Unit 7: Long-Run Economics
7.1: The classical model
We have mentioned several aspects of the difference between the Keynesian and the Classical approaches to macroeconomics throughout earlier units. But we have never laid out in detail the classical model of how the macroeconomy functions. In this section, we go through the classical model, and in subsequent sections, we will compare the classical and Keynesian approaches and finally we will apply the classical approach to the crucial area of long-run economic growth.
Core Principles
There are a few core principles of classical economics.
Classical economics analyzes macroeconomics using microeconomic techniques. In classical economics, the macroeconomy is just a collection of microeconomic markets. The macroeconomy is just the market for apples, oranges, labor, financial assets, etc… all put together. If we understand these markets, we understand the macroeconomy.
Markets clear on their own. In other words, markets of all kinds (e.g. labor markets or markets for goods and services) will automatically gravitate towards the equilibrium where supply and demand are equal. And since the market equilibrium is optimal, the economy works fine on its own.
Downturns in the business cycle are just short-term disequilibrium. In the classical model, equilibrium and good market performance are the normal condition. Recessions and other irregularities in the business cycles are just frictions that will work themselves out of the system, back to equilibrium, on their own.
The Labor Market
The supply of labor describes the number of workers who want to work at different wages. The supply curve for labor slopes upwards. At higher wages, more people are willing to work and people already in the labor force are willing to work more hours.
The demand for labor describes the number of workers that firms want to hire at various wages. The demand curve for labor slopes downwards. At higher wages, firms are not willing to employ as many workers.
The labor market is shown below. The equilibrium wage 𝑤∗ and number of workers 𝐿∗ are shown on the diagram.
Our goal in the labor market is full employment. But what does full employment mean? Remember, it doesn’t mean that every person has a job. It means that everyone who wants to work
is able to find a job. But that’s exactly true at the market equilibrium! At the equilibrium level of employment 𝐿∗, labor supply and labor demand are equal. In other words, the number of people who are want to work (labor supply) equals the number of workers that firms want to hire (labor demand). Everyone who is willing to work at the equilibrium wage is able to find a job. There is no involuntary unemployment.
The labor market reaches full employment on its own. The labor market will gravitate to an equilibrium wage where labor supply is equal to labor demand, which means that there is no involuntary unemployment. No government stabilization or intervention is needed. The key assumption here is that the labor market tends towards equilibrium, which Keynesian economists strongly dispute.
Notice that the production function displays diminishing marginal returns. Output rises when workers are added, but it rises at a slower and slower rate as more workers are added.
The reason for diminishing returns is that the economy always has some resources in limited supply, like land and machines and factories in the short-run. As more and more workers are added, they have to share these resources that are in limited supply, so the first workers add more to output than subsequent workers. Diminishing returns does not say that output falls when more workers are added, just that it rises more and more slowly as additional workers are added.
Full-employment output (potential output) is defined as the level of output when resources are fully employed. But the equilibrium level of employment 𝐿∗ in the labor market generates full employment. So that’s it. In the classical model, the economy’s GDP is equal to potential GDP. No government intervention is needed to get the economy to perform up to full potential.
Say’s Law
As we have said earlier, the classical model is basically supply-driven. The economy’s output is determined by its productive resources. In turn, those productive resources are fully employed in the classical model. Thus, GDP is completely determined by supply.
But what about demand? In other words, even if the economy produces the full-employment level of output 𝑌∗, how is there any guarantee that there will be enough demand to purchase all of this output? In classical economics, the answer is very simple. According to Say’s Law, supply creates its own demand. Therefore, as long as the economy produces potential output 𝑌∗, sufficient demand is there automatically.
In the product market, households buy goods and services from firms. This is illustrated by the red flow. In exchange, there is a monetary flow from households to firms representing payment for goods and services that households buy. This is illustrated by the green flow.
But firms buy resources from households. For example, firms hire workers and they borrow money from households through the banking system. These labor and capital flows are shown by the red flow from households to firms. In turn, firms pay wages and interest payments for these labor and capital resources. These financial flows are shown in green. Even when the firm earns a profit, the profit is returned to households as dividends for the shareholders or owners.
Where do households get the money to buy goods and services? From firms, which pay them. And where do firms get the money to pay households for the resources they provide, like labor? From households, which purchase the goods and services they produce. The economy is a big circle. Resources flow to firms, while goods and services flow to households, with financial flows that exactly accompany these transactions.
In this simple economy, every dollar earned by firms from selling output is returned back to households in some way. All output is income for someone. This is the rationale for Say’s Law. When a firm produces $100 worth of output, this creates $100 worth of incomes – whether wages, capital income, rent, profits, etc… But then this creates $100 worth of purchasing power for households. That’s Say’s Law. $100 worth of production creates $100 worth of income to buy goods and services. Supply creates demand.
Keynesians strongly dispute Say’s Law, and claim that imbalances between purchases and production are a primary driver of economic instability. But we’ll get into that in the next section.
