Lecture 5 _C26_week_5-7_2024-Growth Capital Accum Ideas.pptx

MODERN PRINCIPLES OF ECONOMICS Chapter 26 Growth, Capital Accumulation, and the Economics of Ideas © 2017 Wort...

MODERN PRINCIPLES OF ECONOMICS Chapter 26 Growth, Capital Accumulation, and the Economics of Ideas © 2017 Worth Publishers. All Rights Reserved. C H A P Why growth matters - recap T E R 7 Data on infant mortality rates: – 20% in the poorest 1/5 of all countries E c – 0.4% in the richest 1/5 o In Pakistan, 85% of people live on less than $2/day. n o One-fourth of the poorest countries have had m famines during the past 3 decades. Poverty is associated with oppression of women c G and minorities. r Economic growth raises living standards and o w reduces poverty…. © 2017 Worth Publishers. All Rights Reserved. h  Review Lecture 4: – What makes a country rich?  Factors of Production  Incentives and Institutions Lecture 5: – Turn this into an economic model! © 2017 Worth Publishers. All Rights Reserved.  Outline The Solow Model and Catching-Up Growth – Production function – Marginal productivity The Investment Rate and Conditional Convergence New Ideas and Cutting-Edge Growth The Economics of Ideas The Future of Economic Growth Takeaway © 2017 Worth Publishers. All Rights Reserved.  Introduction In 2010: – U.S. GDP per capita grew by 2.2%. – China’s GDP per capita grew nearly 10%. – How is this possible China is growing much faster than the United States because: – The U.S. economy is on the cutting edge. – The Chinese economy is catching up. © 2017 Worth Publishers. All Rights Reserved.  Definition (1 of 5) Cutting-Edge Growth: Growth due to new ideas. Catching-Up Growth: Growth due to capital accumulation. © 2017 Worth Publishers. All Rights Reserved.  Robert Solow American economist 1924 – present Developed best model of long-run economic growth in 1956 Nobel prize (1987) Sometimes called Solow-Swan model, as a very similar model was developed by Trevor Swan, an ANU economist, in the same year © 2017 Worth Publishers. All Rights Reserved. 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 × Labor (eL) – Ideas (A) A production function expresses a relationship between output and the factors of production: Y=F(A,K,eL) © 2017 Worth Publishers. All Rights Reserved.  The production function denoted Y = F(A,K, eL) shows how much output (Y ) the economy can produce from K units of capital and eL units of human capital and A units of ideas Example: Y=A*K*eL Y=A+K+eL Most often: (Cobb-Douglas) © 2017 Worth Publishers. All Rights Reserved.  Marginal productivity definition: The extra output the firm can produce using an additional unit of input (holding other inputs fixed): E.g. Marginal productivity of labour MPL = F (K, L +1) – F (K, L) © 2017 Worth Publishers. All Rights Reserved. C H A P Diminishing marginal product T E R 3 As a factor input is increased, its marginal product falls (other things equal). N We assume this always holds a i Intuition: o Suppose  L while holding K fixed n fewer machines per worker a lower worker productivity n c o m e © 2017 Worth Publishers. All Rights Reserved. C H A P Check your understanding: T E R 3 Which of these production functions have diminishing marginal returns to labor? N a i o a¿ 𝐹 ( 𝐿)=15 𝐿 n a b ¿ 𝐹 ( 𝐿)= √ 𝐿 n c¿ 𝐹 (𝐾 , 𝐿)=2 √ 𝐾 +15 √ 𝐿 c o m e © 2017 Worth Publishers. All Rights Reserved.  A simple Solow Model If we assume that A, e, and L are constant, then we can simplify our expression for output as: Y=F(k) Where k=K/L, capital per worker. More capital per worker (k) should produce more output (Y), but at a diminishing rate (diminishing productivity of k). © 2017 Worth Publishers. All Rights Reserved.  Self-Check (1 of 6) Catching-up growth is growth due to: a. New ideas. b. Capital accumulation. c. Adoption of new technologies. © 2017 Worth Publishers. All Rights Reserved.  Self-Check (1 of 6) (Answer) Catching-up growth is growth due to: a. New ideas. b. Capital accumulation. c. Adoption of new technologies. Answer: b. Capital accumulation. © 2017 Worth Publishers. All Rights Reserved.  