Assignment for \"The Solow Model Unleashed: Understanding Economic Growth\" Based on Columbia CaseWorks 130304 1 Assignment Introduction & Algebra This case and assignment is intended to enhance your understanding of the Solow model and to see how the Solow framework can be used to better understand the different growth experiences of France and the United States in the mid-20th century. Specifically we're going to try to better understand why France grew so quickly and why growth slowed down and never fully caught up to that of the United States. We will then extend our model to contemplate how economic growth in China in the future will depend on a different number of factors. There's going to be some algebra at the beginning here in order to get to the key production function for the new model. In class we simply looked at capital and labor being key variables. In this assignment we're going to make our model a little richer (i.e., more complex) than what we did in class. In particular, here we're going to allow there to be a difference between the population and the labor force. (I.e., not everyone in the country is going to be working.) We're also going to allow for population growth. So stick with me through the algebra, and then we'll get the key formula that you'll need to use. Here we go: As usual, there's a production function in our economy that's a function of technology (A), capital (K), and labor (L). Specifically, let's assume that all economies we are talking about have the production function: Yt = At Kt0.3 Lt0.7 (1) where the subscript t means that all the variables are being measured in year t, and Yt is total production (output), At is total factor productivity (TFP), Kt is the amount of capital, and Lt is the amount of labor. This relationship implies that total output is increasing in TFP, capital inputs, and labor inputs. It also implies that total output doubles if capital and labor inputs both double. In addition, there are diminishing returns to capital and to labor individually1 . (This is exactly as we discussed in class.) Now, let's introduce the fact that not everyone in the population is working. To handle this, let's do some t simple algebra on equation (1). First, note that just by definition of exponents L0.7 = LL0.3 . (If you didn't t t remember this from high-school algebra, you can trust me. It's true.) Therefore we can re-write equation (1) as: \u0012 \u0013 Lt Yt = At Kt0.3 L0.3 t \u0012 \u00130.3 Kt Yt = At Lt Lt 1 That is, if you hold labor constant and double the amount of capital, the total amount of output increases but does not double. 1 2/5 Now we simply divide both sides by the population in year t: Yt = At Popt \u0012 Kt Lt \u00130.3 \u0012 Lt Popt \u0013 (2) This equation is now a formula for output per person (on the left) as a function of productivity, capital-perworker, and employment-to-population ratio. In terms of growth rates, this becomes: %(Yt /Popt ) = %At + 0.3 %(Kt /Lt ) + %(Lt /Popt ) (3) Or, in words: Output per person growth = TFP growth + 0.3 Capital per worker growth + Employment-to-population ratio growth This equation tells us that growth in output per capita can be broken down into either TFP growth, changes in capital-to-worker ratio, and changes in the employment-to-population ratio. As you'll recall from class, capital changes over time according to the following relationship: Kt+1 = (1 )Kt + It (4) where is some constant depreciation rate and It is the level of investment in year t. This states that capital at t + 1 equals the non-depreciated capital from t plus investment at t. This assignment includes an Excel workbook that will help you simulate economic growth in the Solow model. As you'll see, the model assumes that the following parameters are constant (for any specific country): depreciation rate (), population growth rate (%Pop), employment-to-population ration (L/Pop), investment rate (I/Y , which we called in class), and the TFP growth rate (%A). The workbook uses the capital accumulation equation (4) and the definition of production per capita (2) in order to plot the level of output per capita over time in two countries under different assumptions. Because the model is very simple, we won't take the quantitative output too seriously, but rather will use it to qualitatively compare countries. In particular, we will pick reasonable starting points, but then primarily focus on how the level of output per capita evolves over time qualitatively. Note that in the figure in the workbook, the y-axis, which plots production per capita, is on a logarithmic scale, which means that a straight line corresponds to a constant percent rate of growth. 2 Set Up This section will help you set up the spreadsheet that will be needed to analyze this case. You need not turn in anything for this section, but you will need to complete these steps in order to answer the other questions on the assignment. 