Leakages and Injections
The simple circular flow model is not entirely realistic. While it is true that $100 worth of outputs will create $100 of incomes (this is a simple accounting identity – remember that GDP measures output and incomes), it is oversimplifying to say that $100 worth of incomes will automatically create $100 of demand for goods and services.
The problem is that not all income earned by households is spent. A leakage occurs when income is earned by households but not spent on purchasing goods and services. There are two sources of leakages.
At first, it might seem like leakages invalidate Say’s Law. While $100 worth of output does generate $100 of incomes, it generates less than $100 of spending by households, because some of these incomes will be used for savings and taxes So it seems like $100 worth of supply generates less than $100 of demand for purchasing goods and services.
Does that criticism invalidate Say’s Law? Not necessarily. Leakages don’t fall into a dark pit. There are corresponding injections. Savings provides funds to the financial system that firms use for their investment spending, and taxes fund government spending. In other words, savings and taxes leak out, but the money pays for investment spending and government spending. Summarizing, the two forms of injections are:
Investment (I)
Government Spending (G)
One small subtlety with these definitions. Taxes in this model are defined as net taxes, which is taxes net of transfer payments.
𝑇 = taxes − transfer payments
Basically, if the public pays $500 billion of taxes but receives $200 billion of transfers from the government, then on net, the public pays $300 billion to the government. We define taxes this way just to make accounting simpler and avoid having to keep track of transfers separately.
Now, the definition of savings is income, less what is spent on consumption spending and what is paid in taxes:
𝑆 = 𝑌 − 𝐶 − 𝑇
Rearranging this identity, we obtain:
𝑌 = 𝐶 + 𝑆 + 𝑇
In other words – income is either spent, saved or used to pay taxes. This is an accounting identity.
What about spending? We will consider a closed economy, for simplicity. In this case, spending consists of consumption spending, investment spending and government spending.
Say’s Law asserts that total production/income should be equal to total spending. We know that $100 of output always creates $100 of income. The question is whether $100 of income actually creates $100 of spending. If it does, then Say’s Law holds – supply (production) creates an equivalent amount of demand (spending).
Income = Spending 𝐶 + 𝑆 + 𝑇 = 𝐶 + 𝐼 + 𝐺
𝑆 + 𝑇 = 𝐼 + 𝐺
In other words, Say’s Law holds as long as leakages (𝑆 + 𝑇) equal injections (𝐼 + 𝐺).
This condition makes intuitive sense. If households receive $1000 of income but only spend $700, then there are $300 of leakages in the form of savings and taxes. But as long as there are $300 of injections, then Say’s Law still holds. The $700 spent by households themselves and $300 as injections add up to the $1000 of incomes paid. Income equals spending.
The overall point is that leakages do not create a problem with Say’s Law as long as there are injections equal to the leakages. But why should leakages and injections be equal? This is the subjects of the next section.
The Loanable Funds Market
The loanable funds market is where firms go to borrow money for investment projects. The price of loans is the interest rate, and the demand and supply curves have the usual shape.
The supply of loanable funds represents the money that is available to be lent out. It is upward sloping – at higher interest rates, households are more willing to save and thus there are more funds available to be lent out.
The demand for loanable funds represents the money that firms want to borrow. It is downward sloping – as the interest rate rises, firms are less inclined to borrow.
Household savings 𝑆 is always part of the supply of funds. This is money that households save and is available to be lent out.
Firm investment spending 𝐼 is always part of the demand for funds. This is money that firms use for their capital investment projects.
But what about the government? Here, we have to distinguish between the case where the government runs a deficit and where they run a surplus.
If the government runs a deficit, then the amount of the deficit 𝐺 − 𝑇 becomes part of the
demand for funds. The government needs to borrow money to cover its excess spending over the level of taxes it collects.
If the government runs a surplus, then the amount of the surplus 𝑇 − 𝐺 becomes part of the
supply of funds. The government has surplus funds since it collects taxes in excess of its level of spending.
In the classical model, the loanable funds market is in equilibrium. The market will tend towards an equilibrium interest rate where supply and demand for funds are equal.
CASE 1: When the government runs a deficit, the demand for funds includes funds for investment spending borrowed by firms and funds that the government borrows to finance its deficit. Supply of funds is household savings. In other words, the government and private firms are both competing for the supply of loanable funds. When the market is in equilibrium:
Demand for funds = Supply of funds 𝐼 + (𝐺 − 𝑇) = 𝑆
CASE 2: When the government has a surplus, then the supply of funds includes both private savings and the government’s surplus. Demand for funds in this case is just firm investment. When the market is in equilibrium:
Demand for funds = Supply of funds 𝐼 = 𝑆 + (𝑇 − 𝐺) 𝑆 + 𝑇 = 𝐼 + 𝐺
Leakages = Injections
In both cases, as long as the loanable funds market is in equilibrium, then leakages equal injections. And why is that so important? If leakages equal injections, then Say’s Law holds. Total
production/income is exactly equal to total spending. Supply creates its own demand.
The key assumption here is that the financial market is in equilibrium. Keynesians strongly dispute that this will necessarily be the case.
