Day 3: Solow (done) Flashcards
What’s the theory of capital accumulation in the Solow model?
Capital accumulation is endogenized in the Solow model (turned from exogenous into endogenous variable)
- Solow model allows us to consider capital accumulation as a possible factor of long-run economic growth
What’s econ. growth?
an increase in output/GDP (Y)
Determinants of production?
Capital: machines, factories, roads, etc.
Labor: number of people working
Technology
What’re stock variables?
A quantity that survives from period to period
Eg. tractor, house, factory, wealth, government debt (a debt that persists over time unless paid off).
What’re flow variables?
A quantity that lasts a single period. Time frame/period matters, need it to make sense
The change in a stock is a flow: the change in the capital stock, for example, is the flow of investment.
Eg. savings/investments (quarter, year), meals consumed, withdrawal from ATM
In solow model, what’re the stock variables?
capital and labor
What’s the real interest rate?
Nominal interest rate - inflation
It’s real bc it’s measured in units of output/constant dollars rather than nominal dollars.
What’s savings?
the difference between income and consumption
Y-C = Inv/savings
What’s a production function?
a production function shows how much output/GDP (Y) can be produced given 2 inputs, which are EXOGENOUS variables
What’s the production function for the Solow model?
- 2 Inputs/exogenous variables are the factors of production: capital K and labor L
- Output/endogenous variable: GDP
- Y = F(K,L) = AK^1/3L2/3
- A’s constant
What’re the properties of the production function for the Solow model?
- displays constant returns to scale with 2 exogenous inputs ( labor, capital)
- decreasing returns to scale/marginal returns by increasing 1 input while keeping other constant (increasing K but not L leads to decreasing marginal returns)
What’re constant returns to scale?
constant returns to scale are when an increase in inputs (capital and labour) cause the same proportional increase in output.
Ex.: if you double inputs, you double outputs
Effect of constant RTS on solow growth production function?
This makes the growth model “scale-free”
Meaning returns aren’t affected depending on the specific scale/size of individuals you’re examining
In solow model, what can you do with the final output?
Can either consume or invest (in capital) the final output
Consumption + Investment = Y
Formulas for Consumption?
- C = (Y - I) = (1-s)Y = (1-s)(AK^⅓ L^⅔)
2. per capita consumption C/L = (1-s)AK^⅓ L^-⅓.
What’s a closed economy (solow)?
no imports/exports
What’s a resource constraint in solow ?
Tells you how much you’re consuming/investing.
A constraint on how the economy can use its resources
What’s held constant in solow model?
WORK IN PROGRESS!!!!!!!
- Labor (no population growth)
What’s “s” in the solow model?
S is the savings/investment rate, the fraction of GDP that’s invested in capital
What’s investment in the solow model?
Investment’s a constant fraction of output GDP
I = sY
IMPORTANT: What’s the relationship between growth and investment?
GROWTH causes investment, not the other way around.
What’s consumption in the solow model?
consumption’s is the difference between output and investment.
- C = (1-s)Y
- C = Y - I
How to calculate the change in a variable in 2 periods?
- Divide C(new)/C(old) 2nd formulas for the proportion of new to old
- Then use the percent change formula
Is consumption affected by depreciation?
No! consumption’s is the difference between output and investment.
- C = Y - I
What’s consumption in the solow long-run?
In the long-run consumption’s constant. With transition dynamics, consumption will increase below SS, decrease above SS to reach the steady state.
What happens to consumption as capital K increases and you move along horizontal axis?
consumption always INCREASES as K increases!
What’s the formula for capital accumulation? (moving right along solow)
Next year’s capital is the sum of this year’s capital and the net investment/change in capital.
K(t+1) = K(t) + (I - dK)
What does the capital accumulation formula tell you for solow?
Capital accumulation tells you by how much next period’s amount of capital will increase, by how much you’re investing
What’s the depreciation rate?
The amount of capital that wears out each period
How does depreciation rate work?
Mathematically must be between 0 and 1 for solow.
0: no wear and tear on capital
1: you lose all of your capital
What’s the depreciation rate often?
Often viewed as approximately 10%
What’s A?
- A is the level of total factor productivity (TFP)/technology/productivity parameter
How does productivity affect the solow production function and solow model?
Productivity influences output in both the production function and solow model, but explains a larger difference in the Solow model, bc it also affects the accumulation of capital there.
What’s the net investment or net change in capital?
how much capital/x-axis changes in the next time period, investment minus depreciation
net investment/cc = sY (investment) - dK (depreciation)
How come we always reach the steady state in solow as you increase investment?
- because investment gives you DIMINISHING returns!
As you increase investment by a constant amount, you get diminishing returns on investment, but depreciation increases by a constant amount.
= by adding more capital, depreciation increases at a higher rate than your investment.
