ITFD Growth and Development Slide SET 1Slide 1 ITFD Growth and Development LECTURE SLIDES Professor Antonio Ciccone

ITFD Growth and Development Slide SET 1 Slide 2 I. THE SOLOW MODEL 1. WHY HAVE PRODUCTIVITY LEVELS BEEN RISING? PROXIMATE CAUSES 1. (Physical) Capital per worker Physical capital refers to all durable inputs into production: machine tools, motor vehicles, computer hardware and software etc. One reason for higher productivity today is that workers have on average much more capital to work with.

ITFD Growth and Development Slide SET 1 Slide 3 2. Technology or the Accumulation of Knowledge (“Ideas”) Over the course of time, people have accumulated more and more ideas that allow them to get more output using the same inputs. That is economies have become more EFFICIENT. For example, three field crop rotation.

ITFD Growth and Development Slide SET 1 Slide 4 The mechanisms through which knowledge is accumulated include: Learning externalities: learn how to do things more efficiently based on your own experience or that of others. This experience accumulates over time. Specialization: larger markets allow people to focus on a more limited set of tasks; in the past for example the same people would be both dentists and hairdressers. Research and development: some people do nothing but try to come up with ideas all day; for profit, they hope to be able to patent them.

ITFD Growth and Development Slide SET 1 Slide 5 3. Human capital Today, almost everybody can read and write in industrialized countries while in the past these capacities were limited to very limited segments of society only. The capacity to R&W makes people more productive. In some industrialized countries almost half of the students go on to get a higher education. This makes them able to produce more efficiently and also be more involved in generating new ideas.

ITFD Growth and Development Slide SET 1 Slide 6 2. WHY THE SOLOW MODEL 1. Focus on the accumulation of physical capital Capital accumulation evidently and always part of the growth process. - Makes it empirically relevant - Necessary ingredient in growth models who focus on other drivers of economic growth.

ITFD Growth and Development Slide SET 1 Slide 7 2. Capital accumulation and savings alone cannot explain long-run growth Its main result was at the time “counterintuitive” but is based on solid fundamentals and has been show to be consistent with many empirical observations: Capital accumulation and savings alone CANNOT explain why income per capita keeps growing.

ITFD Growth and Development Slide SET 1 Slide 8 3. A dynamic general equilibrium model Solow model is the first (reasonable) general equilibrium model about how the economy evolves over time. And it is still the backbone of the models used in macro.

ITFD Growth and Development Slide SET 1 Slide 9 4. Many things are left out of the Solow model Including: - learning externalities - R&D - human capital  Modern growth theories

ITFD Growth and Development Slide SET 1 Slide STATIC AND DYNAMIC GENERAL EQUILIBRIUM MODELS 1. A GE model is simply a model of the economy as a whole This means that it treats together markets that in microeconomics would be dealt with separately. Economic growth has implications for many different but related markets and studying it therefore requires a GE model For example, if firms have access to better technologies: this will affect their labor demand, and therefore the labor market through the labor market this will affect the wage/income workers earn and therefore their capacity to save the savings of workers will affect how much new investment firms are able to do

ITFD Growth and Development Slide SET 1 Slide 11 Tractable GE models: - have to focus on the INTERACTING MARKETS that appear essential for the question asked - otherwise there is no way one could make progress given the many markets and market participants that are part of even a small economies like Luxembourg

ITFD Growth and Development Slide SET 1 Slide Static GE models Are snapshots of an economy at one moment in time. For example, the following extremely simple model to determine: - output Y(t) of an economy - real real wages w(t)

ITFD Growth and Development Slide SET 1 Slide 13 FIGURE 1 HH (preference for leisure and consumption; aggregate labor endowment L(t)) FIRMS (technology of production) GOODS MARKET LABOR MARKET To determine PRICES and ALLOCATIONS what is going on we therefore need to specify:  preferences  technology  markets that exist and their structure