Summarizing the Classical Model
In the classical model, the labor market is always at full employment where labor supply is equal to labor demand. Therefore, the economy’s GDP is always at potential, full-employment output. Proper functioning of the labor market takes care of the supply side of the economy. Output in this model is supply-driven – the economy will produce whatever level of output corresponds to full-employment output with its current level of resources.
As for the demand side of the economy, the Classical Model asserts that Say’s Law holds. Supply creates its own demand. So, if the full-employment level of output is supplied, then this production automatically generates incomes and demand sufficient to purchase this level of output. Even though there are leakages, proper functioning of the financial system implies that leakages are equal to injections. Overall, Say’s Law holds.
7.2: The classical system and the Keynesian system
As we have mentioned before, classical and Keynesian economics come to very different conclusions about macroeconomic performance. Classical economists emphasize market adjustments and self-correction, with little need for government intervention. Keynesian economists emphasize market imperfections, with a role for government involvement to stabilize the economy. Now that we have studied both systems in detail, we can compare the two.
Classical economists and Keynesian economists have different views on how the macroeconomy operates, which leads to different conclusions about policy formation. In this section, we will discuss some of the main differences and then at the end we will see how the two can fit together.
Using Microeconomic Tools to Analyze Macroeconomics
Classical Keynesian
Microeconomic supply and demand principles are appropriate for macro-level markets like labor markets and financial markets. Large-scale markets follow the same principles as the markets for apples or soap.
Example: Labor market reaches equilibrium, generating full employment.
Example: Financial markets reach equilibrium, so leakages and injections are equal.
Market rigidities are mostly created by the government, so we should aim for markets that are as flexible as possible. For example, shoot for as little regulation as possible.
Real-world markets don’t work like this at the macro level.
Problem 1: Serious wage and price rigidities. Even when economic conditions imply that markets should adjust, the market may not adjust to equilibrium on its own.
Labor markets – Regulations and long-term contracts. Market might not adjust to equilibrium wage and can feature permanent unemployment.
Financial markets – Information problems make it difficult for financial markets to function efficiently. Leakages and injections may not be equal, so Say’s Law may not hold.
macroeconomy, which isn’t true in an individual market.
Example: An individual firm that can cut wages would see an increase in profit. But if
all firms cut wages, then profits would fall because firms would have fewer customers.
Example: For a household or firm, spending less will lead to a better financial position. But that’s not true for macroeconomy because if
everyone spends less, the economy is poorer. Your spending is my income. Production and income and spending are inextricably linked, which isn’t true for an individual market.
Business Cycles and Recessions
Classical Keynesian
Markets self-adjust to equilibrium. Economic downturns are just short-term bumps while the economy experiences a shock and adjusts to a new equilibrium. Normal condition is good performance.
If economy is in recession, there are unemployed resources and resource costs fall. This leads firms to increase output and employment, so the economy self-adjusts out of recession.
Economic downturns are a normal part of how the economy functions. Not an aberration because the economy is out of equilibrium.
Economy may not self-adjust out of recession.
Problem 1: Sticky wages and prices may prevent resource costs from falling.
Problem 2: Even if wages do adjust downwards, firms will not expand if they have bad expectations about the prospects for future sales.
Government Stabilization Policy
Classical Keynesian
Let the market clear itself out if the economy is not performing well. Economy will eventually adjust back to full-employment equilibrium.
Government can break cycle of bad expectations and low performance. By increasing purchases of goods and services, firms see a market for future sales and will expand. With expansions, incomes are higher, spending goes up and the problem is fixed.
Supply and Demand as Drivers of the Economy
Classical Keynesian
𝐺𝐷𝑃 = 𝐶 + 𝐼 + 𝐺 + 𝑁𝑋
Production creates incomes.
Supply-driven view: When firms produce more output, this generates incomes and spending. Keynesian view has the economy totally backwards.
𝐺𝐷𝑃 = 𝐶 + 𝐼 + 𝐺 + 𝑁𝑋
Spending can stimulate production.
Demand-driven view: More purchases can generate more production. That’s why fiscal and monetary policy can help the economy grow, with a multiplier effect.
Varying Perspectives on Say’s Law
Classical Keynesian
Production creates incomes, which creates spending. Say’s Law holds.
No government spending needed to supplement demand. Demand is always equal to supply.
Say’s Law is unrealistic.
No particular reason that production and incomes must generate purchases – at least not anytime soon. Recessions are created when there is not enough demand relative to output supplied.
Business cycles are normal occurrences stemming from imbalances of supply and demand, potentially permanent.
If there is not enough demand to purchase output produced, government can help stimulate demand for goods and services using fiscal and monetary policy.
Money and Interest Rate Determination
Classical Keynesian
Interest rate comes from an equilibrium of supply and demand for loanable funds. That’s why leakages and injections are always equal.
In the short-run, the interest rate comes from equilibrium in the money market – depends on liquidity preferences and the public’s desired mix between money and interest-bearing assets.
Rationality and Information
Classical Keynesian
Consumers and producers are rational and take into account all the information they have at hand.
