Economic growth and the solow model eric sims university of notre dame fall 2012 1 introduction we begin the course with a discussion of economic growth. Solows model of growth with diagram economics discussion. At k the economy is in a steady state and it is the only level of capital, where all variables grow. Firms are competitive and maximize profit taking prices as given. In this work we deal with the solowswan economic growth model, when the labor force is ruled by the malthusian law added by a constant migration rate i. The solow model describes the optimal saving in steady state. Derive the steadystate value of k in terms of the exogenous parameters. A cobbdouglas production function is of the form ytk t. K real capital stock l real employment solow estimates a cobbdouglas production function for the us. Technically growth just refers to the periodoverperiod percentage change in a variable. Nov 02, 2017 at its core it is a neoclassical aggregate production function, usually of a cobbdouglas type, which enables the model to make contact with microeconomics. Cobbdouglas production function 3 solow model with a ces production function 3. No aggregate production function the centerpiece of every growth model is the aggregate production function does an aggregate production function exist.
Intermediate macroeconomics lecture 4 growth models. The production function model was applied to the study of growth problems by robert solow american economist, massachusetts institute of technology, nobel prize 1990. However, for concreteness, i am going to be speci c and limit us to the case in which the production function takes the cobb douglas form. I the solow model is the basis for the modern theory of economic growth. Daron acemoglu mit economic growth lecture 4 november 8, 2011. Factor accumulation and technological growth are also exogenous. We will also assume that f is a neoclassical production function. A note on the solow growth model with a ces production. Y t atk l1 t 0 model looks like the step function in figure 1. At k all absolute variables k, y, c, i, s grow at rate n. Estimation of the solowcobbdouglas economic growth model.
Lets assume a standard cobb douglas aggregate production function. For this example, our cobb douglas production function is. In other words, production exhibits constant returns to scale. In the case of a cobbdouglas production function, neutral and laboraugmenting technological progress are equivalent. In economics, a production function is an equation that describes the relationship between input and output, or what goes into making a certain product, and a cobbdouglas production function is a specific standard equation that is applied to describe how much output two or more inputs into a production process make, with capital and labor being the typical inputs described. Lets assume a standard cobbdouglas aggregate production function. Y t a tk l1 so output y t is a function of productivity a t, physical capital k t, and labor l t at time t. The rate of convergence in the solow model andthensome. An important equation from the solow growth model is. All markets both input and output markets are assumed to be perfectly competitive. As a result he came to a modified version of the cobbdouglas production function. Solow postulates a continuous production function linking output to the inputs of capital and labour which are. A note on the solow growth model with a ces production function.
Solow demonstrates in his model that, this fundamental opposition of warranted and natural rates turns out in the end to flow from the crucial assumption that production takes place under conditions of fixed proportions. At k, all percapita variables k, y, c, i grow at rate 0 they are constant. Solows contribution was to extend the cobb douglas production function with a third factor of growth technological progress, which he understood as operating autonomously in time. Pdf modelling the economic growth rate of ghana using the. The constant acaptures tfpand should be interpreted in a broad sense. But by the second quarter, the value of y has grown, so the amount of increase in y in the second quarter will be. This can be represented using a broad range of production functions, but for concreteness, well stick with the cobbdouglas formulation. Solow began with a production function of the cobb douglas type. The neoclassical growth model and twentiethcentury. Return to basic solow model with constant population growth and. It attempts to explain longrun economic growth by looking at capital accumulation, labor or population growth, and increases in productivity, commonly referred to as technological progress.
The solowswan model of economic growth postulates a continuous production function linking output to the inputs of capital and labour which leads to the steady state equilibrium of the economy. Solow model demonstrated why the harroddomar model was not an attractive place to start. Mechanics of production, saving, and capital accumulation. Daron acemoglu mit economic growth lectures 2 and 3 november 1 and 3, 2011.
Solow builds his model of economic growth as an alternative to the harroddomar line of thought without its crucial assumption of fixed proportions in production. Unlike the solow model as we typically set it up with laboraugmenting technological progress, productivity. Macroeconomics solow growth modelexample neoclassical onesector growth model consider the solow neoclassical onesector growth model with cobbdouglas production function y f k, l k 1 3 l 2 3. Integrated macroeconomic production function for open economies. I the solow model is the basis for the modern theory of.
On the other hand, it is very interesting to note that, aside from the above consideration, it should be possible to estimate the whole solowcobbdouglas model by using only the economic data commonly used for estimating the cobbdouglas production function y f k, l. The solowswan model is an economic model of longrun economic growth set within the framework of neoclassical economics. We discuss the models variables, parameters, and notation and discuss the models assumption. The human capital augmented solow model in a 1992 article in the quarterly. The solow growth model the robert solow growth model presents a highly simpli. Next plot capital deepening for the intensive solow model in fig ure 2. Y ak b l 1b where 0 production function is known as the cobb douglas production function, which is the most widely used neoclassical production function. Pdf the debate over the cobbdouglas production function has been.