ITFD Growth and Development Slide SET 1 Slide Capital An dynamic general equilibrium model (growth model) needs: a way to transfer resources from the present to the future This will be accomplished by having a production factor called CAPITAL in the model: FOREGO CONSUMPTION TODAY  BUILD UP NEW CAPITAL  PRODUCE MORE GOODS TOMORROW

ITFD Growth and Development Slide SET 1 Slide Snapshot of economy with capital as a production factor FIGURE 2 HH (preference for leisure; aggregate labor endowment L(t) plus property rights in firms) FIRMS (technology of production; capital owned at the beginning of the period K(t))). GOODS MARKET LABOR MARKET RENTAL MARKET FOR CAPITAL GOODS The rental market for capital goods determines the RENTAL PRICE OF CAPITAL

ITFD Growth and Development Slide SET 1 Slide From the static to the dynamic model The static model determines aggregate output Y(t) and the real wages w(t) and real rental prices of capital R(t) for a given labor supply L(t) and the capital stock K(t). The Solow model tells us how to determine the whole evolution of capital stocks and output levels over time, from time 0 to infinity. As a result it tells about factors prices, income distribution, and income/output.

ITFD Growth and Development Slide SET 1 Slide 17 The key to going from the static to the dynamic model: -understanding the evolution of the capital stock over time -imagine time going from period 0 to period 1, 2, 3, 4, and so on -what is the link then between the capital stock at period t and the period before that t-1?

ITFD Growth and Development Slide SET 1 Slide 18 Machines available for production at time t = Machines available for production at time t-1 MINUS Machines that broke during production in period t-1 PLUS New Machines produced by firms at time t-1 (E1) CAPITAL ACCUMULATION EQUATION, a key equation in the Solow model -- “delta” fraction of capital stock that breaks in use -- I investment (machines produced)

ITFD Growth and Development Slide SET 1 Slide 19 We will work in continuous time. The capital accumulation will therefore look a bit different. It can be derived from the equation above by letting the time between periods becomes smaller and smaller. Denote the time between periods by  then: (E2) where I(t) is now the investment flow, i.e. the investment per (very small) unit of time and  is depreciation per unit of time. Rewriting yields: (E3) Taking the limit as  goes to zero becomes:

ITFD Growth and Development Slide SET 1 Slide 20 (E4) - From now on DOTS over symbols will denote TIME DERIVATIVES. - (E4) says that the change in the capital stock over time (net investment) is equal to (gross) investment minus the capital that depreciates while being used in production. - This is the capital accumulation equation in continuous time, which will end up linking different time periods.

ITFD Growth and Development Slide SET 1 Slide THE SOLOW MODEL AT A MOMENT IN TIME 1. A model of output and factor prices given factor stocks The goal is to understand the determination of output (the precise economic statistic is called gross domestic product, GDP), wages, the rental price of capital, and the distribution of income among factors of production (functional income distribution).

ITFD Growth and Development Slide SET 1 Slide 22 To do that we need to: (1) specify preferences of HH (2) specify technology of production of firms (3) specify structure of the labor market, the goods market, and the rental capital market (4) define an equilibrium

ITFD Growth and Development Slide SET 1 Slide Preferences Households supply all their labor L(t) to the labor market, whatever wages may be (they supply L(t) inelastically). For the dynamics we will have to specify how they save, for what we do now it doesn’t matter. 2. Production Production of investment as well as consumption goods Firms produce investment and consumption goods using the following technology Where: K is the capital they use in production L is the labor they use in production (E5)

ITFD Growth and Development Slide SET 1 Slide 24 Hence there are two inputs in production that the firm can control. A is a factor that will capture technological progress or improvements in efficiency The greater A, the more the firm produces with a given amount of resources K and L (the “more efficient” is the firm). Technological progress is taken as given; the firm cannot control it. Technological progress multiplies labor, it is as if it increased the efficiency of labor. This is called LABOR-AUGMENTING TECHNICAL PROGRESS.

