countries with different savings rates have different steady states and they will not converge (i.e. does not predict absolute convergence)
When saving rates are different, growth is not always higher in a poorer country (country with lower initial capital stock)??
Solow model predicts both countries will converge to the same level of capital per work and output per worker and the poor country will catch up with the rich country with regard to living standards
If rich and poor countries have the same labour force growth rate, their long-run growth rates in aggregate output will be identical
Across countries, real per capita income and the investment rate are positively correlated
g enters the steady state result: intuitively if investment only covers depreciation, capital per effective worker must be falling
So investment must cover both depreciation and growth in B for capital per effective worker to remain constant)
Increase in s
Increase in saving rates increases growth rate temporarily but no effect on long run growth
Higher k* and thus higher y*
Converges to a new higher steady state in short run
Trade-off as higher s reduces consumption share of income
The Golden Rule
Best steady state in the one with highest consumption per person: c = (1-s)zf(k*)
Given quantity of capital per worker that maximises consumption per worker in the steady state
This implies that an increase in the savings rate could cause a decrease in the steady state consumption per worker, even though an increase in the savings rate always increases output per worker
When capital is accumulated at a rate that maximises consumption per worker in the steady state, the marginal product of capital equals the population growth rate plus the depreciation rate
Increase in z
Shifts up saving curve, increase steady state k* and y*
Growth and output per worker increased temporarily
No effect in long run growth rate of output per work, which is equal to zero
Sustained increase in Z? Sustained increase in growth?
Productivity improvements are an exogenous variable independent of amount of capital investment
Labour Augmenting Technoloigcal Progress and TFP
One of the key reasons why our living standard is much higher than before is technological progress
Higher z makes both capital and labour inputs more productive
Capital per effective worker can only be constant if investment covers depreciation, population growth and technological progress
Convergence in the Solow Model for countries that are identical in d,s,n and the same technology
The rich country has higher initial physical capital than the poor one
Why Do Countries Experience a Growth Slow Down
Poorer countries can catch up initially by accumulating capital per capita
Over time, returns to capital decreases, the economy attains a steady state
Key condition: a < 1 - this means there is a diminishing marginal product to capital
Increase in Labour Force Growth
- Higher labour force growth ultimately causes aggregate output to grow at a higher rate
- Solow model predicts that capital per worker and output per worker will decrease in the steady state when the labour force growth rate increases, but aggregate output will grow at a higher ate, which is the new rate of labour for growth
- Capital per worker falls and output per worker falls (lower steady state)
- When the labour force growth rate increases, growth in all of these variable must also increase
- Higher growth in aggregate income need not be associated, in the long run, with higher income per worker
Two Economics Mechanisms by means of which the Higher Savings Rate Affects Consumption
1) Higher savings imply higher investment which translates into higher capital stock, output and consumption. However diminishing returns to capital sets in.
2) As we rise above the golden rule saving rate, the cost of increasing savings further outweighs the benefit of an additional unit of invested capital. Additional saving becomes inefefctciaint (in terms of consumption but not in terms of output)
Solow Model Shocks
If q = k, capital per worker does change so steady state stays the same hence output per worker and growth rate does not change in short or long run
If q > k, capital per worker and output per worker increases in short run but starts decreasing until economy runners to steady state (i.e. depreciation rate has increased as there has been greater capital accumulation but no extra savings to fund it), SR negative growth and 0 LR growth
If q < k, savings rate relative to depreciation will be greater as more people are in the economy and saving so there will be SR positive growth but 0 LR growth as we return to steady state
Growth and Development Accounting
Growth accounting shows the important contribution of technological progress to growth within a country
Development accounting shows differences in the levels of technology are needed to account for large cross-country income differences
Why doesn’t capital flow from rich to poor: large differences in Y/N must imply large differences in K/N, which implies that returns to capital in the poor countries must be much higher than in the rich, so why doesn’t capital flow from rich to poor?
