layout: true background-image: url(figs/tcb-logo.png) background-position: bottom right background-attachment: fixed; background-origin: content-box; background-size: 10% --- class: title-slide .row[ .col-7[ .title[ # Principles of Macroeconomics ] .subtitle[Growth] .author[ ### Dennis A.V. Dittrich ] .affiliation[ ] ] .col-5[ ] ] --- ### GDP Data is only available after the fact ...sometimes long after the fact .row[.col-6[ ![](fig04/unnamed-chunk-1-1.png)<!-- --> ] .col-6[ ![](fig04/unnamed-chunk-2-1.png)<!-- --> ]] --- # The Classical Growth Model .col-7[ * The Classical growth model is a model of growth that focuses on the role of capital accumulation in the growth process * According to the Classical growth model, the more capital an economy has, the faster it will grow * Classical economists focused their analysis and their policy advice on how to increase investment because saving leads to growth ] .center[ Savings `\(\rightarrow\)` Investment `\(\rightarrow\)` Increase in capital `\(\rightarrow\)` GROWTH ] --- ## Diminishing Returns and Population Growth .row[.col-7[ <img src="img04/2604.jpg" width="100%" /> ] .col-5[ * Diminishing marginal productivity of labor causes per capita income to decline as labor supply increases * As output per person declines at some point output is no longer sufficient to feed the population ]] --- ## Diminishing Marginal Productivity of Capital .col-7[ * The predictions for the long term were incorrect because increases in technology and capital overwhelmed diminishing marginal productivity * The focus then became the law of diminishing marginal productivity of capital, not labor * As capital grew faster than labor, capital would become less productive and lead to slower and slower growth * Eventually the per capita growth would stagnate ] --- # The Convergence Debate .row[.col-6[ The Classical growth model leads to the idea of convergence * The **convergence hypothesis** is the hypothesis that per capita income in countries with similar institutional structures will converge toward the same level of income per person ] .col-6[ * The U.S. will grow slower than developing countries because the marginal product of capital is higher in developing countries * This difference causes capital investment flows and %production to move from the U.S. to developing countries * As of today the predictions of convergence have not come true * Economists have several explanations for why convergence has not taken place: * Lack of factor mobility * Differing institutional structure * Incomparable factors of production * Technological agglomeration effects ]] --- class: practice-slide # 1. .col-8[ Which countries are likely to grow faster: Countries doing “cutting-edge” growth or those doing “catch-up” growth? ] ??? Catch up: It’s often easier to just imitate those who are doing it right already. --- # Catch-up vs Cutting-edge Growth .col-7[ * Catch-up growth takes advantage of ideas, technologies, or methods of management already in existence focuses on capital accumulation * Cutting-edge growth developing new ideas focuses on developing new technology for resources. ] --- class: practice-slide # 2. .col-8[ Consider the following three countries that produce GDP this way: `$$Y=5\sqrt{K}$$` ``` Illia: K = 100 machines Caplania: K = 10000 machines Hansonia: K = 1000000 machines ``` What will GDP (Y) be in these three countries? Hansonia has 10,000 times more machines than Ilia, so why isn’t it 10,000 times more productive? ] ??? Ilia will produce 50 units of output. Caplania will produce 500 units of output. Hansonia will produce 5,000 units of output. Hansonia has 10,000 times more machines than Ilia, but there are diminishing returns to capital. This force of diminishing returns is very powerful, so extra capital really isn’t worth all that much. --- # The Solow Model and Catch-Up Growth .col-7[ Total Output, Y, of an economy depends on: * Physical capital: K * Human capital: education x Labor = eL * Ideas: A This can be expressed as the following **production function**: `$$Y= F(A,K,eL)$$` For now, ignore changes in ideas, education, and labor so that A, e, and L are constant. The production function becomes: `$$Y=F(K)$$` * If L is constant, then increases in K mean more capital per worker * `\(MP_K\)` : marginal product of capital : The additional output resulting from using an additional unit of capital. * `\(MP_K\)` diminishes the more capital is added. ] --- # The Solow Model and Catch-Up Growth .col-8[ <img src="img04/c26-2.jpg" width="100%" /> ] --- class: practice-slide # 3. .col-8[ Consider the data in the previous question: ``` Illia: K = 100 Y = 50 Caplania: K = 10000 Y = 500 Hansonia: K = 1000000 Y = 5000 ``` If 10% of all machines become worthless every year (they depreciate, in other words), then how many machines will become worthless in these three countries this year? Are there any countries where the amount of depreciation is actually greater than GDP? ] ??? Ilia: 10 machines Caplania: 1,000 machines Hansonia: 100,000 machines In Caplania and Hansonia, depreciation is actually larger than GDP: The number of machines wearing out is more than the economy’s entire output. --- class: practice-slide .col-8[ # 4. What is the opportunity cost of investing in capital? ] --- # Investment is forgone Consumption .col-9[ ![](img04/c26-3a.jpg) ] --- class: practice-slide # 5. .col-8[ No country makes only investment goods like machines, equipment, and computers. They also make consumer goods. ``` Illia: K = 100 Y = 50 D = 10 Caplania: K = 10000 Y = 500 D = 1000 Hansonia: K = 1000000 Y = 5000 D = 100000 ``` Let’s consider a case