Growth, Capital Accumulation, and the Economics of Ideas

Chapter 8 MODERN PRINCIPLES OF ECONOMICS Third Edition Growth, Capital Accumulation, and the Economics of Ideas

Outline The Solow Model and Catching-Up Growth The Investment Rate and Conditional Convergence New Ideas and Cutting-Edge Growth The Economics of Ideas The Future of Economic Growth 2

Introduction In 2010: U.S. GDP per capita grew by 2.3%. China s GDP per capita grew by 10%. The U.S. has never grown as fast as the Chinese economy is growing today. China is growing much faster than the U.S. because: The U.S. economy is on the cutting edge. The Chinese economy is catching up. 3

Definition Cutting-edge growth: Growth due to new ideas. Catching-up growth: Growth due to capital accumulation. 4

The Solow Model and Catching-Up Growth The Solow model begins with a production function. The total output of an economy (Y) depends on: Physical capital (K) Human capital, or education x Labor (el) Ideas (A) A production function expresses a relationship between output and the factors of production: Y = F(A,K,eL) 5

The Solow Model If we assume that A, e, and L are constant, then we can simplify our expression for output as: Y = F( K ) More capital (K) should produce more output (Y) but at a diminishing rate. Because L is constant, an increase in K always implies an increase in the amount of capital per worker, K/L, and an increase in Y is also always an increase in output per worker, Y/L. 6

Self-Check Catching-up growth is growth due to: a. New ideas. b. Capital accumulation. c. Adoption of new technologies. Answer: b capital accumulation. 7

Definition Marginal product of capital: The increase in output caused by the addition of one more unit of capital. The marginal product of capital diminishes as more and more capital is added. 8

The Solow Model: Capital, Production and Diminishing Returns More capital (K) should produce more output (Y) but at a diminishing rate. The MP K diminishes because the first unit of capital is applied where it is most productive, the second where it is slightly less productive, and so on. The following graph shows the production function Y = F (K ) = K In this case, output is the square root of the capital input: If K = 4, then Y = 4 = 2 If K increases to 16, then Y = 16 = 4 9

Diminishing Returns Output, Y 3.2 3 Creates just a little output Y= K 1 Creates a lot of output 0 0 1 2 3 4 5 6 7 8 9 10 11 12 Capital, K The first unit of input The tenth unit of input 10

Growth in China and the United States Chinese growth has been rapid because: China began with very little capital, so the marginal product of capital was very high, and with the new reforms the investment rate increased dramatically. China has benefited by opening up to trade and investment with the developed world. Improved productivity in agriculture. China s growth rate will fall because the marginal product of capital will fall, a poor banking system to a lack of experience with the rule of law to a poorly educated population.

Capital and Investment Capital is output that is saved and invested rather than consumed. For example, out of 10 units produced, 7 are consumed and 3 are invested in new capital. We write the fraction of output that is invested in new capital as gamma (g), and in the example just given, g = 3/10 = 0.3 Capital also depreciates, or wears out. For example, if there are 100 units of capital, 2 units might depreciate, leaving 98 for the next period. 12

Self-Check Output that is invested rather than consumed is called: a. Capital. b. Depreciation. c. Marginal product. Answer: a output that is invested is called capital. 13

Consumption and Investment Output Y 15 When K = 100, Output = 10 Y = K 10 Consumption = (1-0.3) x 10 = 7 5 3 0 Investment = (0.3) x 10 = 3 0 100 200 300 400 Investment = 0.3Y Capital K 14 N28

Slide 14 N28 Disposition of Slide: To maintain the subject flow this slide can be moved upward, below slide 12. Nawshaba, 5/8/2015

Capital and Depreciation Capital also depreciates, or wears out. For example, if there are 100 units of capital, 2 units might depreciate, leaving 98 for the next period. We write the fraction of capital that wears out or depreciates as delta (δ ); in the example just given, δ = 2/100 = 0.02. capital depreciation increases the greater the capital stock this will turn out to place another constraint on economic growth 15

Depreciation Depreciation 8 Depreciation = 0.02K 6 4 2 0 0 100 200 300 400 Capital K 16

Steady-State Level of Capital At some point, the capital stock will reach a level such that every unit of investment is needed just to replace the capital that depreciates in that period. When investment just covers capital depreciation, the capital stock stops growing, and when the capital stock stops growing, output stops growing as well. Investment > Depreciation The capital stock grows and output next period is bigger. Investment = Depreciation The capital stock and output are constant(the steady state). Investment < Depreciation The capital stock shrinks and output next period is smaller. 17

Steady-State Level of Capital GDP Y Depreciation = 0.02 x K 7 5 At K = 100, investment > depreciation increase in K Investment = 0.3 x Y 3 2 0 0 100 200 225 300 400 Capital K 18