1. The \"Inputs and Figures\" tab is where you enter (and later will change) the parameters of the model in order to analyze various scenarios. To begin with, let's enter some initial values in the US: Population in 1950: 150 (in millions, but just enter it as \"150\") Stock of capital in 1950: 10,000 Total factor productivity in 1950: 10 Population growth rate: 2% 3/5 Employment-to-population ratio: 40% Investment rate in 1950: 30% Total factor productivity growth: 0% (We will change this later) Depreciation rate: 5% Set France to be identical to the US in 1950 with the following exceptions: France's population in 1950 was 45 million. France's capital stock in 1950 was 250. France's employment-population ration in 1950 was 50%. Exhibit 2 in the case provides data on what the actual situation was in France and the US in 1950. In particular it shows that output per capita in France was 54% of that in the US in 1950 and that (K/L)0.3 in France was 44% of that in the US. To make sure that we're starting our model in the right place, calculate those two ratios in the model for 1950. You should see that the starting point for our model generally consistent with the real-world data. 2. Next turn to the \"US Projected Growth\" tab. You'll see that the first few cells in the 1950 row are filled in for you automatically based on the parameters you just entered. Using the equations from the Solow model, and the parameters you just entered, fill in the missing cells in the row corresponding to 1950. Note 1: To practice good spreadsheet hygiene you should always reference the parameter cells in your formulas; never type in the parameters directly. We will be changing some of these parameters later, and you don't want to have to go back and re-do all of your formulas. Note 2: Most of the calculations should be very straight forward. For total output you'll need to remember that the production function we're using is Yt = At Kt0.3 Lt0.7 . 3. Now that you've figured out all of the values in 1950 (the starting point), let's fill in the rest of the rows for the US. Based on what happens in 1950, you should be able to figure out what happens in 1951. Then from 1951 you can get 1952. Etc. For example, the population in 1951 is just going to be the population in 1950 times the population growth rate you put in the parameters. Note 1: Again, never type numbers into your formulas directly; always just reference the parameters in the \"Inputs and Figures\" tab. Note 2: The \"US Partial Answer\" tab contains some of the answers, so you should check your work using the numbers there. 4. Now repeat steps 2 and 3 for France in the \"France Projected Growth\" tab to fill in the entire table on that tab. 3 Questions for analysis For each of the sub-parts below, please write up a brief response. Feel free to include graphs as appropriate. To show understanding you should justify your responses with references to the workings of the Solow model; don't just quote numbers that the spreadsheet spits out. (I.e., the spreadsheet is a tool to help you better understand how the Solow model works, not an end unto itself.) 1. Short-run growth dynamics. Grandpa Frank used to say, \"Out of the ashes of destruction have risen the wings of opportunity.\" We'll use the following questions to see if we agree with this statement: 4/5 (a) (4 pts) First let's think theoretically about the model. (I.e., without referencing the details of the spreadsheet.) Think about the growth in capital-labor ratio in France. Given that France suffered a large drop in capital-labor ratio during WWII, what does the Solow model say about what growth should be in the 1950s? (I.e., fast? slow? can't tell?) What should happen to that growth rate over time and why? Would you expect the growth in France in the 1950s to be sustained forever? Why or why not? (b) (4 pts) If France had not suffered a large drop in its capital-labor ratio during the war, what would we expect to see about its growth rate? Why? What does this tell you about the main reason for such strong growth rates in the years right after the war? 2. Long-term growth dynamics. Following the war, Grandpa Frank was very bullish on the potential of the French market. He saw a country that would not only experience short-term growth through its rebuilding effort, but also eventually catch up to the standard of living of the United States. As Exhibit 1 in the case clearly shows, this prediction never quite materialized. This question will help you understand what actually happened. (a) (4 pts) Based on the initial setup parameters in your spreadsheet, what is the steady-state level of output-per-capita in the US? What is it in France? If they are the same, why? If they are different, what is causing them to be different? (b) (4 pts) Based on the initial setup parameters in your spreadsheet, what is the eventual year-overyear growth rate in output-per-capita in the US? What about France? What causes these to be the same or