No wage illusion – Workers fully incorporate diminished value of real wages when making decisions, so inflation does not affect the labor market.
Money has no influence on real economic activity – If the Fed prints more money, people realize the money is devalued, so printing money does not create new goods and services.
Rational expectations – Government policy is less effective because people anticipate the effects in advance. For example, they adjust to inflation expectations when the Fed implements expansionary monetary policy.
Emphasizes limited information and limits to rational decision-making capacity when consumers and firms make decisions.
Wage illusion is possible – Workers are tricked by rising nominal wages when there is inflation, so inflation and employment outcomes are related to each other.
Money illusion is possible – Firms and workers do not immediately realize that new money is devalued, so they can be “tricked” into working and producing more.
Firms and workers have imperfect information, so their expectations do not fully counteract the intended effects of government policy.
Assessing Keynesian and Classical Economics
Now we have seen the two main branches of macroeconomics. Classical and Keynesian economists have very different ideas about how the economy works and in turn very different views on macroeconomic policy. Which is correct? Unfortunately, there really is no easy answer to that question. Both traditions have survived for a long time and have strong intellectual grounding, and so there are probably useful insights from both. But with such radically different approaches, how can we resolve these insights into a coherent whole?
On the other hand, when the economy is already at full employment, stimulating demand for goods and services further won’t increase output. If resources are already fully employed, stimulating demand even further will not generate more growth. In this case, supply is the only driver of growth, so classical economics makes more sense here.
However, the larger point in resolving the Keynesian and classical approaches has to do with the short-run and the long-run. Keynesian economics is about demand – making sure there is enough spending to purchase the output that the economy can produce. Classical economics is about supply – about our level of productive resources and how to grow them in the long-run.
In my view, this is the most coherent way to resolve the two. While classical economics is about long-run growth in productive resources, Keynesian economics is about the economy reaching its full potential in the short-run. That is, Keynesian economics is about short-run economic performance for a given level of resources. Classical economics is about long-run growth in this resource base.
Basically, the story of economic performance in developed countries is that it goes up and down in cycles, but the long-term trend is upwards. Keynesian economics is about managing the ups and downs. Classical economics is about the long-run upward trend.
If we think about it this way, there really is no dispute between the two. Which one is correct depends on what kind of question you ask or what kind of issue you want to address. Some issues, like short-run stabilization and performance, are more appropriately addressed by Keynesian models. Other issues, like long-term growth in productive capacity and resources, are better addressed by classical economics.
For long-run growth, the classical model is the appropriate model. While Keynesian economics might help us stabilize the economy and reach full potential in the short-run, there is no question that the only way for the economy to grow in the long-run is for there to be growth in productive resources and technology and skills. Spending does not generate long-run growth.
7.3: Economic Growth
As we discussed in the last section, the classical model is the appropriate model for studying long-run economic growth. Questions about whether existing resources are fully employed are short-run questions that are best addressed in the context of the Keynesian model. But, for discussing long-run economic growth, we need to understand how these resources themselves grow.
Sources of Long-Run Growth
In the classical model, the economy’s level of output is determined by the number of workers and by the production function.
We here assume full employment of resources, meaning that the economy is always at full employment 𝐿∗ and producing the full-employment level of output 𝑌∗. We’re not worrying about the short-run problem of whether the economy is actually at full employment.
Basically, either we need more people working or we need existing workers to become more productive. In this section, we will address public policy choices that can further these objectives.
But before we do this, let’s formalize these sources of growth a bit more. We first need to define two concepts. Productivity is output per worker.
Productivity = Output Labor Force
The labor force participation rate (LFPR) is the proportion of the total population that is in the labor force.
LFPR =Labor Force Population
When economists talk about economic growth, we are referring to growth in standard of living, which is output per capita.
Standard of Living = Output Population
Using simple math, we can express standard of living as follows:
Output Population=
Output Labor Force×
Labor Force Population
Substituting in definitions:
Standard of Living = productivity × LFPR
This equation makes good sense. If each worker produces 100 units of output (productivity) and 75% of the population is in the labor force (the labor force participation rate), then there are 75 units of output per person in the economy.
Now, we can always express products as the sum of growth rates. So, finally, by rewriting the equation above in terms of growth rates, we have:
%Δ Standard of Living = %Δ productivity + %Δ LFPR
force participation rate, which is the percentage of the population that works. We either need workers to be more productive or we need more people to work.
Before we move on, there is one final point to make. Note that population increases do not increase standard of living. While population growth increases the output produced by the economy as a whole, it does not increase standard of living. Although output rises, there are also more people, and so output per person (standard of living) does not rise.
We turn now to strategies that can promote growth in the labor force participation and in productivity, which are the ultimate drivers of long-run economic growth. These are strategies for increasing the economy’s productive capacity and ability to produce output.
Growth in the Labor Force Participation Rate
Remember that when we are discussing growth in the labor force participation rate, we do not mean more people in the population. What we are referring to is a higher percentage of the population that works and is in the labor force.