Steady-State Level of Capital GDP Y Depreciation = 0.02 x K 7 5 3 2 Investment = 0.3 x Y At K = 300, investment < depreciation decrease in K 0 0 100 200 225 300 400 Capital K 19

Steady-State Level of Capital GDP Y Depreciation = 0.02 x K 7 5 The steady-state stock of capital is where investment = depreciation Investment = 0.3 x Y 3 2 0 0 100 200 225 300 400 Capital K 20

Steady-State Level of Capital Check the Math At K = 100, Y = 100 = 10 Depreciation = 0.02 100 = 2 Investment = 0.3x10 = 3 Investment > Depreciation Result: K and Y grow. Check the Math At K = 400, Y = 400 = 20 Depreciation = 0.02x400 = 8 Investment = 0.3x20 = 6 Investment < Depreciation Result: K and Y decrease. Check the Math At K = 225, Y = 225 =15 Depreciation = 0.02x225 = 4.5 Investment = 0.3x15 = 4.5 Investment = Depreciation Result: 1. Investment = Depreciation 2. K and Y are constant. This is steady state. 21

Steady-State Level of Capital As the capital stock gets larger, investment increases but at a diminishing rate. Depreciation, however, increases with the capital stock at a linear (constant) rate. At some point investment = depreciation. This is the steady-state level of capital. There is no new (net) investment and economic growth stops. 22

Steady-State Level of Capital The logic of diminishing returns means that eventually capital and output will cease growing. Therefore, other factors must be responsible for long run economic growth. Consider: Human capital: knowledge, skills, experience Technological knowledge: better ideas 23

Catching-up Growth Long-run economic growth cannot be due to capital accumulation. Diminishing returns mean that eventually capital and output will cease growing. The logic of diminishing returns applies to human capital as well. Changes in the capital stock drive output, so when Investment = Depreciation and K is at its steady-state level, then so is output. 24

Definition Steady-state level of capital: Where the capital stock is neither increasing nor decreasing. 25

Steady-State Level of Capital Output Y 7 5 The steady-state stock of capital is where investment = depreciation Depreciation = 0.02 x K Investment = 0.3 x Y 3 2 0 0 100 200 225 300 400 Capital K 26

Steady-state Level of Output Output Y 20 15 Steady state output Y= K 10 When capital is in the steady state, output is in the steady state. Depreciation = 0.02 x K 5 Steady state capital stock 0 100 200 225 300 400 Investment = 0.3 x Y Capital K 27

List of Equations Output: Y = F (K ) Investment: I = gy = g * Depreciation: D = δ * K Capital Stock in Year T: K T = K T-1 + I D Where g is the savings rate, δ is the depreciation rate 28

Self-Check If investment is greater than depreciation, the stock of capital K will: a. increase. b. decrease. c. remain the same. Answer: a the stock of capital will increase. 29

The Investment Rate In the Solow model, a greater investment rate means more capital, which means more output. This increases a country s steady-state level of GDP. Thus the Solow model predicts that countries with higher rates of investment will be wealthier. The level of the capital stock determines the output level but not its growth rate, at least not in the very long run. 30

Steady-state Level of Output Output Y 20 15 Y= K 10 5 Increased investment raises steady-state output Depreciation = 0.02K Investment = 0.4Y Investment = 0.3Y 0 100 200 225 300 400 Capital K 31

Investment and GDP GDP per Capita Is Higher in Countries with Higher Investment Rates 32

Self-Check A higher rate of investment will: a. Increase capital but decrease output. b. Decrease capital but increase output. c. Increase both capital and output. Answer: c higher investment will increase both capital and output. 33

Definition Conditional convergence: The tendency among countries with similar steady-state levels of output for poorer countries to grow faster than richer countries and thus for poor and rich countries to converge in income. 34

Conditional Convergence This figure is using data from 18 of the 20 founding members of the OECD (Organisation for Economic Co-operation and Development). Over time the OECD countries have converged to a similar level of GDP per capita. The poorer the country was in 1950, the faster growth was between 1960 2000. 35

Cutting-edge Growth The simplest form of the Solow model predicts zero economic growth in the long run. The United States, however, has been growing for more than 200 years. Better ideas can keep the economy growing even in the long run. A computer today has about the same amount of silicon and labor input as 20 years ago, but today s computer is much better. The difference is ideas. 36

Cutting-edge Growth A stand for ideas that increase productivity, our production function is: Y = A Κ Better ideas or technological knowledge as represented by increases in A increases output even while holding K constant, that is, an increase in A represents an increase in productivity.

Cutting-edge Growth An Increase in A Increases Output Holding K Constant Conclusion: Technological knowledge / better ideas are the key to long run economic growth. Solow estimated that better ideas are responsible for ¾ of our increased standard of living.