different? (Be sure to understand the difference between levels (previous question) and growth rates (this question).) (c) (4 pts) So far, the graph (of output-per capita over time) that we've produced doesn't really look at all like exhibit 1 from the case (the real data). Since most of our initial parameters are correct, the main reasons our graph looks wrong is that we're assuming a 0% growth rate in productivity (a.k.a. TFP). To fix this, set the TFP growth rate for both countries to 2%. With this, what happens to the steady-state level of output-per-capita in the US and in France? What about the growth rate in output-per-capita in the two countries? Do these lines look closer to the real data from Exhibit 1? If it's still not quite right, what's wrong about it? (d) (4 pts) Let's further improve our model by examining the role of the labor market. France's labor markets have evolved very differently than those in the United States in the decades following WWII. While the employment-to-population ratio was significantly higher in France in 1950, it declined steadily afterward and now sits much lower than the United States' level (see Exhibit 2 in the case). To model this, adjust your spreadsheet so that the US employment-to-population ratio is constant, but in France: From 1950-55 the employment-population ratio in France is 125% of that in the US From 1956-75 the employment-population ratio in France is the same as in the US From 1976 onward the employment-population ratio in France is 75% of that in the US Show the resulting graph of US and French output-per-capita. Does this graph look closer to the real data? Do these changes in employment-population ratio effect the long-run level or the long-run growth rate of output-per-capita or both? 5/5 3. Synthesis. (5 pts) Use what you have learned to analyze the performance of Durabuild Inc. I.e., what was the one main reason for the strong growth of the business in the 1950s and 1960s? What is the main reason for the slowdown in growth rate in later years? What did Grant Stone's grandfather miss in forecasting future growth (or in assuming that the high growth would continue forever)? 4. Application to China. China is much more different from the US today than France ever was. Not only is its initial capital stock (K0 ) much lower, but there are many other important differences as will be discussed below. For this question, we're going to adapt our model to examine differences between the US and China. To do this, adapt the spreadsheet (or make a copy) so that \"France\" is now labeled \"China\" everywhere. (a) (4 pts) France and the US have always had very similar levels of TFP. This is not true when comparing China and the US, where China has often had a much lower level of TFP. Let's examine what the impact of these differences in TFP may cause. In the model, pick some reasonable starting parameters for the US. Then make China have the exact same starting parameters as the US with two exceptions: (1) China starts with a much lower level of capital (K0 is smaller), and (2) China's initial TFP (A0 ) is smaller. (Pick values for K0 and A0 for China to input into your spreadsheet that match these assumptions.) Over the very long run (i.e., in steady state), how does China's level of output-per-capita compare to the US in the model? How do their growth rates compare? What is causing the difference and how might this help explain why some countries seem stuck being poorer than others? (b) (4 pts) Another big difference between the countries is that China's investment rate is dramatically larger than that of the United States, and this very high investment rate may be maintained for many years to come. Let's do an experiment to test the effect of a higher investment rate: adjust the parameters so that the US and China have identical parameters except for the investment rate. Make the investment rate in China much higher. With this, how do China and the US's level of output-per capita compare over the long run? How do their growth rates compare? Explain conceptually why it makes sense that they are the same or different. (c) (4 pts) Until very recently (2015), China had a \"one child\" policy that made its population growth rate much lower than that of the US. Let's do another experiment to test the effect of this: Assume that the employment-population ratios don't change, and that the two countries are identical except that the population growth rate in China is lower than the US. Now how do China and the US's level of output-per capita compare over the long run? How do their growth rates compare? Explain conceptually why it makes sense that they are the same or different. ID#130304 CU81 PUBLISHED ON NOVEMBER 7, 2018 The Solow Model Unleashed: Understanding Economic Growth BY NICOLAS VINCENT * AND PIERRE YARED Background DURABUILD: SEEKING NEW INSIGHTS The peeling Durabuild Inc. sign, desperately in need of a touch up, caused Grant Stone to