Fundamentally, there are two ways to create growth in labor force participation. Either the supply of labor (people willing to work) must rise, or the demand for labor (job openings) must rise.
What kinds of things can promote growth in the supply of labor? In other words, what kinds of public policy makes people willing to work more?
Increase in the number of women who work: Female labor force participation has been a primary driver of growth over the last few decades. Thus, eliminating discrimination is important – not just for groups being discriminated against, but for everyone. All society benefits when more people have the opportunity to be as productive as they can.
Lower income tax rate: When people can keep more of their earnings, this makes more people willing to work and raises the number of hours that people choose to work.
Limits to unemployment compensation: Unemployment compensation that is too generous or that lasts for too long might not give people good incentives to search for a new job quickly.
Now, what kinds of things can promote growth in the demand for labor? In other words, what kinds of things make employers create more jobs at higher wages?
More / better capital equipment: Increases in capital make workers more productive and, overall, increase the number of jobs. Importantly, some people mistakenly believe that capital and workers are substitutes – that more machines will result in workers being laid off. But, overall, data show that the effect is the opposite. Increases in mechanization require accompanying increases in the number of workers, and make these workers more productive. Overall, capital and labor are complementary to each other, not substitutes.
Improved education and training: A sure way to increase the number of workers that employers want to hire is for workers to have more skills, making it more worthwhile for employers to hire them.
Wage subsidies: Finally, for groups that historically have difficulty finding jobs, the government can outright subsidize their wages, making it more likely for employers to hire these workers. Many countries use this policy to help open job opportunities for handicapped people, for example.
The key point about all of these things is that growth in labor force participation is good for the whole economy. While it’s certainly good for individuals for them to work and be productive, getting more people into the labor force creates economic growth and is good for the whole economy.
Growth in Productivity
There is no question that getting more people into the labor force is good for economic growth. Countries where most people work are certainly richer than countries where lots of people don’t have jobs. But, ultimately, this is not a sustainable source of growth. Once an economy is at the point where most healthy adults are working, the labor force participation rate can’t be pushed much further. Thus, while having a high labor force participation rate is good, it cannot be a source of permanent growth. The only real source of permanent growth in standard of living is growth in productivity.
Increases in the size of the capital stock: More machines and tools, which make workers more productive.
Technological improvement: New production processes and innovations.
Growth in human capital: Improved skills and training of the workforce
We will treat each one of these in turn.
Increases in the Size of the Capital Stock
Increasing the size of the capital stock requires investment – business purchases of new plant machinery and equipment.
Fundamentally, firms undertake investment projects when the present value of the project exceeds the cost of the project. What kinds of public policies can stimulate firm investment in new capital, thus increasing productivity?
First are policies that directly impact the demand for capital among firms.
Lower taxes on corporate profits: A firm builds a new factory or buys a new machine when it earns sufficient profits from the project to justify the cost of the investment. Thus, business investments in new capital are greater in economies with low taxes on corporate profits – new investments are more profitable and attractive when the tax rate is low.
Investment tax credits: Another government strategy to promote investment in new capital is to allow firms to write the cost of these investments off of their taxes. The United States has been doing this for a long time.
In order to increase the supply of available funds, we need to increase savings in the economy. What kinds of things contribute to an increase in savings?
Higher life expectancy: People who expect to live longer, especially with long retirement periods, save more for the future.
Reduction in capital gains taxes: Capital gains taxes are taxes that people pay on the profits earned from their financial assets. Reducing these taxes will let people make more of a return from their savings, and thus stimulates savings.
Tax consumption rather than income: Many economists support increased use of sales taxes and reduced use of income taxes. The main difference is that an income tax taxes all
income earned, regardless of whether the income is saved or spent. But a sales tax only taxes the part of your income that you spend. Thus, sales taxes encourage savings and discourage consumption.
Lower government deficits: When the government borrows lots of money to finance its operations, this reduces the funds available for private investment by firms and raises the interest rate. Lower deficits would reduce the demand for funds and reduce the interest rate, thus making more funds available for business investments.
Overall, the first set of policies directly increase the demand for funds by making business investments more profitable. The second set of policies indirectly increase business investment by raising the supply of funds, consequently lowering interest rates and stimulating firm investment.
Again, keeping our eye on the ball, the point of these measures is to raise productivity – more capital means a more productive workforce, and higher productivity means a higher standard of living economy-wide.
Technological Improvement
The second strategy for growing productivity is to promote technological innovations. Note that, the way economists use the word, technology refers to new ideas and methods in production. A machine itself is not technology – a machine is capital. The technology is the idea or the innovation.
Direct spending on research and development: A lot of research and development is done by the government or in government-sponsored university settings. An example is biomedical research, a significant fraction of which is government-funded.
Subsidies and tax breaks for private research and development: While some research and development comes from government-funded projects, most has come from the private sector. The government can promote private-sector research by providing tax credits for funds that firms spend money on research and development.
Patent protection: A patent gives an inventor exclusive rights to sell his invention for some limited period. Without patent protection, firms that invent new things wouldn’t make much money from them because other firms would be able to copy them immediately. Patents give firms an incentive to invest in new innovations by ensuring that they have an exclusive right to sell their products.
