Introductory Macroeconomics Lecture 14: Long Run Growth Overview PDF

Introductory Macroeconomics Lecture 14: Long Run Growth Overview Jonathan Thong Daniel Minutillo 2nd Semester 2024 1  This Lecture Overview of economic growth – growth over long horizons – supply-side fundamentals...

Introductory Macroeconomics Lecture 14: Long Run Growth Overview Jonathan Thong Daniel Minutillo 2nd Semester 2024 1  This Lecture Overview of economic growth – growth over long horizons – supply-side fundamentals: capital, labour, productivity, etc – the aggregate production function – factor shares BOFAH Chapter 13 and 14 – partial derivatives and non-linear algebra 2 Growth over Long Horizons 3  Long Run Growth So far, we studied short run economic fluctuations around trend – short run shocks, long run reversion to trend Y ∗ e.g. the AD-AS model By long run growth, we mean growth in potential output Yt∗ – to simplify notation, we will now just refer to this as output Yt i.e. we focus on trends abstracting from cyclical fluctuations 4 Long Run and Short Run Output in Australia 5  Living Standards Specially, we will focus on output per person or output per worker – simple measure of living standards of the typical person e.g. housing, clothes, food, education, healthcare, etc But remember that this is not the only thing worth caring about – omits all non-market activity, including leisure – does not capture changes in income inequality, etc – does not capture natural resources, environmental damage, etc sustained increases in living standards is relatively recent – essentially a post-industrial revolution phenomenon 6 Sustained Increased in Living Standards 7 Catching Up and Convergence? 8  Output Per Person or Per Worker? Output per person is the product of output per worker and the employment/population ratio output output employment = × population employment population Long run growth in output per person is driven by growth in output per worker, also known as labour productivity Trends in employment/population ratio evolves slowly over time due to changing demographics (e.g., ageing population) We will focus on output per worker, denoted Y /L 9 Supply-Side Fundamentals: Capital, Labour, Productivity, etc... 10  What Determines Output Per Worker? Some possibilities – technology – ’human capital’ — skills, talents, education, training – ’physical capital’ — robots, tools, equipment, machinery – ’organisational capital’ — robots, entrepreneurship, management – political and legal institutions, property rights – land, natural resources We will focus on a simplified version of all this 11  Factors of Production Main idea: economy-wide output Y is a function of inputs These inputs are also known as factors of production – Focus on two key variable inputs physical capital K and labour L – Put everything else in a ’catch-all’ total factor productivity A * technology, human capital, organisational capital, institutions, land, natural resources, etc... The production function and its inputs represents the ’long run supply-side fundamentals’ of the economy. 12 The Aggregate Production Function 13  Aggregate Production Function We write the aggregate production function Y = A × F (K, L) where – Y is aggregate output, i.e., real GDP – K is the value of physical capital – L is the labour force – A is ’total factor productivity’, i.e., everything else and where F (K, L) is a function of K, L to be described 14  Cobb-Douglas Production Function Production function most commonly parameterised as Y = A × K α L1−α , 0 0, holding K fixed ∂L L Symbol ∂ (latex: ’\partial’) indicates these are partial derivatives 17  (ii) Diminishing Returns to Each Input Diminishing returns to an input if using more of it decreases its marginal product, again holding all other inputs fixed For the Cobb-Douglas production function – diminishing returns to capital is negative ∂2Y = −α(1 − α)AK α−2 L1−α < 0, holding L fixed ∂K 2 – marginal returns to labour is negative ∂2Y = −α(1 − α)AK α L−α−1 < 0, holding K fixed ∂L2 18  (i) and (ii) Together in Words Using more capital (or labour) always gives more output – But impact of adding capital is greatest when capital is scarce – And impact of adding capital is least when capital is abundant 19  (iii) Constant Returns to Scale (CRS) Constant returns to scaling all inputs by the same amount Scaling by any amount x > 0 gives A(xK)α (xL)1−α = xα x1−α AK α L1−α = xY e.g. A(2K)α (2L)1−α = 2α 21−α AK α L1−α = 2Y ’Diminishing Returns’ vs. ’Constant Returns’ – Diminishing returns to each input individually (holding other inputs fixed) – Constant returns to scale (all inputs scaled together by common proportion) 20  ’Standard Properties’ of F (K, L) (i) Positive marginal products ∂F ∂F > 0 and >0 ∂K ∂L (ii) Diminishing returns to each input ∂2F ∂2F < 0 and 0 21  Output per Worker Output per worker, i.e., labour productivity, is given by   Y F (K, L) K = A = AF , 1 , using CRS L L L For given L, output per worker increases either due to (i) increases in capital per worker K/L, i.e., capital intensity (movements along the production function), or (ii) increase in ’total factor productivity’ A (shifts in the production function) Which of these is more important? (Answer next week!) 22 Move along vs. Shift in Production Function 23 Factor Shares 24  Factor Shares Where does α = 1/3 come from? Recall income approach to GDP Y = rK + wL Factor income shares rK capital income share = Y wL labour income share = Y Now recall that for Cobb-Douglas production function Y Y MPK = α , and MPL = (1 − α) K L 25  Factor Shares Big assumption: Factors paid their marginal products r = MPK, and w = MPL With this assumption rK α= = capital income share Y wL 1−α= = labour income share Y So with this big assumption, α is just the share of capital income which we can measure in the data This varies from around 0.3 to 0.4 depending on the country and the time period, giving rise to the 1/3 rule of thumb Can use other values for α if uncomfortable with this assumption 26 Labour Share of Income (1 − α) 27  Learning Outcomes 1 Understand and explain the importance and limitations of economic growth, and its relationship with living standards. 2 Be familiar with historical trends and stylized facts about economic growth. 3 Understand and describe the long run supply-side fundamentals, and how the are commonly modelled in Macroeconomics. 4 Understand and explain the three desirable properties of an aggregate production function and demonstrate (mathematically) how a Cobb-Douglas function satisfies these properties. 5 Critically reflect on the relative importance of increasing capital intensity and increasing total factor productivity in driving sustainable growth. 28  New Formula(s) and Notation Production Function (with Cobb-Douglas specification) Y = F (K, L) = AK α L1−α A total factor productivity F (·) some unspecified function, e.g. production function w real wage α elasticity of capital ∂y partial derivative of y with respect to x ∂x 29  Next Lecture The Solow-Swan Growth Model I – savings, investment and capital accumulation – steady-state - solving the model – implications of diminishing returns to K - transitional dynamics BOFAH Chapter 15 30