cringe slightly as he entered the company's St. Louis headquarters. He had mixed feelings about the meeting he had scheduled with the company's presidenthis father, Frank Stone Jr. Grant's agenda was a tough one: to try to get a better sense of what he viewed as his father's (and his grandfather's) less-than-perfect business acumen. In the weeks since Grant had left his analyst position in New York to join the family's firm as vice president for business development, he had become concerned about the company's future and had also grown curious about details of its early growth. Durabuild Inc. was a diversified, family-held business in the construction industry, with significant interests in France as well as in the United States. The president's spacious corner office looked out over the faded glory of an industrial brick skyline. Grant's father, finishing up what appeared to be a customer call, silently motioned for his son to settle into the most comfortable spot in the rooman overstuffed, butter-soft, leather armchair. A large-scale aerial photo of Durabuild's operations in France circa 1962 hung on the wall. As soon as his father hung up the phone, Grant cut right to the chase. \"I've been studying our books, Dad, trying to make sense of where Durabuild has been and where we are headed. From what I can see, the company's best growth period was in the middle of the last century, right after we opened operations in France. I want to work with you to understand that growth in a larger context so we can try and recapture it. Maybe, as we discussed last week, in China.\" DURABUILD: THE EARLY YEARS Frank Jr. loved to tell stories, and especially liked to sprinkle them with facts about US history, his passion. He poured himself a glass of chilled water from the carafe before he began. \"Grant, Author affiliation * Assistant Professor, Institute of Applied Economics, HEC Montral Roderick H. Cushman Associate Professor of Business, Columbia Business School Acknowledgements Jennifer Freeman '91 provided writing support for this case. Copyright information 2013-2018 by The Trustees of Columbia University in the City of New York. This version of the case replaces an earlier version that was published on May 9, 2013. This case is for teaching purposes only and does not represent an endorsement or judgment of the material included. This case cannot be used or reproduced without explicit permission from Columbia CaseWorks. To obtain permission, please visit www.gsb.columbia.edu/caseworks, or e-mail ColumbiaCaseWorks@gsb.columbia.edu This document is authorized for use only in Ari Shwayder's EMBA 637 E25 at University of Michigan - Ann Arbor from Jul 2019 to Jan 2020. I think you know how this story started. First, some history... At the end of World War II your grandfather saw a great opportunity in the G.I. Bill of Rights. Right after the war, the G.I. Bill provided free college tuition to the millions of soldiers who came home from the war. That bill gave veterans the opportunity to go to college, but it also gave them\"here he ticked the benefits off on his fingers \"housing subsidies, business loans, and other help in getting their lives back on track.\" \"When Grandpa Frank came back from France, he took out a business loan and established Durabuild in 1947 with offices in the United States and France. The construction industry was a good choice. After 15 years of the Depression and five years of war, housing in America was in bad shape, or at least in need of renewal. Mortgage loan guarantees provided by the G.I. Bill were helping the war veterans buy homes, which started a big housing boom. Those were some of our best years.\" \"But why expand into France? I never quite understood that choice.\" Frank Jr. gazed out the window. \"As you know, during the war, your grandfather fought on the front lines in Normandy. He saw firsthand the destruction of factories, the ashes of villages, the wreckage of schools and bridges. As the US housing market shot up after the war, he saw that once the recovery got underway in Europe, France would have an even greater need to rebuild than we did here in America. And he was right. For nearly two decades, France's economy soared.\" \"I remember once when I was about 10 years old, your grandfather told me about the miracle of postwar Europe. 'Out of the ashes of destruction have risen the wings of opportunity,' he said. We, Durabuild, were helping to make that happen.\" \"But Dad, did Grandpa Frank think the growth was going to continue forever?\" \"Well, there's the catch. The housing market in France that had boomed so impressively in the 1950s and 1960s leveled off in the 1970s, and my father didn't understand what was happening. He fully expected the French market to get back on track any minute. He kept thinking opportunity was just around the corner, because there was still so much room left for France to grow.