Reductions in corporate profits taxes: Lower taxes on corporate profits increase the stream of potential profits that a company can earn from new innovations, which in turn incentivizes more innovations.
Growth in Human Capital
The final pillar for increasing productivity is growth in human capital, which basically describes the set of skills and knowledge that workers have. Better-trained workers increase productivity (output per worker) and shift the production function up. There are a few government policies that are important in promoting growth in human capital.
Direct funding for education: The US government provides free primary and secondary education, and also provides grants and heavily subsidized loans for college education. Again, this is good for all of society (not just the students themselves) because it increases the productivity of the workforce, promoting economic growth.
Tax credits for education and job training: Students in the US do not have to pay income taxes on money that they use to pay for education or job training programs.
The Government and Economic Growth
A lot of the discussion in this section seems to rationalize smaller government. Lower taxes on individuals promote work and savings. Lower taxes on businesses promote employment of more workers along with new investments and innovation. Furthermore, high government spending sucks up funds and crowds out private investment spending by reducing the pool of available funds. Is “the government that governs least the government that governs best”?
Like most things in economics, life isn’t this simple. The relationship between the government and economic growth is complicated. A government that is too large and sucks too much money out of the economy can crowd out private business and create disincentives for work and investment. On the other hand, the government does lots of things that directly stimulate long-run economic growth. For example, education and infrastructure development are both key for sustainable long-run growth. If we gut the government and stop investing in education and infrastructure, the result will be worse for economic growth, not better. The government also provides research and development funding for technological innovations and provides a legal system that protects private property rights. Both of these are critical to maintaining an environment conducive to economic growth.
Basically, the private sector can blow money and the government can blow money. In thinking about reducing the size of the government as a way to promote economic growth, we have to think about what we’re cutting and where the savings are going. If we cut waste and fraud and use the money to reduce taxes on capital investments and innovation, that’s good for the economic growth. But if we cut spending for education and roads and use the funds lower taxes for people who buy luxury yachts, that’s reduction in government that’s bad for economic growth.
7.4: Growth Dynamics
In the previous section, we outlined the concept of economic growth and we went through some public policy issues that are important for promoting economic growth. In this section, we will go into some detail about the mechanics of optimal economic growth, and in doing so, we will examine differences in growth performance internationally.
Capital Accumulation
A central pillar of economic growth is growth in the capital stock from year to year. As we said in the last section, growth in the capital stock requires investment in new capital. But let’s be a little bit more precise. If we let 𝐾𝑡+1 be next year’s capital stock, and we let 𝐾𝑡 be this year’s capital stock, then the evolution is as follows.
𝐾𝑡+1= 𝐾𝑡+ investment − depreciation
In words, next year’s capital stock is equal to whatever this year’s capital stock is plus what was added in new capital (investment) minus what wore out (depreciation). We are here defining investment as additions of new capital and depreciation as the decline in the existing capital stock due to wear and tear.
Think of the capital stock like water in a sink. The amount of water in the sink in one minute is equal to whatever is in there now, minus what drained out (depreciation) plus the new water that flowed in through the faucet (investment).
From here, we can see the conditions under which the capital stock is going to grow. When investment is greater than depreciation, the capital stock will grow from one year to the next. As long as the additions to the capital stock are greater than what wore out, then next year’s capital stock will be larger than this year’s. Going back to the sink analogy, if the amount of water that flows in through the faucet is greater than the amount that goes down the drain, then the water level will rise. Conversely, when investment in new capital is less than depreciation, then the capital stock will fall.
Capital Accumulation and the Steady State
a tractor. But a farmer that is already very capital intensive will not experience as much of an increase in output when $1000 worth of capital is added for him. Thus, the production function for different capital levels looks like this.
Now, we assume that economies save a certain fraction of their output. If we let this savings rate be 𝑠, then an economy’s savings is just a fraction of the output produced. In turn, savings is invested in new capital. In other words, the economy’s savings is its investment in new capital.
Now, as we outlined in the previous section, an economy’s accumulation of capital has to do with the relationship between investment in new capital and depreciation. Depreciation is assumed to be at a constant rate. For example, in the US the depreciation rate is around 4%. This means that 4% of the capital stock wears out each year. That is, the amount of depreciation is a constant, increasing function of the amount of capital.
Now, remember what we said in the previous section. When investment is greater than depreciation, the capital stock grows – the economy is adding more capital than what wears out, so the economy’s capital stock increases over time. This is like adding more water into the sink than what goes out the drain – the water level will rise.
Conversely, when investment is less than depreciation the capital stock shrinks – more capital wears out than what the economy saves and invests in new capital, so the economy’s capital stock decreases from one year to the next. This is like more water going down the drain than what goes in through the faucet – the water level will fall.
The diagram below shows this dynamic visually.