There is missing capital in the model (e.g. human capital)? TFP is different across countries
Growth rate will be higher in country one:
The economist can come to this conclusion if the growth accounting exercise suggested that TFP growth was a larger component of output growth in in country 1
This is because the Neoclassical model assumes that factor accumulation can only have a temporary (SR) effect on growth in output per worker, but only TFP growth has a (LR) effect on growth per worker
Even if both countries have same SR growth rate, they can end up at different LR growth rates if consumption of current SR growth is different
Why doesn’t Capital Flow from Rich and Poor Country
Poor countries do not need to carry out R&D, they can adopt the technology of the rich countries
TFP is the effective level of technology but technology operates with different efficiencies in different countries
One potential answer is: institutions. There is a gap between the marginal product of capital and private incentives to save/invest due to tax rates, corruption, risk of expropriation
A lower y (output per worker) translates into higher MPK
A poor country should attract large capital inflows because it’s marginal product of capital is high however this has not been observed in reality
Introducing land into the production function breaks the one-To-one relationship between MPK and
If rich countries had a higher level of land per worker, then this would raise their MPK relative to poor countries
I.e. large countries can have more land and so higher levels of land per worker
Institutions
A broad concept that captures a set of rules which govern the process of decision making
Focus on the set of institutions that encourage productive activities such as investment in physical and human capital or technology adoption over diversion or rent-seeking
Growth Accounting
Measure how much of the growth in aggregate output is accounted for by: factor accumulation (capital, labour, human capital) and by increases in total factor productivity
If the fast growth rate is due to a high rate of technological progress (rate g) then it implies higher steady state growth that will last in the long run
If fast growth is due to high capital accumulation then growth in the short run exceeds steady state growth g but will eventually fall back to it due to the diminishing marginal products of capital
Growth accounting implies growth in technology z is an important component for growth in output
Development Accounting
Solow model predicts a country is poorer if it has a lower saving rate, a higher population growth rate or a higher depreciation rate
Depreciation and population growth rates similar across countries (assume for simplicity)
Therefore any differences in steady state output per worker must be due to differences in saving
Left with saving/investment rate -> investment rate for poor countries is about five times lower than for the rich
E.g. for a = 1/3, the ratio of y* rich to poor countries is equal to (5)^1/2 = 2ish which is much smaller than observed cross-country income differences. Difference in B is needed (TFP)
Growth accounting implies growth in technology z is an important component for growth in output
Development accounting shows differences in the level of technology are needed to account for large cross-country income differences
Development accounting model shows differences in their savings rates are too small to account for their income differences and therefore we need to examine differences in the level of technology to explain large cross-country income differences (can’t just assume B is the same for each country)
Why is there Technological Progress
Learning-by-doing: acquire knowledge as a by-product whilst working
Human Capital: accumulated skills and talent of workers that puts ideas into production
Research and development: produces new ideas and knowledge
These are endogenous growth models in the sense that long-run growth is endogenously determined by the model
Endogenous Growth Models
The endogenous growth model does not predict convergence in levels of per capita income across countries when countries are identical except for being initially rich and initially poor
Predicts that differences in per capita income persist forever
The growth mechanism that is endogenous to the Solow model is capital accumulation
The presences of diminishing MPK implies that the incentive to accumulate capital declines as the capital stock increases
Endogenous growth not possible in the Solow model
If A is constant, then MPK falls as k rises, so the incentive to accumulate capital will eventually disappear -> this is why there is no growth in the steady state of the Solow model when A in constant
If A is growing at a constant rate, then MPK might not be dismissing as k rises. More specifically, if the fall in k^a-1 is cancelled out by the rise in A, then MPK is constant -> this is why there is constant growth in the steady state of the Solow model at rate g
The AK model: there is positive growth in the long run even if A is constant
The savings curve becomes a straight line so there is no steady state for k, i.e. there is long run growth even if A is constant
Learning by Doing
Total factor productivity differs across countries
Could take time for workers and manager to learn to use new technology, we should expect a learning period for the technologies that are used in rich countries to spread to poor countries
Productivity differences can persist across countries because of barriers to the adoption of new technology, a protected industry will be less inclined to invest in research and development that makes it more competitive in world markets
The level of aggregate technology can differ across countries because of the efficiency with which factors of production are allocated across firms in the economy
With countries with different TFP, in the steady state, standards of living are permanently different but aggregate output grows at the same rate
Skills or knowledge are accumulated during the production process
So the skills or knowledge accumulation are free and is a by-product of production
Investment by a firm generates a positive externality for the economy
So there is no dismissing marginal product of capital at the aggregate level
There is endogenous growth because the stock of knowledge is determined by the endogenous level of K through learning-by-doing