\" He shook his head. \"Expecting the building industry to come roaring back, Grandpa invested Durabuild's capital year after year in factories and warehouses from Calais to Cannes. While the US part of the business held steady, Durabuild's French affiliates suffered. The demand for new construction in France was drying up, but Grandpa Frank refused to see it. I was a young apprentice at your grandfather's side at that time, and I admit I was taken in by his view of the world. Or maybe blind to the same things.\" Grant felt himself growing impatient. \"What's frustrating to me is that you guys waited around for more than 30 years, just hoping that Europe would return to the high growth rates of the postwar times. Thirty years in the twentieth century and beyond! Didn't you even try to understand what was going on? It seems like the best tool in your whole analytical toolkit was hope!\" The Solow Model Unleashed: Understanding Economic Growth | Page 2 NICOLAS VINCENT* PIERRE This document is authorized for use only in Ari Shwayder's EMBA 637 E25 at UniversityBY of Michigan - Ann Arbor fromAND Jul 2019 to JanYARED 2020. \"Hindsight is always 20/20, Grant. Why don't you bring your MBA toolkit in here and show me how we should have done it.\" LESSONS FROM THE PAST A few days later, when Grant had calmed down, he opened his laptop in the company conference room and dug into the kinds of source material he had not looked at since his days at Columbia Business School, nearly a decade before. The growth of the construction and building materials industry was closely tied to the overall economy, so he spent many hours looking at macroeconomic trends in France and the United States since the end of World War II. He also tried to recall the precise modeling tool that would help him to understand how Grandpa Frank had so inaccurately forecast the longer-term potential of Durabuild's operations in France. Drawing on his experience as an analyst, he prepared a report for his father. Grant's report highlighted a number of important macroeconomic trends in the United States and France. \"In the decades following World War II,\" he wrote, \"France grew at a much faster rate than the United States. GDP per capita growth in France from 1950 to 1980 averaged 3.8%, compared to 2.2% in the United States. Between 1980 and 2000, however, GDP per capita growth in France averaged 1.6%, compared to 2.3% in the United States. In other words, economic activity expanded at a much more rapid pace in France during the early years after the war, but the growth rate of the economy eventually tapered off.\" (See Exhibit 1.) Grant's report continued, \"Part of the reason why France grew so quickly at first was that it started at a much lower level relative to the United States. As a consequence of the destruction of the war, in 1950 France's GDP per capita was 54% that of the United States', and its capitalto-labor ratio was less than 10% of the United States'. France and the United States had similar investment rates during this period, and because France started from such a low capital base, its capital stock grew very rapidly, achieving the same capital-to-labor ratio as the United States by 2000. Nonetheless, France never caught up. In 2000 its GDP per capita was 75% that of the United States'.\" (See Exhibit 2.) Grant's report then went on to try to analyze some of the problems with the French economy and to describe some of the differences between the French and the American labor market, which may have been behind the slowdown. \"In the decades following World War II, unemployment in France was so low, around 3%, that US economists wondered how the United States could replicate the labor miracle of France and the rest of Europe. By the end of the century, however, France's unemployment rate had risen to over 11%, more than twice that of the United States'. Moreover, total labor hours per capita in France were 72% that of the United States'.\" (See Exhibits 2 and 3.) \"The French live very differently than Americans,\" the report went on. \"At the end of the century, in France, the work week could not legally be longer than 35 hours, with a mandatory five-week vacation. The average French worker put in 40 weeks per year, while the average US worker put in 46.2 weeks.\" The report then explained some of the possible reasons behind these differences: \"The French unemployment insurance program, which replaces 60% of prior pay for up to two years, may discourage individuals from seeking work, while high marginal tax rates make working additional hours less interesting. Furthermore, firms have little Page 3 | The Solow Model Unleashed: Understanding Economic Growth BYThis NICOLAS VINCENT* AND YARED document is authorized for PIERRE use only in Ari Shwayder's EMBA 637 E25 at University of Michigan - Ann Arbor from Jul 2019 to Jan 2020. incentive to hire new workers, given the high minimum wage regulation as well as the legal restrictions which make it difficult to fire workers.