Cutting-edge Growth Output Y 33 Output new 27 b 15 a Better ideas Output old Depreciation Investment old 225 506 Capital K 39

Cutting-edge Growth Output Y 33 27 b More capital, more output c Output new 15 a Better ideas Output old Depreciation Investment new Investment old 225 506 Capital K 40

Self-Check Long-run economic growth is largely due to: a. Better ideas. b. Lower depreciation. c. Higher investment. Answer: a long-run growth is largely due to better ideas. 41

The Economics of Ideas 1. Ideas for increasing output are primarily researched, developed, and implemented by profit-seeking firms. 2. Ideas can be freely shared, but spillovers mean that ideas are underprovided. 3. Government has a role in improving the production of ideas. 4. The larger the market, the greater the incentive to research and develop new ideas. 42

1. Research for Profit Institutions and incentives drive the generation of technological knowledge. These institutions include: A setting that helps innovators to connect with capitalists. Intellectual property rights. A high-quality educational system. The U.S. has a very good cultural and commercial infrastructure for supporting new ideas and their commercialization. 43

1. Research for Profit All kinds of people come up with new ideas. Business culture and institutions are also important. Ideas without financial backers are dead. The U.S. is good at connecting innovators with businessmen and venture capitalists. American culture supports entrepreneurs. 44

1. Research for Profit Patents New processes, products, and methods can be copied by competitors. Imitators have lower costs and tend to drive innovators out of the market unless barriers prevent quick imitation. Patents give innovators temporary monopoly rights, typically 20 years. 45

1. Research for Profit Patents Patents increase the incentive to develop new products, but they also increase monopoly power. Monopoly power raises prices and slows the spread of innovations throughout the economy. The trade-off between creating incentives for R&D while avoiding too much monopoly power is one of the trickiest in economic policy. 46

1. Research for Profit John Kay, destroyer of jobs. John Kay (1704-1780) invented the flying shuttle used in cotton weaving, the single most important invention launching the industrial revolution. Kay was rewarded for his efforts by having his house destroyed by machine breakers, afraid of job loss. He died a poor man. 47

2. Spillovers STOCK MONTAGE/GETTY IMAGES He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me. Thomas Jefferson 48

Definition Non-rivalrous: When one person s consumption of a good does not limit another person s consumption. 49

2. Spillovers Even with patents, ideas tend to spill over and benefit other firms and consumers. Since ideas are non-rivalrous and many can be shared at low cost, they should be shared. However, if the originator doesn t get enough of the benefits, ideas will be underprovided. Economists know that idea spillovers are good, they also know that spillovers mean that too few good ideas are produced in the first place. 50

2. Spillovers

3. Government s Role The Government can increase the incentive to produce new ideas through patents. The government could also encourage the production of new ideas through subsidies or tax breaks. Universities train the scientists who research and develop new products. The large spillovers to basic science suggest a role for government subsidies to universities. 52

3. Government s Role The Government can increase the incentive to produce new ideas through patents. The government could also encourage the production of new ideas through subsidies or tax breaks. Universities train the scientists who research and develop new products. The large spillovers to basic science suggest a role for government subsidies to universities. 53

Self-Check Governments should play a role in encouraging new ideas because new ideas provide: a. Non-rivalry. b. Spillovers. c. Market power. Answer: b governments should encourage new ideas because of spillover effects. 54

4. Market Size Larger markets mean increased incentives to invest in research and development. Innovations like pharmaceuticals, new computer chips, software, and chemicals require large R&D expenditures. Companies will avoid investing in innovations with small potential markets. As countries become wealthier, companies will increase their worldwide R&D investments. 55

The Future of Economic Growth Growth in per capita world GDP has been increasing. Worldwide per capita GDP is currently growing by a little over 3% per year. The number of new ideas is a function of the number of people, the incentives to innovate, and the number of ideas per hour that each person has. A(ideas) = Population Incentives Ideas per hour 56

The Future of Economic Growth The number of people is increasing. As the world gets richer, the number of people whose job it is to produce new ideas is increasing. Because of spillovers, these ideas will benefit everyone. Increased consumer wealth and integrated markets boost the incentive to innovate. Economic growth might be even faster in the future than it has been in the past. 57

The Future of Economic Growth Many people say that if people save too much, the economy will be hurt. They often refer to the fact that consumer spending is two-thirds of GDP to make this point. This is sometimes called the paradox of thrift. Do you agree with the paradox of thrift for longrun growth? a) Yes, since a high savings rate makes a country poorer in the long run. b) No, since a high savings rate makes a country richer in the long run. 58

Takeaway The Solow model tells us that: Countries that devote a larger share of output to investment will be wealthier. Growth will be faster the farther away a country s capital stock is from its steady-state. Capital accumulation cannot explain long-run economic growth. New ideas are the driving force behind long-run economic growth. 59

Takeaway Ideas can be easily copied, so the originator of a new idea won t receive all the benefits and the incentive to produce ideas will be too low. Governments can play a role in supporting the production of new ideas. There is a trade-off between providing incentives to produce new ideas and providing incentives to share new ideas. 60