where the countries in the earlier question devote 25% of GDP to making investment goods (so `\(\gamma = 0.25\)`). What is the amount of savings in these three countries? In which countries is Investment < Depreciation? When is Investment > Depreciation? ] ??? Savings: Ilia: 12.5 units of output Caplania: 125 units of output Hansonia: 1,250 units of output In Ilia, investment is greater than depreciation, as in question 2. In the other two countries, depreciation is greater than investment. --- class: practice-slide # 6. .col-8[ One of the key ways China succeeded in generating growth is through massive capital accumulation. Does the Solow growth model help to explain why growth is now starting to slow? ] ??? --- .row[ .col-6[ ## Capital Growth Equals ### Investment minus Depreciation * Capital is output that is saved and invested. * Let `\(\gamma = 0.3\)` be the fraction of output that is invested in new capital. * Depreciation: amount of capital that wears out each period * Let the depreciation rate `\(\delta\)` be the fraction of capital `\(K\)` that wears out each period. As capital increases, * depreciation increases at a constant rate of `\(\delta\)` * output increases at a diminishing rate. * Because investment is a constant fraction of output, at some point depreciation will equal investment. * The capital stockand output will stop growing. ] .col-6[ .col-10[ ![](img04/c26-3b.jpg) ![](img04/c26-3c.jpg) ]]] --- class: practice-slide # 7. .col-8[ After World War II, a lot of France’s capital stock was destroyed, but it had educated workers and a market-oriented economy. Do you think the war’s destruction increased or decreased the marginal product of capital? ] ??? The war probably increased the marginal product of capital: One more machine was worth much more in post–World War II France than in pre-World War II France. --- ## The logic of diminishing returns largely explains why... .col-7[ The Chinese economy is able to grow so rapidly. * It turned toward markets which increased incentives. * The capital stock was low. * The MP was high. `\(\rightarrow\)` China will not be able to achieve these high growth rates indefinitely. Bombing a Country Can Raise Its Growth Rate: * Much of the capital stock was destroyed during WWII --- so MP was high. * After the war, Germany and Japan had much higher growth rates than the U.S. as they caught-up. ] --- ## The Solow Model --- Details and Further Lessons .col-7[ What we know so far: * If Investment > Depreciation `\(\rightarrow\)` K and Y grow. * If Investment < Depreciation `\(\rightarrow\)` K and Y fall. * If Investment = Depreciation `\(\rightarrow\)` K and Y are constant. Two important conclusions: 1. Steady state equilibrium occurs when investment equals depreciation. 2. When K is in steady state equilibrium, Y is in steady state equilibrium. ] --- ## The Solow Model ### and an Increase in the Investment Rate .row[ .col-6[ What happens when the fraction of output that is saved and invested increases? `$$\uparrow\gamma \rightarrow K \rightarrow \uparrow Y$$` Conclusion: an increase in the investment rate increases a country's steady state level of GDP: ![](img04/c26-03a.jpg) ] .col-6[ Countries with higher rates of investment will be wealthier: ![](img04/c26-03.png) ]] --- class: practice-slide .col-8[ # 8. What is the opportunity cost of investing in human capital? ] --- # Investment and Accumulated Capital .col-7[ * Capital is much more than physical machines and includes: * **Human capital** are skills that workers gain from experience, education, and on-the-job training * **Social capital** is the habitual way of doing things that guides people in how they approach production * Although capital is a key element in growth, capital accumulation does not necessarily lead to growth * Capital may become obsolete ] --- # Human Capital Investment Pays Off ![](fig04/unnamed-chunk-5-1.png)<!-- --> --- class: practice-slide # 9. .col-8[ Apply the Solow model to a chef ’s skill at cooking. ] ??? It takes a long time to learn to be a good cook, and learning is like “investment in human capital.” If you don’t use your cooking knowledge very much, it will wear out: Cooks need to stay up to date by reading the latest recipes and by reviewing old favorites. Also, there may be diminishing returns: After reading the hundredth cookbook, there may just not be that many good new ideas for a cook to learn. --- class: practice-slide # 10. .col-8[ What determines the growth rate of an economy in the very long run? ] --- ## Better Ideas Drive Long Run Economic Growth .row[ .col-5[ Technological knowledge: * Is a way of getting more output from the same input (an increase in productivity). * We represent this in our model by letting A stand for ideas that increase productivity. Now the production function is: `$$Y=A\times F(K)$$` #### Technological knowledge / better ideas are the key to long run economic growth Solow estimated that better ideas are responsible for 3/4 of our increased standard of living. ] .col-7[ ![](img04/c26-02.png) ]] --- # Solow and the Economics of Ideas .col-11[ New ideas results in long run economic growth. ![](img04/c26-5.jpg) ] --- ## Solow Growth Model: New Growth Theory .col-7[ * Modern growth theory is named new growth theory * Technology is recognized as an important ingredient in growth * New growth theory is a theory that the emphasizes the role of technology rather than capital in the growth process ] .center[ Tech Advance `\(\rightarrow\)` Investment `\(\rightarrow\)` Further Tech Advance `\(\rightarrow\)` GROWTH ] .col-7[ Technological advance is the result of what the economy does, it: * Invests in research and development * Makes advances in pure science * Works out new ways to organize production * The common knowledge aspect of technology creates positive externalities which is a key to growth * **Positive externalities** are positive effects on others not taken into account by the decision maker ] --- class: practice-slide # 11. .col-8[ Many inventors decide that patents are a bad way to protect their intellectual property. Instead, they keep their ideas a secret. Trade secrets are actually quite common: The formula for Coca-Cola is a trade secret, as is Colonel Sander’s secret recipe. What is one major strength of keeping a trade secret rather than applying for a patent? What is a major weakness inherent in going down the trade secret route? ] ??? One major strength is that a corporation never needs to tell its secret. By contrast, when a patent expires, everyone in the world will know exactly what was in the patent application form, since it’s a public government record. One major weakness of trade secrets is that if a competitor finds out the secret or creates it independently, the corporation can’t go to the government and ask it to prevent the competitor from using the idea. But a government will enforce a patent. So businesses face an important trade-off when they decide whether to request a public, government-enforced patent or to just keep a private, unenforceable trade secret. --- ## Research and development is investment for profit .col-7[ All kinds of people come up with new ideas. * Business culture and institutions are also important. * Appreciation of entrepreneurs is a relatively recent (identified) phenomenon. Institutions that are especially important: * Commercial settings that help innovators to connect with capitalists * Ideas without financial backers are dead. * Intellectual property rights * New processes, products, and methods can be copied by competitors. * Patents grant temporary monopoly. But they can slow down the spread of technology. * A high-quality education system * Important at all levels of education. * Universities generate basic and applied research. ] --- ## Spillovers, and why there aren't enough good ideas .row[ .col-6[ * Ideas are non-rivalrous. * Ideas can be used simultaneously. Use of an idea by one individual does not mean less of the idea available to someone else. * The spillover (or "diffusion") of new ideas generates widespread economic growth. * Implication: Spillovers mean that the generator of the idea doesn't get all of the benefits. Result? Too few ideas are produced. ] .col-6[ ![](img04/c26-6.jpg) ]] --- ## Government's Role in the Production of New Ideas .col-7[ * Ideas in science have many applications so spillovers can be large. * Problem: Even if the social benefits are large, the private benefits can be small. * Solution: Subsidize the production of new ideas or give tax breaks for R&D expenditures. * Both shift the MC of R&D down. * Large spillovers to basic science suggest a role for government subsidies to universities. Especially those parts of the universities that produce innovations and the basic science behind those innovations. * Universities produce scientists. Most scientists were trained in government-subsidized universities. ] --- class: practice-slide # 12. .col-8[ When will people work harder to invent new ideas: when they can sell them to a market of 10,000 people or when they can sell them to a market of 1 billion? Does your answer tell us anything about whether it’s good or bad from the U.S. point of view for China and India to become rich countries? ] ??? People would rather sell to a market of 1 billion: So if India and China become rich, people around the world will be trying to invent new products for Indians and Chinese to buy. There will likely be many idea spillovers that help people living in other countries. --- # Market Size and Research and Development .col-7[ * Innovations like pharmaceuticals, new computer chips, software, and chemicals require large R&D expenditures. * Companies will avoid investing in innovations with small potential markets. * Larger markets mean increased rewards (thus incentives) for R&D. * As the world market grows some companies get bigger and will increase their R&D investments. ] --- # The Future of Economic Growth .col-7[ A (ideas) = Population x Incentives x Ideas/Hour `\(\uparrow\)` population `\(\rightarrow \uparrow\)` number of people with new ideas At the moment, much of the world is poor: * thousands of potentially great scientists are laboring in menial jobs. ] .col-8[ As the world gets richer: `\(\uparrow\)` production of ideas `\(\rightarrow\)` everyone benefits ] --- ## ~~"The rich grow richer and the poor grow poorer."~~ .col-7[ In the recent past, did the rich countries grow more quickly or more slowly than the poor countries? ] ### The Solow Model and Conditional Convergence .row[ .col-5[ Among countries with similar steady state levels of output (i.e. with similar institutions and available technology), poorer countries tend to grow faster than richer countries, and so converge in income. The Solow model predicts that a country will grow faster the farther its capital stock is below its steady state value. ] .col-7[ ![](img04/c26-04.png) ]] --- # Growth Policies .col-7[ General policies that are good for growth include: * Encouraging saving and investment * Formalizing property rights and reducing %bureaucracy and corruption * Providing more of the right kind of education * Promoting policies that encourage technological innovation * Promoting policies that allow taking advantage of specialization ]