The steady-state in this diagram occurs when the level of capital is 𝑘∗. The steady state is the point where investment and depreciation are equal – what is added exactly replaces what wore out. When capital is exactly at this level, the capital stock is constant and does not change from year to year. Back to the sink analogy one last time, if what goes in through the faucet is exactly equal to what goes out through the drain, the water level in the sink is constant.
Convergence
The model of capital accumulation outlined in the previous section leads to an important implication. Any two economies with the same savings rates will eventually reach the same steady state. This property is known as convergence. Regardless of the initial levels of capital, any two economies with the same savings rates will eventually have the same level of capital and thus will enjoy the same standard of living.
In understanding why convergence happens, it is important to understand the difference between a country’s current standard of living and its rate of growth. A country can be poor, but growing fast. At the same time, a country could be rich but not growing very fast.
This is the key to convergence. When a country is poor and starts adding a little bit of capital, it grows rapidly – those first small investments in capital lead to rapid growth initially. But once a country is already very capital-intensive, these same investments wouldn’t create nearly as much growth. Using the example from earlier, $10,000 worth of equipment for a farmer who is using a horse will probably create huge growth in his output. But $10,000 of additional equipment for a farmer that is already highly mechanized will not lead to as much growth. This is how convergence happens – a country may start out poor, but growing fast. If this is the case, it will eventually catch up to a country that is richer, but whose growth is not as rapid.
Practically, countries like China and India – while poorer than the US – grow at a much faster rate than the rate at which the US and other developed countries grow. If this continues, these countries will eventually catch up to richer, developed countries. This is convergence. It doesn’t matter if you start out poor; any two economies with the same savings rates will eventually end up at the same steady state.
Optimal Savings: The Tradeoff between Present and Future
This is a critical point. Saving and investing does help a country grow more rapidly. But every time a society invests $1 million in new capital, this is $1 million that can’t be used for today’s consumption. Put very simply, there is a tradeoff between current consumption and future consumption. Saving a lot of your income will lead to rapid growth in the future, but it requires a lower standard of living today.
Because of this tradeoff, it’s not necessarily optimal to invest and grow as fast as possible. You can grow fast in the future by starving yourself today, but this is not balanced growth. Balanced growth, as economists use the term, requires harmonizing standard of living today with future growth. It’s not a good idea for a country to blow all of its income today and invest nothing for future growth. But it’s also not optimal in a long-term sense for a country to reduce its present standard of living to an extremely low level just so it can grow in the future. These competing interests have to be balanced. Precisely, balanced growth means that a country’s standard of living grows at the same rate as its investments in the future.
The overall point is that a country’s objective should not be to grow as fast as possible. There is an intermediate savings rate that maximizes the country’s welfare – allowing it to invest in the future and grow, but not saving so much that its current standard of living drops too low.
Growth in Poor Countries and the Development Trap
The idea of convergence seems to present a pretty simple answer for how a poor country should grow. Save and invest in the future – the country will grow rapidly, and eventually the standard of living will catch up with richer countries. But is life really this simple?
In reality, many poor countries have had trouble getting started. Remember that there is always a tradeoff between current consumption and future growth. According to the development trap hypothesis, an economy might be so poor to begin with that it can’t afford to pull any of its
resources away for investment in the future. If a country only earns enough income for its people to live at a subsistence level, it can’t afford to make substantial investments in the future. But this lack of investments in the future guarantees that the country will stay poor, and the cycle continues.
Cross-Country Differences in Growth Performance
How can we account for huge disparities in growth performance across countries? Comparing the US and Ethiopia isn’t very instructive, since the US started out significantly richer. But there are some puzzles. It’s hard to believe, but after World War II East Asian countries like South Korea and Singapore were as poor as sub-Saharan countries were. But the East Asian economies have had great success pulling themselves out of poverty – Singapore and South Korea, despite being poor 60 years ago, now have a standard of living comparable to the US. But man sub-Saharan countries have had very little success pulling themselves out of poverty and the development trap.
What explains why some countries grow fast and get rich, but other countries stay poor? More generally, if we believe the convergence hypothesis, how can we explain persistent, long-run differences in standard of living that don’t appear to be going away?
This is an extremely active area in economic research, but here are a few explanations that seem to come up a lot.
Differences in population growth rates: In many poor countries, population growth is very rapid. Output cannot grow as fast as population is growing, so standard of living for each person is falling. It is important to note that most of this population growth isn’t coming from women getting pregnant more often, but rather from medical advances that have lowered the infant mortality rate. Other factors for some poor countries are a cultural expectation that parents should have lots of kids to support them when they get older, or because they need children as labor at home. Some economists also talk about differences in access to birth control.
Political institutions: One strikingly consistent feature of countries with more successful growth performance is a stable government. Many persistently poor countries have unstable governments and insecure property rights. It is difficult to attract investment in new capital in a place with lots of wars, constant regime changes, or without a legal system that protects property rights.
the sea. Countries that are large, with their populations spread out, with rugged terrain or a bad climate, or that are landlocked, will face a lot more problems overcoming their infrastructure underdevelopment.