What’s the steady state?
- where investment equals depreciation
- Capital K is constant in the long-run here, as investment is just enough to cover depreciation, none left over to invest in more capital stock.
What’re the parameters in the solow model?
these are given and unless shocked, stay constant
- A, s, d, L, K0
What’re the exogenous variables in solow?
All starting point variables (Capital K0, Y0, L0, C0, and I0)
What’re the endogenous variables in solow?
GDP (Y) and the new points after the model’s in motion (K, I, Y)
What’re the nature of solow variables?
Everything’s ENDOGENOUS except the starting point, bc the model updates itself continuously until you reach the steady state.
Is solow dynamic or static, why?
it’s DYNAMIC: the 5 equations hold at each point in time (t=0,1,2,etc.)
What happens when investment’s greater than depreciation?
- level of capital K is less than steady state causes inevitable increasing progression to the “steady state”
- The capital stock will increase until investment equals depreciation.
- Then, the change in capital is equal to 0 (bc depreciation and investment cancel each other out)
- Reach the “steady state”: The capital stock stays constant forever, and no long-term growth bc all investment’s eaten up by depreciation.
Is the steady state inevitable?
Yes, sy will always intersect dk, investment will always equal depreciation at some point
how to represent variables in steady state?
use an asterisk *
What happens when investment’s less than depreciation?
- level of capital K is greater than the steady state causes inevitable decreasing progression to the “steady state”
- same dynamics but in reverse
What happens to solow when you change the amount of capital K?
changing K DOES NOT change the steady state!
- it causes a movement ALONG the curves, bc Solow shows investment and depreciation at each possible level of capital.
- Location among the horizontal axis (level of capital K) changes, causing transition dynamics to go back to the SAME steady state
What happens to solow when you change the amount of labor L?
changing L DOES change the steady state!
- increasing L rotates UPWARDS the output and investment curves, INCREASING the steady state
What’s the effect of changing amount of labor L on per-capita GDP in the long-run?
L changing doesn’t change per-capita GDP in the long-run
1. L increases first, decreasing Y/L because capital and output haven’t caught up yet.
- But then returns to normal as output catches up
Why doesn’t changing labor L change per-capita GDP in the long-run?
Because we have constant returns to scale with L and K, so any percent change in L causes the same percent change in K, which in turn equals the percent change in output
Since solow model has constant returns to scale with labor L and capital K, what happens if one of the variables change?
any percent change in one variable causes the SAME percent change in the other which in turn equals the percent change in output
- so, changing L and K don’t change output and output per person.
Does changing L or K change output/output per person in the long-run?
NO! bc constant returns to scale
- any percent change in one variable causes the SAME percent change in the other which in turn equals the percent change in output
How does changing amount of labor L in solow change the growth rate of per-capita GDP?
- growth rate of per-capita GDP quickly increases before returning back to 0
1. At steady state, growth rate’s zero, so we start at zero
2. Then, there’s a short burst of transitory growth after the output/investment curves shift upwards as you progress to the new steady state, where growth rate’s zero again
What’s the steady state, mathematically?
the intersection of the investment and depreciation curves (dK = sy)
- In the steady state, sY* = dK*
what’s the variable for GDP per capita in the long-run?
lowercase y with an asterisk: y*
What’s the steady state level of capital positively and negatively correlated with?
- positively correlated with investment rate, labor, and productivity A
- negatively correlated with depreciation
How come increasing labor L INCREASES the steady state level of capital?
if you increase L bar, you’re producing more and therefore investing more given you’re investing a fraction of production, increasing capital
What’s the steady state in the long-run of solow?
- growth rate’s zero
2. net investment is zero bc Investment = depreciation, all investment goes to fixing capital from depreciation
How do we check how good a model is?
look at the model’s predictions and verify if the predictions are true with data
How do we check how good the Solow model is?
Check if the steady state is true (sY* = dK) with the capital-output ratio: K/Y= s/d
- can easily measure K, Y*, and s with data, and assume d
What’s the capital-output ratio?
capital-output ratio: K/Y= s/d
Steps/results of checking solow model with capital-output ratio?
According to this equation/model, countries with high savings rates should have high capital-output ratios.
- data SUPPORTS this!
With solow model, how can we understand why some countries are much richer than others?
- Take the ratios of y* (GDP per-capita) for 2 countries and assume depreciation’s the same.
- use the y* formulas and separate A and s ratios
- shows that A is a bigger factor in p/c GDP (ratio of A’s 54 vs. 2)
How can we use the solow model to create economic policy?
to better increase the poor country’s well-being, you would increase the technology (A) rather than the savings rate, bc it’s the biggest factor.
What does solow tell us about the main explaining factor of differences in a country’s GDP?
the MAIN explaining factor of GDP differences in A: TOTAL FACTOR PRODUCTIVITY.
