Introductory Macroeconomics Lecture 15: The Solow-Swan Growth Model I PDF

Introductory Macroeconomics Lecture 15: The Solow-Swan Growth Model I Jonathan Thong Daniel Minutillo 2nd Semester 2024 1  This Lecture The Solow-Swan Growth Model I (1) savings, investment and capital accumu...

Introductory Macroeconomics Lecture 15: The Solow-Swan Growth Model I Jonathan Thong Daniel Minutillo 2nd Semester 2024 1  This Lecture The Solow-Swan Growth Model I (1) savings, investment and capital accumulation (2) steady-state - solving the model (3) implications of diminishing returns to K - transitional dynamics BOFAH Chapter 15 2  Solow-Swan Growth Model Introduction Based on two important long-run relationships (i) amount of capital determines output produced (per period) (ii) amount of output determines new investment (per period) Together, determines the amount of capital accumulation over time Question: Can capital accumulation sustain long-run growth? (Answer: to be discussed this lecture.) 3  Solow-Swan Growth Model Introduction Aggregate production function with ’standard properties’ Yt = AF (Kt , L) (for simplicity, A and L constant — until next lecture) National income account Yt = Ct + It (for simplicity, a closed economy and no government purchases) 4 Savings, Investment and Capital Accumulation 5  (1) Savings and Investment Key behavioural assumption of the Solow-Swan model: A constant fraction s of output is saved each period St = sYt , 0 s – increases the level of capital and output in the long run – but has no long run effect on the growth of capital and output Increase in savings rate moves us along production function, increasing capital per worker for a given level of productivity A. 19 Level Effect 20 But No Long Run Growth Effect 21  Reflection Question: So what can generate sustained growth? Answer: Productivity Growth A! Increases in A shift up the production function, allowing more output at any given level of capital per worker – we model this in the next lecture 22  Learning Outcomes 1 Understand and describe the key mechanisms underpinning the Solow-Swan Growth Model, including key assumptions and equations. 2 Mathematically derive key equations of the Solow-Swan Growth Model, including the Capital Transition equation and the Steady-State condition. Understand and explain how to solve the model algebraically and graphically. 3 Understand and explain disequilibrium dynamics of the Solow-Swan Growth Model. Discuss whether capital accumulation will lead to growth in the short-run and/or the long-run. 4 Understand and explain the role that diminishing returns to capital has in the outcomes of the Solow-Swan Model. 5 Understand and explain the consequences of changing the savings rate, differentiating between level effects and growth effects. 23  New Formula(s) and Notation s savings rate Note, the steady-state solution, e.g.,   1 sA 1−α K∗ = L δ (see Appendix) is an important result, not an equation to be memorised. You should understand the logic of how to derive this result from more fundamental equations on your equation sheet, in this case ⋆ the production function, e.g., Y = F (K, L) = AK α L1−α ⋆ the capital transition equation, e.g., Kt+1 − Kt = It − δKt ⋆ the relationship between investment, savings and income (slide 7). 24  Next Lecture The Solow-Swan Growth Model II – productivity growth and employment growth – convergence hypothesis – growth accounting BOFAH Chapter 15 25 Appendix: Worked Example Using Cobb-Douglas Recall Cobb-Douglas production function F (K, L) = K α L1−α Find steady-state capital stock K ∗ by solving (K-SS) sAK ∗α L1−α = δK ∗ The solution is (see algebra on next slide)   1 ∗ sA 1−α K = L δ 26 Appendix: Worked Example Using Cobb-Douglas Algebra: – divide both sides of steady state condition by δK ∗α to get sA 1−α K ∗1−α = L δ – raise both sides to the power 1/(1 − α) to get  1  1−α sA K∗ = L δ Implications: steady state capital K ∗ is – increasing in savings rate s, in productivity A, and in labour L – decreasing in depreciation rate δ 27