Public Policy on Growth in Poor Countries
Given that some countries have been much more successful than other countries in pulling themselves out of the development trap, what kinds of public policy choices can promote solutions?
Some countries have pulled themselves out of the development trap by force. A country that wants to industrialize quickly could just confiscate resources and use them for capital stock development. The Soviet Union did something like this in the 1930’s: an amazing transformation that turned the country from a poor, agrarian economy into a modern, industrialized economy in just a couple of decades. They did it by confiscating farming output, selling it, and using the proceeds to build factories. Lots of people starved to death in the meantime. This example illustrates the importance of a balanced growth path.
Also, it appears that poor countries that control their population growth rates have more economic success than countries with high population growth rates. For example, China maintains a strict one-child policy. On the other hand, some economists have suggested that this is a “chicken-or-egg” problem. While lower fertility rates might have a positive impact on economic development, it also seems to be the case that economic development and increasing income naturally reduces population growth on its own.
Finally, foreign aid can help, but it has to take the right form. The most effective foreign aid is aid that is directed towards capital development and other investments in the future like infrastructure and education. The only real way to help economies out of poverty permanently is to help them start growing on their own – then they’ll be able to save and invest some of their own income for even more growth, and the problem solves itself. As the saying goes, if you give a man a fish you feed him for a day, but if you give him a fishing pole, you feed him forever.
Slowdown in Worldwide Growth
Approaching convergence: Maybe our most rapid gains are already behind us and we’re getting closer to a steady state. It does seem to be the case that most innovations are “inventing around” something that already exists rather than new, big ideas. For example, we have better airplanes and cleaner power plants, but that’s different from building airplanes in the first place.
Changing composition of the labor force: The baby boomers who were born in the 1950’s started entering the workforce in the 1970’s. As a result, the workforce became composed of higher and higher proportions of younger and less experienced workers. This could account for part of the slowdown in growth.
Government regulation: The 1970’s saw a sharp increase in regulations, especially environmental and labor regulations that made firm production more costly. Of course, the air and water are much cleaner than they were back then. Maybe slower growth is the cost.
Oil prices: Even in real, inflation-adjusted terms, energy was extremely cheap in the 1970’s compared to the cost of energy today. But as demand rose, energy resources became more scarce, and the cost rose sharply. One big effect of this change is that much of the capital stock added before the 1970’s relied on intensive energy inputs, so much of this capital became obsolete once firms started worrying more about reducing energy usage.
Growth at the Steady State and the Very Long Run
Countries grow as they approach the steady state, and the previous section discussed some of the tradeoffs in determining how countries should choose their savings rates and how fast they should grow.
But, once the steady state is reached, the level of capital is constant from year to year. The key point is that increases in the size of the capital stock can only increase standard of living so far. There is some optimal level of capital and, once this capital stock is reached at the steady state, there is no more growth that results from continued capital accumulation. New investments just replace depreciated capital from year to year.
To reiterate, the only factor that can create persistent, permanent growth in standard of living is technological progress. Growth in capital can get us so far – but once we’re at the optimal level of capital, we need new ideas and new production techniques to keep growing.
Economists sometimes distinguish between three time periods in order to think about the sources of growth over different time horizons.
In the short run, capital is fixed. The way to promote high standard of living in the short-run is to ensure that existing resources are fully employed. This is mostly what Keynesian economics is about.
In the long run, capital can change. The way to promote long-run growth in standard of living is optimal savings and investment in new capital. But technology is regarded to be fixed in the long run. That is, we can invest in new capital, but with the same production processes.
In the very long run, technology changes. That is, we can not only add capital, but we can also develop new innovations and production processes.
Why are we so much better off than people were 100 years ago? Most of it isn’t because more people are working or people are working harder. And it’s not even because there are more machines and tools. At the end of the day, it’s new technologies and ideas that have driven the increases in our standard of living; it’s the person who thought up the idea for the refrigerator or the vacuum cleaner or the iPod.
New technologies are the reason that we are better off than our grandparents, and it will be the reason that your grandchildren are better off than you are. Technology is the real driver of very long-run growth.
This suggests that, for a country to have real vision and foresight about the future 50 or 100 years down the road, society needs to keep its eye on new innovations. It’s easy to get lost in day-to-day problems and to put things 50 and 100 years down the road on the back burner, but you have to keep your eye on the prize. The reason we’re better off now than we were 100 years ago is that someone back then was thinking about new ideas and innovations.
research and development are strongly pro-growth, especially growth looking 50 or 100 years into the future.
Endogenous Growth and Non-convergence
Some economists have suggested that the concept of convergence doesn’t really describe the way the economy works. Convergence relies on diminishing marginal returns in the production function – economies that grow slow down as they continue to grow, and so poor countries will eventually catch up to rich countries.
But suppose that the production function looked like this – with increasing returns rather than diminishing returns.
In a model like this, there is no convergence. Growth creates even more growth, and the process just takes off. A model with increasing returns in the production function can easily explain differences in growth convergence across countries. The riddle was that countries should converge to the same steady state eventually – but if there is no steady state, then there is no reason to expect convergence.