ITFD Growth and Development Slide SET 1 Slide 25 Assumptions about the production function F 1. Constant returns to scale (CRTS) to the inputs K and L (E6) for any b>0 So, if you double inputs, you double output. This make sense in long run because you can always at least “replicate”. An important implication of this is that output per worker only depends on capital per worker. To see this take b=1/L (E7)

ITFD Growth and Development Slide SET 1 Slide 26 Hence CRTS implies that small firms produce as much output per worker as small firms if they have the same K/L. It will be useful to introduce the notation of output per efficiency worker (which because of CRTS depends only on capital per efficiency worker) (E8)

ITFD Growth and Development Slide SET 1 Slide Positive but decreasing MARGINAL PRODUCTS (MP) to capital and labor taken separately (E9) (E10)

ITFD Growth and Development Slide SET 1 Slide 28 An important implication of CRTS is that the MPK ONLY DEPENDS ON capital per efficiency worker To see this note: Hence, the MPK will not change over time if is constant E11

ITFD Growth and Development Slide SET 1 Slide 29 CRTS also implies that MPL depends on and A (E12) Hence, the MPL will increase over time with A even if constant

ITFD Growth and Development Slide SET 1 Slide 30 -Finally, CRTS also implies that if firms pay the MP to their inputs K and L, there will be no (pure/economic) profit left, i.e. all output will be paid to production factors. (E13)

ITFD Growth and Development Slide SET 1 Slide So-called Inada conditions Which say that the marginal produce of capital is very high when there is little of it and very low when there is a lot (E14)

ITFD Growth and Development Slide SET 1 Slide 32 - FIGURE 3 The production function in labor-efficiency units

ITFD Growth and Development Slide SET 1 Slide Market structure and equilibrium All markets are assumed to be perfectly competitive HH satisfy their budget constraint Demand=Supply in all market

ITFD Growth and Development Slide SET 1 Slide The static equilibrium Output depends on K and L employed in production, i.e. on factor use. Factor use is determined in factor markets. Let us take a look at the two markets: - labor market - rental market for capital

ITFD Growth and Development Slide SET 1 Slide 35 1.Labor market - Labor supply is inelastic, as assumed under preferences - Labor demand For any given capital stock firms hire labor to maximize profits (bars to make clear what is taken as given by firms) which gives rise to labor demanded as a function of w for any w, firms demand labor to equalize MPL and w. (E15) (E16)

ITFD Growth and Development Slide SET 1 Slide 36 Wage LABOR SUPPLY CURVE LABOR DEMAND CURVE=MPL SCHEDULE L(t) W(t) Employment - FIGURE 4 Labor market equilibrium Equilibrium employment L; Equilibrium real wage w=MPL

ITFD Growth and Development Slide SET 1 Slide Rental market for capital Firms own their capital, but that does not prevent them from renting it out if they think they can make money doing so - Capital supply is inelastic at a given moment in time - Capital demand For any given level of employment firms rent capital to maximize profits (bars to make clear what is given) which gives rise to capital demanded as a function of rental cost of capital R (use one period then return what is left) for any R, firms demand labor to equalize MPK and R. (E17)

ITFD Growth and Development Slide SET 1 Slide 38 Rental Price CAPITAL GOODS SUPPLY CURVE CAPITAL GOODS DEMAND CURVE=MPK SCHEDULE K(t) R(t) CAPITAL GOODS FIGURE 5 Rental capital market equilibrium

ITFD Growth and Development Slide SET 1 Slide Summarizing the static equilibrium The factor market (static) equilibrium conditions for given K(t), L(t), A(t) and hence are : see E11 see E12 or

ITFD Growth and Development Slide SET 1 Slide 40 Capital per Efficiency Worker FIGURE 6 The production function in intensive form and wages/rental price of capital