New implications compared to the Solow model: saving rate affects not only the level of income but also the growth rate as x depends on s, the growth rate is constant in both the short and long run and there is no convergence
There are scale effects: the growth rate depends on the size of the population
Larger N implies stronger knowledge spill overs and therefor higher growth rate
If we assume that the level of economy-wide knowledge is not exogenous then we can explain differences in income levels through differences in knowledge accumulation which, using an LBD model is due to differences in savings rates
Idea of LBD model
i) The production function holds for individual firms ii) For the economy as a whole, there are knowledge spillovers across firms which make B a positive function of average capital stock
Despite diminishing marginal product of capital at the firm level, the presences of knowledge spillovers implies that the aggregate production function displays no diminishing MPK
We get LR endogenous growth if the saving rate is high enough
A difference in saving rates between high and low income countries would now mean that they grow at different rates and incomes will diverge over time, this can explain any level of income difference
Human Capital
The representative consumer allocates his or her time between supplying labour to produce output and accumulating human capital where human capital is the accumulated stock of skills and eduction taxation a worker has at a point in time
Higher level of human capital means economy can grow at a faster rate as workers can produce more
Skills are required to put ideas or knowledge into practice
Unlike learning-by-doing, there are costs and returns to education
Production of new human capital is proportional to existing human capital, i.e. AK for the production of human capital, there are no dismissing marginal product in the production of human capital
Model predicts positives growth in the long run (without exogenous growth in technology)
If b(1-u)>1, human capital increase forever - there is endogenous growth
No diminishing returns as increasing human capital has no limit (non-rivalry?), physical capital has diminishing marginal returns and is rivalrous
Growth rate of human capital increases if b increases or if u decreases
B determines efficient of human capital accumulation technology, efficiency of the educational sector (countries with more efficient education systems should experience higher rates of growth in human capital)
If u decreases this means more time is spent devoted to human capital accumulation and less to producing output in current period
Growth rate of consumption Is identical to growth rate of human capital
Human capital, consumption and output all grow at same rate in equilibrium
Growth occurs due to endogenous forces (b and u) and not from population growth and not from technology growth as z remains fixed
Convergence does not occur even if countries are identical (same b, z and u)??
Rich country has a higher initial human capital than the poor one
Conditional Convergence
Poor countries will tend to catch up with or converge towards the income levels of rich countries if poor countries have similar savings rates for both physical and human capital
Research and Development
New ideas and knowledge are developed in the market through devoting resources to research and development
Ideas are like capital -> cost to producing them, can be used in production, there is a price for them (value of a patent)
Capital and ideas are very different -> ideas are rivalrous or nonrivalrous and have a degree of excludability??
One-Country Model
No diminishing marginal returns in the production of ideas
Production of new knowledge is proportional to the numbers of workers engaged in R&D
Growth rate does not depend on existing stock of ideas (no diminishing returns)
A growth in yA (fraction of workers engaged in R&D) leads to a permanent increase in the growth rate
There are scale effects: the growth rate depends on the size of the population, larger L implies more workers engaged in R&D (for given yA)
Implies countries with larger population have higher growth rates, levels of technology and are richer
One interpretation of the model is that a country’s level of technology depends on R&D done around the world
Two Country Model
Countries acquire new technologies either by invention or by imitation. The option of imitation is open only to the country that is the technology follower
Cost of imitating a given technology is less than the cost of reinventing the technology
In the steady state, the growth rates of A1, and A2 are equal
An increase in yA2 shifts up the growth rate of A2, the new steady state is lower
An increase in yA2 leads to a temporary increase in the growth rate for the follower
Appropriate Technology
Technologies developed in the leader might not be appropriate for the follower e.g. rich country may have more physical or human capital
Different types of technological change: Neutral/Capital-biased
Neutral technological change: a proportional shift upward in the production function means a poor country would benefit as much as a rich country from technological change
Capital-biased technological change: Only capital-rich countries benefit
Enforcement of property rights (institutions) means R&D labs in developed countries don’t create technologies that developing countries could use
Capital per effective worker
The derivation of equilibrium in the Solow model with technological progress is similar to before once we re-interpret
the labour input in terms of “effective” units
When N is constant, the dynamic equation for capital per worker (k=K/N) implies that steady state k is constant if investment covers depreciation
When the number of workers N is growing, then if investment only covers depreciation, k must be falling
So investment must cover both deprecation and population growth for capital per worker to remain constant
Following the same intuition, capital per effective worker can only be constant if investment covers depreciation, population growth and technological progress
Instead you state, both capital per effective worker and output per effective worker are constants, both are growing at the rate g (the growth rate of B)
Convergence in the Solow model for countries that are identical (same d,s,n and the same technology)