\"1 LESSONS FOR THE FUTURE Grant was now walking along the Mississippi River, lost in his thoughts, envisioning Durabuild's future plans. Did China present the best long-term potential, or would its current high-growth phase peter out as it had in France? China's rate of investment was extraordinarily high; it had never been replicated by either the United States or France and was driving very rapid economic growth. Nonetheless, doing business in China was difficult, given the difference between its regulatory environment and the United States' or France's. How easy would it be to apply new technologies in China? How does China's one-child policy affect its economic growth? When Grant had gotten about a mile down the river, the tool he was searching for finally dawned on him: the Solow model. The Solow Model Unleashed: Understanding Economic Growth | Page 4 NICOLAS VINCENT* PIERRE This document is authorized for use only in Ari Shwayder's EMBA 637 E25 at UniversityBY of Michigan - Ann Arbor fromAND Jul 2019 to JanYARED 2020. Exhibits Exhibit 1 Real GDP per Capita in France and the United States Source: Original 1950-2000 GDP per capita data for France and US is from Penn World Tables 7.1. Exhibit 1 compares the logarithm of the GDP per capita data. Exhibit 2 Comparison of Factors in GDP per Capita (France/United States) Year Y/POP A (K/N)^0.3 N/POP 1950 0.54 0.99 0.44 1.25 1980 0.86 1.05 0.88 0.93 2000 0.75 1.02 1.01 0.72 Source: Population (POP) and GDP per capita (Y/POP) are from Penn World Tables 7.1. Total hours worked (N) is from the Conference Board. Capital (K) in 2000 is assumed to be 3 time total GDP at 2001, and capital at other dates is calculated using investment and a depreciation rate of 4.4%. (A) refers to total factor productivity. Page 5 | The Solow Model Unleashed: Understanding Economic Growth BYThis NICOLAS VINCENT* AND YARED document is authorized for PIERRE use only in Ari Shwayder's EMBA 637 E25 at University of Michigan - Ann Arbor from Jul 2019 to Jan 2020. Exhibit 3 Labor Force Participation in France and the United States Source: 1950-2000 population data France and US is from Penn World Tables 7.1. Total hours worked is from the Conference Board. The Solow Model Unleashed: Understanding Economic Growth | Page 6 NICOLAS VINCENT* PIERRE This document is authorized for use only in Ari Shwayder's EMBA 637 E25 at UniversityBY of Michigan - Ann Arbor fromAND Jul 2019 to JanYARED 2020. Endnote Robert Solow, \"Unemployment in the United States and in Europe: A Contrast and the Reasons,\" Working Paper no. 231 (January 2000); Olivier J. Blanchard, \"Explaining European Unemployment,\" NBER Reporter: Research Summary (Summer 2004); Richard Rogerson, \"Understanding Differences in Hours Worked,\" Review of Economic Dynamics 9, no. 3 (July 2006). 1 Page 7 | The Solow Model Unleashed: Understanding Economic Growth BYThis NICOLAS VINCENT* AND YARED document is authorized for PIERRE use only in Ari Shwayder's EMBA 637 E25 at University of Michigan - Ann Arbor from Jul 2019 to Jan 2020. The Solow Model Unleashed: Understanding Economic Growth Nicolas Vincent and Pierre Yared Columbia CaseWorks ID:130304 France Years from Now (t) 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 Population (Pop) 0 Labor (L) Capital (K) 0 0 Capital-Labor Ratio (K/L) #DIV/0! Total Factor Productivity Output (Y) Investment (I) Depreciation (K) Output per Capita (Y/Pop) The Solow Model Unleashed: Understanding Economic Growth Nicolas Vincent and Pierre Yared Columbia CaseWorks ID: 130304 Enter all of the parameters of your model here: United States France Starting Population (Pop0) Starting Capital (K0) Starting Total Factor Productivity (A0) Population Growth (%DPop) Employment to Population Ratio (L/Pop) Investment Rate (I/Y) Total Factor Productivity Growth (%DA) Depreciation Rate Output per Capita 16,000 8,000 4,000 2,000 United States 1,000 1950 1960 1970 1980 1990 2000 2010 2020 2030 France 2040 2050 The Solow Model Unleashed: Understanding Economic Growth Nicolas Vincent and Pierre Yared Columbia CaseWorks ID: 130304 UNITED STATES - Partial answers Years from Now (t) Population (Pop) Labor (L) Capital (K) Capital-Labor Ratio (K/L) Total Factor Productivity Output (Y) Investment (I) Depreciation (dK) Output per Capita (Y/Pop) 1950 150 60 10000 167 10,00 2784 835 500 18,562 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 153 61 10335 169 10,00 2851 855 517 18,635 223 89 17492 196 10,00 4345 1303 875 19,493 331 132 27505 208 10,00 6567 1970 1375 19,826 492 197 41721 212 10,00 9818 2945 2086 19,949 The Solow Model Unleashed: Understanding Economic Growth Nicolas Vincent and Pierre Yared Columbia CaseWorks ID: 130304 United States Years from Now (t) Population (Pop) Labor (L) Capital (K) Capital-Labor Ratio (K/L) 1950 0 0 0 #DIV/0! 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 Total Factor Productivity Output (Y) Investment (I) Depreciation (K) Output per Capita (Y/Pop)