This is because of the compounding of growththe effect of the expansion over time in the base to which the growth rate is applied. For example, one production function that satisfies these properties is the. Romers chapter 1, covering the solow growth model and related theories. Consider cobbdouglas production function y t atk t. Production functions generally take the form of yfk,l so it would be interesting to find what the per capita form. There are many ways for the production function to shift over time. Solow growth model overview, assumptions, and how to solve. The model was developed independently by robert solow and trevor swan in 1956, and superseded the postkeynesian harroddomar model. Technical change and the aggregate production function.
Economic growth before we get to the model econ 4960. Intermediate macroeconomics lecture 3 the solow model zs o a l. Intermediate macroeconomics lecture 3 the solow model. When the saving rate cannot adjust, can k increase. Technically growth just refers to the periodoverperiod percentage change in. By this we mean shifts in the production function over time. But the 1% increase in aalso implies a 1% increase in kwhich causes an additional increase of 0. A cobb douglas production function has the form y k. Under the assumption of the cobbdouglas technology, labour augmenting technological change is also hicks neutral. Pdf this article examines the growth theory of robert solow, which has been.
However, for concreteness, i am going to be specific and limit us to the case in which the production function takes the cobbdouglas form. In continuoustime models, time flows continuously and variables can change to new values at any moment. Output is regarded net output after making allowance for the depreciation. Algebraic production functions and their uses before cobbdouglas. Third, we derive the rate of convergence in the augmented solow model. Lecture 4, the solow growth model and the data daron acemoglu mit november 8, 2011. When we endogenous capital in the solow model we learn that one reason some countries have higher. This implies that the production function exhibits constant returns to scale in its three factors. This is the cobbdouglas production function written in inten sive form and then multiplied. How to derive a per capita production function from a general. Macroeconomics solow growth model example neoclassical onesector growth model consider the solow neoclassical onesector growth model with cobb douglas production function y f k, l k 1 3 l 2 3. The production model is different from the solow model in that capital is assumed to be exogenous. Chapter 2 the solow growth model and a look ahead 2. Rewrite production function y k l 2 3 in perworker terms.
For him, technological progress is an exponential function of time. Population growth and technological progress gdp y t fk. Technological progress in the solow model in the basic solow model, growth occurs only as a result of factor. The solow growth model starts with an aggregated cobbdouglas production function, which assumes that real output in an economy is produced using capital and labor only.
When the cobbdouglas production function is used, the per capita output growth rate is posi tive even if the technological progress rate is zero. Steadystate analysis of the solow model conclusions. Solows model allows us to decompose growth into these three components. So the total increase in y is 1% the same as the increase in productivity. The illusions of calculating total factor productivity and.
The cobbdouglas production function and the steady state. At the center of the solow growth model is the neoclassical aggregate production function. Humphrey fundamental to economic analysis is the idea of a production function. One production functions f k, l that satisfies the requirements imposed by the solow model is the production cobbdouglas function. Douglas and developed this famous model of aggregate production.
We discuss the model s variables, parameters, and notation and discuss the model s assumption. It and its allied concept, the utility function, form the twin pillars of neoclassical economics. In our analysis, we assume that the production function takes the following form. Using the solow model diagram, illustrate and explain the dynamic response of k to a. The main objective of this study was to use the solow growth model augmented cobb douglas production function as a basis to model the economic growth of ghana during the period 1990 to 2010. Assumptions savings and investment decisions are exogenous no individual optimization.
Neoclassical onesector growth model university at albany. Macroeconomic production functions such as the cobbdouglas function. Jul 26, 2011 deriving a per capita production function from a general production function. For other neoclassical production functions this is not the case. However, the key parameter of solows model is the substitutability between capital and labour. In economics and econometrics, the cobbdouglas production function is a particular functional form of the production function, widely used to represent the technological relationship between the amounts of two or more inputs particularly physical capital and labor and the amount of output that can be produced by those inputs. The solow swan model of economic growth postulates a continuous production function linking output to the inputs of capital and labour which leads to the steady state equilibrium of the economy. The solow models production function the starting point for the solow model is the assumption that there is a production function with dimishing marginal returns to capital accumulation.
Mapping the model to data introduction solow growth model and the data use solow model or extensions to interpret both economic growth over time and crosscountry output di. In the case of a cobb douglas production function, neutral and laboraugmenting technological progress are equivalent. The cobbdouglas form was developed and tested against. Wilson mixon jr and others published the solow growth model find, read and cite all the research you need on researchgate. Production function, with physical capital k, labor l. However, for concreteness, i am going to be speci c and limit us to the case in which the production function takes the cobbdouglas form. A typical variable in a continuoustime model might have a time path like the smooth line in figure 1. Cobbdouglas is a production function satisfying these prop. For this example, our cobbdouglas production function is. Nonetheless, it does give us some grip on the factors governing longrun macroeconomic outcomes, in particular the dynamics of the accumulation of capital. Ytafkt,nt, which it is assumed to satisfy a series of technical conditions.
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