Definition (2 of 5) 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. © 2017 Worth Publishers. All Rights Reserved. C H A P T E The production function R 7 Output per worker, y E f(k) c o MP_k = f(k +1) – f(k) n 1 o m Note: Note:this this production productionfunction function c exhibits exhibitsdiminishing diminishingMP_k. MP_k. G r o Capital per w worker, k © 2017 Worth Publishers. All Rights Reserved. h The Solow Model: Capital, Production, and Diminishing Returns More capital per worker (k) should produce more output (Y) but at a diminishing rate. The MPk 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) © 2017 Worth Publishers. All Rights Reserved.  Diminishing Returns Output, Y 3.2 𝑌 =√ 𝑘 3 Creates just a little output 1 Creates a lot of output 0 Capital per 0 1 2 3 4 5 6 7 8 9 10 11 12 worker, k The first unit of input The tenth unit of input © 2017 Worth Publishers. All Rights Reserved.  Growth in China and the United States (1 of 2) Chinese growth has been rapid because: – China began with very little capital, so marginal product of capital was high – With new reforms the investment rate increased dramatically. – China has benefited by opening up to trade and investment with the developed world. – China has improved productivity in agriculture. © 2017 Worth Publishers. All Rights Reserved.  Growth in China and the United States (2 of 2) China’s growth rate will fall because: – The marginal product of capital will fall – It faces a poor banking system – It lacks experience with the rule of law – It has a poorly educated population. © 2017 Worth Publishers. All Rights Reserved.  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 s, and in the example just given, s = 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. © 2017 Worth Publishers. All Rights Reserved.  Consumption and Investment Output, Y 15 When k = 100, 𝑌 =√ 𝑘 Output = 10 10 Consumption = (1 – 0.3) × 10 = 7 5 Investment = 0.3Y 3 Investment = (0.3) × 10 = 3 Capital/worker, k 0 0 100 200 300 400 © 2017 Worth Publishers. All Rights Reserved.  Self-Check (2 of 6) Output that is invested rather than consumed is called: a. Capital. b. Depreciation. c. Marginal product. © 2017 Worth Publishers. All Rights Reserved.  Self-Check (2 of 6) Answer) 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. © 2017 Worth Publishers. All Rights Reserved.  Capital and Depreciation We write the fraction of capital that wears out or depreciates as delta (δ); in the example just given, δ = 2/100 = 0.02. The greater the capital stock, the greater the depreciation. This will turn out to place another constraint on economic growth. © 2017 Worth Publishers. All Rights Reserved.  Depreciation Depreciation 8 Depreciation = 0.02 × k 6 4 4 −2 𝑆𝑙𝑜𝑝𝑒= =𝛿 200−100 2 Capital per 0 worker, k 0 100 200 300 400 © 2017 Worth Publishers. All Rights Reserved. C H A P T Capital accumulation E R 7 The basic idea: Investment increases the capital E stock, depreciation reduces it. c o Change in capital stock = investment – depreciation n k = i –  k o m Since i = sF(k) , this becomes: c G r o k = s F(k) –   k w © 2017 Worth Publishers. All Rights Reserved. h  Steady-State Level of Capital (1 of 6) 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. © 2017 Worth Publishers. All Rights Reserved.  Definition (3 of 5) Steady-State Level of Capital: When the capital stock is neither increasing nor decreasing. © 2017 Worth Publishers. All Rights Reserved.  Steady-State Level of Capital (2 of 6) Output, Y Depreciation = 0.02 × k At At kk == 100, 100, 7 investment investment >> depreciation depreciation → Investment → increase increase inin kk = 0.3 × Y 5 3 2 Capital per 0 0 100 200 225 300 400 worker, k © 2017 Worth Publishers. All Rights Reserved.  Steady-State Level of Capital (3 of 6) Output, Y Depreciation = 0.02 × k 7 Investment = 0.3 × Y 5 At At kk == 300, 300, 3 investment investment