Endogenous Growth Models Notes

Endogenous Growth Models Topics * Learning-by-Doing * Human Capital * Research and Development * International Technology Transfer Reading * Reasons for going beyond Solow model (3) * Learning-by-doing model * Learning-by-doing algebraically * Learning-by-doing vs. Solow model Learning-by-Doing * 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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