Lecture Outline – Growth, Capital Accumulation, and the Economics of IdeasA. The Solow Growth Model and Catch-up Growth1. What is a production function? What are the inputs to the production function? What is the output?a. Production function: Y= F(A,K,eL)b.Physical capital: Kc. Human capital: e X Ld.Ideas (productivity): Ae. We assume A, e and L are constant: Y=F(K)f. Properties of F? More K. more Y but at a diminishing rate: Y=sqrt(K)2. What simplifying assumptions are used to derive the production function in the Solow Model?3. What are the properties of Solow’s simplified production function? Give an ex-ample of a functional form that embodies these properties.4. What does the term “diminishing returns” mean?a. First tractor that helps produce ten units of output but the second tractor cat run as often due to the first tractor so it doesn’t produce as much. Thirdtractor, produces even less etc...b. According to the model, if a country starts with a relatively small stock of capital, then it should grow slowly or rapidly? Explain.1. Small capital stocks should grow rapidly due to diminishing re-turns to capital2. China: prediction: China will grow slow as K accumulates. China adopted more capitalist institutions, improved incentives, and then has grown very rapidlyc. What should happen to a country’s growth rate as it accumulates more capital?1. Conditional Convergence: countries can grow rapidly toward their GDP per capita. Growth rate slows as K (capital) accumulatesd. What is meant by “catch-up growth?”1. Conditional Convergence: the tendency (among countries with similar steady-rate levels of output) for poorer countries to grow 1faster than richer countries and thus for poor and rich countries to converge in income.e. Explain why bombing a country can increase its growth rate.1. Huge amounts of capital stock are destroyed so these countries have a low capital stock but fundamental convergence GDP per capita rate was high so capital stock was very productive and they can invest a lot. Growth rates are high2. As capital accumulates, growth rates fall5. The model assumes there are two things a country can do with the output that it produces. What are those two things?a. Investment and Consumptionb.Output goes on Y axis, Capital goes on X axisc. What assumption is made regarding the percentage of output that a country saves? Invests? What is the relationship between saving and investment?1. People will save and invest at a constant rate. People take a con-stant fraction of output and save and invest a constant fraction. There is a savings rated. Explain how the investment curve is related to the production function.1. Investment curve = %of investment x sqrt(K)6. What is depreciation? How is depreciation related to the capital stock?a. Capital depreciates: Ex. a care gets old and needs workb.Depreciation is a constant fraction of the capital stockc. Under what condition is the capital stock growing?1. When investment is bigger than depreciation and when you are in-vesting more capital than is depreciatingd. Under what condition is the capital stock shrinking?1. When depreciation is increasing: more capital is depreciating everyperiod than you are investing2. What is meant by the “steady state?” At the steady state, what is happening to the growth of the capital stock?2a. Where investment is = depreciation. Capital stock is con-stant. You are investing every period to replace the capital which has depreciated7. What is meant by steady state output? How is output measured in the Solow growth model?a. Output where investment = Depreciation. GDP per capitab.Model of GDP per capita. Has to do with the savings rate. If the savings rate is higher there will be a bigger steady state outputc. You will grow when you are below your steady state capital stock8. According to the model, can capital growth alone be responsible for long-run growth? Explain. Can increases in human capital drive long-run economic growth? Explain.a. Growth slows down. Capital stock will grow so large that all of the invest-ment will be used to maintain capital stock. This is when growth stopsb.Model tells us that capital growth cannot be responsible for long run growthB. Comparative Statics 1. Key to the model is the steady state where investment = depreciation2. How does a change in the savings rate affect economic growth? Explain (the fol-lowing questions will guide you through the process).a. Y = A(sqrt(K)) more output from the same capital stock. A represents ideas(productivity)b.Better ideas increases outut. More output means more investment. Capital accumulation increases GDP per capita. Increase investment until invest-ment = depreciationc. Does a change in the savings rate affect the production function?1. Yesd. Does a change in the savings rate affect the investment curve?1. Yese. Does a change in the savings rate affect the depreciation curve?1. Yes3f. Does a change in the savings rate lead to capital accumulation? Explain.1. Yesg. Does a change in the savings rate affect GDP per capita?1. Yesh. What impact do incentives and institutions have on investment rates? Give anexample of an incentive that would encourage more investment. Give an ex-ample of an institution that would encourage more investment.3. How do new ideas affect output given the same level of capital stock? Explain (the following questions will guide you through the process).a. Better ideas lead to more productivity which increases output. You can get more output from the same capital stock.b. Do new ideas affect the production function?1. Yesc. Do new ideas affect the investment curve?1. Yes. More output means more investment. We get capital accumu-lation because investment is greater than depreciationd. Do new ideas affect the depreciation curve?e. Do new ideas lead to capital accumulation? Explain.1. Yesf. Do new ideas affect GDP per capita?1. Yes. GDP increases.4. What is meant by “cutting edge” growth?a.C. The Economics of Ideas1. What institutions are important for the development of ideas?a. Ideas for increasing output are primarily researched, developed, and im-plemented by profit-seeking firms. Key to increasing Research and devel-opment are incentives and institutionsb.Institutions that increase R&D: a commercial setting that helps innovators connect with capitalists1. Ideas without financial backers are dead42. American culture supports entrepreneursc. Intellectual property rights