- Countries aren’t poorer than US bc of savings rate, but bc their labor/capital isn’t as productive as the US.
Is there long-run growth in solow?
NO! when you reach the steady state, growth stops and everything’s constant (output, capital, consumption, etc.)
Is solow right on long-run growth?
NO! bc empirically, economies appear to continue to grow over time.
Why’s solow useful even though it doesn’t show long-term growth?
it teaches us where sustainable growth does NOT come from: accumulating capital, savings rate, and investments.
What’re the 4 ways to cause transitory growth in solow?
- increasing investment rate
- decreasing depreciation
- increasing A
- decreasing L
Effect of increasing investment rate on solow?
- investment curve rotates upwards, depreciation curve unchanged
- capital K increases to new, higher, steady state.
Effect of decreasing depreciation rate on solow?
- depreciation curve rotates downwards
2. capital K increases to new, higher, steady state.
Effect of increasing A on solow?
- output curve rotates upwards
- this rotates upwards the investment curve too, bc it’s a fraction of output
- this increases the steady state without decreasing consumption, bc Y moves too
What’s transitory growth?
- Increases the steady state BUT decreases consumption bc the output curve doesn’t move, which makes ppl poorer.
Example of transitory growth?
Eastern Europe was once a command economy and did forced industrialization (artificially increased investment rate by building more factories)
Example of sustainable long-term growth?
Market economy (western europe 50s-70s): can do sustainable long-term growth by increasing A w/ technological innovation
What’s sustainable long-term growth?
- Increases steady state without decreasing consumption, bc you’re increasing BOTH output and investment curves.
- only way is continually increasing A, and adjusting all savings rate, depreciation, A, and L
What’s the principle of TRANSITION DYNAMICS?
It’s a prediction of solow model, which says the farther the economy from the steady state in either direction, the FASTER output will grow/the HIGHER the output growth rate
If we assume all countries have same A, S, D, GDP, and steady state, what does the solow model predict?
- With everything the same, the only way u can have a lower GDP is if they’re in the transitory state and start off at a lower GDP.
- countries with lower levels of GDP (further from the same steady state) should grow faster.
What’s the Basic idea behind development aid with solow?
if you want to help countries reach their steady state faster, give them/increase their level of capital
- this assumes they’re BELOW their steady state though
Does transition dynamics hold in real life?
No, we find on average rich and poor countries grow at the same rate. This means that
- Most countries have already reached their steady states
- Most countries are not playing technological catch-up
With solow model and data, why are countries poor?
Countries are poor not bc of a bad shock/bad starting point (in which case you’ll give them more capital to help them out), but bc they have a bad steady state (they have parameters that yield a lower steady state)
What’re the strengths of solow?
- Provides a theory that determines how rich a country is in the long run w/ its steady state
- Provides the principle of transition dynamics
Why’s the solow transition dynamics principle important?
Allows us to understand the differences in growth rates across countries
What’re the weaknesses of solow?
- Main weakness: The solow model doesn’t provide a theory of sustained long-run economic growth (by increasing A)
- focuses on factors that don’t increase growth: increasing investment/capital
- doesn’t explain A and differences in A
- Doesn’t explain why different countries have different investment and productivity rates
How can we improve A to get long-term sustainable growth?
- improve technology
2. institutions
How do institutions cause long-term sustainable growth?
- they encourage investment in R&D which causes tech innovation
- do this by providing political/legal stability, and protecting investments in intellectual property with patents, etc.
examples of institutions?
political system, gov’t, economy
What’re public goods?
A good that’s non-rival and non-excludable in consumption (example’s a streetlight, ideas)
What’s a non-rival good?
one person’s use doesn’t reduce the inherent usefulness to someone else
What’s a non-excludable good?
You can’t easily/physically exclude people from using a good.
Are firms going to invest in ideas in a perfectly competitive market?
No, bc u need the prospect of monopoly profits to invest serious money into R&D, bc if u set P = MC in PC, you can’t recoup R&D costs
Solution to cause firms to invest in ideas in a perfectly competitive market?
patents: bc they act as a temporary monopoly leading to monopoly profits, gives you a property right on your ideas
What type of institutions do we need for tech. innovation?
- gov’t that protects intellectual property with patents
- stable political system
- stable legal system that fights inside trading/trusts
Why do institutions need to fight trusts?
trusts are monopolies, that stop competition, which prevents tech. innovation and economic growth.
Effect of transitory growth in the long-run?
- higher steady state
2. but per-capita GDP and p/c Consumption remain the same bc of constant returns to scale
Effect of transitory growth in the short-run?
In the short run per-capita Y and per-capita C will fall, but then it goes back up to its initiate steady state value.
