MACROECONOMICS I March 7th, 2014 Class 3. Explaining Economic Growth. The Solow-Swan Model Homework assignment #1 is now posted on the web Deadline: March 21st, before the class (12:00) Submission: One hard copy of answers from a group N!B! NO late submissions will be accepted Announcement The evolution of GDP per capita, 1960-2010 USA UK Singapore Guatemala S. Korea India Nigeria Botswana Log GDP Solow-Swan Model of Economic Growth(1956) § What drives changes in GDP per capita in the long run? • Robert Solow (1956) Economic environment (a set of assumptions) • A single composite good • Two factors of production: capital and labor • Two agents: firms and households • A closed economy Solow-Swan Model: Supply Side Production function (technology) • Maximum output for given inputs Capital Labor Factor Inputs Aggregate output (GDP) § Production of movies Solow-Swan Model: Returns to Scale What would happen to GDP is both inputs increase twice? • Constant returns to scale (CRS) If the quantity of both inputs doubles, the output also doubles - Decreasing vs. Increasing returns to scale • Output is a positive function of inputs Solow-Swan Model: Returns to Factor Inputs • Diminishing returns to factor inputs For a fixed L, an increase in K would lead to smaller and smaller increase in Y For a fixed K, an increase in L would lead to smaller and smaller increase in Y • Increasing returns to factor inputs What would happen to GDP if only one input increases? Solow-Swan Model: GDP Per Capita GDP per capita Capital per worker § Transforming the model to per capital terms N!B! The level of capital per worker determines the level of output per worker or Capital/Labor ratio Solow-Swan Model: Diminishing Returns Production function: Implication: Countries with small capital stock (k) are more productive => grow faster GDP per capita Capital per worker Solow-Swan Model: Diminishing Returns (Cont.) Country Average annual growth rate of GDP per capita 1950-1960 1980-1990 Germany 6.6 % 1.9 % Japan 6.8 % 3.4 % France 9.6 % 2.8% USA 1.2 % 2.3 % Source: Blanchard et al (2010) Solow-Swan Model: Demand Side Consumption Investment • A fixed fraction of HH income is saved I=sY & C= (1-s)Y • Constant savings rate (s): s=30 % • Savings rate determines the allocation of income between consumption and investment Solow-Swan Model: Demand Side (Cont.) • Transforming to per capita terms I=sY & C= (1-s)Y i = sf(k) & c = (1-s)f(k) • y =f(k) – GDP per capita • i =0.3y – Investment per capita • c =(1-0.3)y – Consumption per capita Solow-Swan Model: Capital Accumulation •No population growth: L= const • GDP per capital will increase only due to increase in capital stock • Households’ savings are used as investment into capital accumulation (K) - New capital -Replacement of old capital • Capital depreciation: every year a fraction of capital δ breaks down and becomes useless Solow-Swan Model: Capital Accumulation (Cont.) • Capital accumulation kt+1=sf(k)+(1-ẟ)kt • Change in capital from year t to year t+1 kt+1 - kt =s f(k)-ẟkt Δk – change in capital stock • If Δk >0 (capital stock increases) if sf(k)>ẟkt • If Δk <0 (capital stock decreases) if sf(k)<ẟkt 3 7 Output per capita Investment Solow-Swan Model: Graphical Representation Solow Model: Steady-State (Cont.) § Steady-state: the long-run equilibrium of the economy The amount of savings per worker is just sufficient to cover the depreciation of the capital stock per worker • Economy will remain in the steady state (unless additional channels of growth are introduced) • Economy which is not in the steady state will go there => convergence to the constant level of output per worker over time • Different economies have different steady state value of capital Solow Model: Steady-State § Steady-state: investment and depreciation just balance Solow Model: Steady-State Level of Capital per Worker §Convergence to steady state Solow Model: Increase in Savings Rate • Savings rate increases from 30 % to 40 % • Economy moves to a new steady state => Higher capital and output per capita Solow Model: Steady-State (Cont.) Implications § Savings rate (s) has no effect on the long-run growth rate of GDP per capita Ø Increase in savings rate will lead to higher growth of output per capita only for some time, but not forever. Ø Saving rate is bounded by interval [0, 1] § Savings rate determines the level of GDP per capita in a long run Solow Model: The Role of Savings § A nation that devotes a large fraction of its income to savings will have a higher steady-state capital stock and a high level of income Source: Mankiw (2009) The Solow-Swan Model: Steady State § Steady state: the long-run equilibrium of the economy •Savings are just sufficient to cover the depreciation of the capital stock N!B! Savings rate is a fraction of wage, thus is bounded by the interval [0, 1] v In the long run, capital per worker reaches its steady state for an exogenous s v Increase in s leads to higher capital per worker and higher output per capita v Output grows only during the transition to a new steady state (not sustainable) v Economy will remain in the steady state (no further growth) v Economy which is not in the steady state will go there => Convergence Government policy response? The Solow-Swan Model: Numerical Example Production function Production function in per capita terms GDP per capita: Savings rate: Depreciation rate: Initial stock of capital per worker: Year k y i c δk Δk 1 4 2 … Consumption: C = (1-s)Y Consumption per capita C/Y = c Steady state capital/labor ration: The Solow-Swan Model: Numerical Example (Cont.) The Golden Rule Level of Capital § Increasing savings rate means less present consumption What is the optimal savings rate? N!B! Optimal savings rate maximizes consumption per capita The Solow-Swan Model: Convergence to Steady State N!B! Regardless of , if two economies have the same s, δ, L, they will reach the same steady state • The property of catching-up is known as convergence • If countries have the same steady state, poorest countries grow faster • Not much convergence worldwide Different countries have different institutions and policies • Conditional convergence: comparison of countries with similar savings rates Log income per capita in 1960 (100=1996) World Wide Convergence Changes in Log income per capita in 1960 -1990 Next class: Solow-Swan Growth Model (Cont.) N!B! Reading Assignment: Handout “Theories that don’t work”