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Endogenous Growth Models Notes

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Endogenous Growth Models Topics

* Learning-by-Doing

* Human Capital

* Research and Development

* International Technology Transfer


* Reasons for going beyond Solow model (3)

* Learning-by-doing model

* Learning-by-doing algebraically

* Learning-by-doing vs. Solow model


* You should know the 3 reasons for going beyond the Solow model

* There is a steady state where everyone who shares the same technology will have the same growth rate
* The growth rate will be determined exogenously

* When we talk about the AK model, the power of K is the thing we focus on
* K^1 tells us the MPK will independent of the level of K
? i.e. very rich with lots of capital, MPK can still be high
* However, microeconomists do not like brute force modelling

* Why at aggregate level can production function be AK?
* These are the three stories we discuss in this lecture

* Bromer (1986) - JEP
* made the Learning by Doing model more user friendly

* The learning by doing method differentiates the micro and macro level
* At micro level we have diminishing MPK
* At aggregate (macro) level because of spill over we have constant MPK
* We can write this in algebraic form or graphically

* When a firm invests, other firms learn from its experience too
* The key to the learning by doing method is this positive externality Learning-by-doing algebraically
* How do we capture this difference between micro and macro level?
* We use subscript (i) to express an individual firm
* At micro level:
? When a<1, it implies diminishing marginal product at the firm level
? B is the economy-wide knowledge
# It is proportional to economy-wide stock of capital
? B depends on the total aggregate capital in the economy* How do we capture the idea of a positive externality?
? The best way is by looking at B?
measures the efficiency of how the economy captures knowledge
# It is not important other than the fact it is greater than 0
? Because we use the idea of a representative firm
* Because (i) is a representative firm, it represents aggregate output and aggregate capitaland
? Along with we can determine the aggregate production function
? Only the aggregate economy knows where B comes from
# Individual firms are only aware of the knowledge frontier and where its employees are in relation to it
* The aggregate production function:
? This is an AK production function
# No diminishing MPK at the aggregate economy level we can determine long run endogenous
* Using the capital accumulation equation growth
? When we focus on the case of a constant N,
# Implies growth rate

Key Points

is equal to a constant

# Long run endogenous growth if
? i.e. if the saving rate is sufficiently high
? Because the stock of knowledge is determined by the endogenous level of K through learning-by-doing


Implications compared to the Solow model
* Savings rate affects not only the level of income but also the growth rate
? Because x depends on s
* The growth rate is constant in both the short and long run
? There is no convergence
* There are "scale effects"
? The growth rate depends on the size of the population
? Larger N implies stronger knowledge spillovers and therefore higher growth rate x We can remove this scale effect by replacing by

Course Notes Page 18

* Human capital model

* Human capital model graphically

* Human capital vs. Solow model

* Research and development

* Capital vs. ideas

* One country R&D model

* Two country R&D model

* Appropriate technology

* Neutral technological change

* Capital-biased technological change Formulae






* At micro level:

* Output per worker is therefore

* The aggregate production function:

* The firm's profits are

* The growth rate of knowledge is therefore

* The production function for the R&D model is

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