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lecture5 - Economics 202A Lecture Outline#5(version 1.3...

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Economics 202A Lecture Outline #5 (version 1.3) Maurice Obstfeld Endogenous Growth We have already seen one crude endogenous growth model, the so-called °AK±model. It is crude because it does not give a realistic account of the channels through which productivity grows over time ²namely, innovation and the creation of new knowledge. We now turn to a class of models that indeed endogenize the innovative process. The challenge in thinking about these problems is that the creation of knowledge, which has a public-good aspect, is di/erent from the production of other economic goods. The endogenous growth literature began with contributions of Robert Lucas and especially Paul Romer in the 1980s and 1990s, although the ideas certainly had important precursors in the growth literature of the 1960s. A Model of Endogenous Growth: The Basic Idea The model builds on some of the ideas about di/erentiated products that also underlie the °new trade theory±developed by Paul Krugman and others in the late 1970s and early 1980s. In the model, additional °varieties± of di/erentiated capital goods will boost productivity, and the process through which new capital goods are invented is endogenized. In this economy, production of a °nal consumption good is given by Y t = F ( K 1 ;t ; :::; K A t ;t ; L Y;t ) = A t X j =1 K ° j;t ! L 1 ° ° Y;t = A t X j =1 K ° j;t L 1 ° ° Y;t ; where L Y;t is the amount of labor employed in the ³nal goods sector at t and j 2 f 1 ; 2 ; :::; A t g indexes the di/erent types of capital that can be used in production as of t . Labor not devoted to ³nal-goods production will, as we shall see, be devoted to research and development into new capital goods. We assume that the capital depreciation rate is ° = 1 ; so that the price of a machine is its rental rate. Note some interesting features of this production setup : At any point in time, there are constant returns to scale with respect to the existing factors of 1
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production, no matter how many there are. But while the marginal product of an existing capital good is ³nite, the marginal product of a new capital good is in³nite. A di/erent thought experiment gives a good illustration of why the pre- ceding production function can generate endogenous growth. Imagine com- bining 1 unit each of N capital goods with 1 unit of Labor; we get Y = N . Instead, imagine we combine N= ( N + 1) units each of N + 1 capital goods with 1 unit of labor. We get Y = N +1 X j =1 ° N N + 1 ± ° = ( N + 1) ° N N + 1 ± ° = N a ( N + 1) 1 ° ° > N: So with more capital goods, the output/labor ratio rises holding constant the amount of capital input (measured in terms of consumption goods). Thus, the creation of new capital goods has the potential to raise productivity and per-worker output over time. Notice, ³nally, that if K j;t = ~ K t for all varieties j (as is the case in equilibrium when all goods are symmetric), then Y t = A t X j =1 ~ K ° t L 1 ° ° Y;t = A t ~ K ° t L 1 ° ° Y;t = ~ K ° t ° A 1 1 ° ° t L Y;t ± 1 ° ° ; so the production side looks equivalent to what we assumed for the Solow model.
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