20060830_econ_101b_lecture_notes - 1 Lecture Notes: Econ...

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Unformatted text preview: 1 Lecture Notes: Econ 101B: August 29-31 2006 Introduction to the Theory of Economic Growth Questions Why is the world so much richer today than it was fifty or a hundred years ago? What are the prospects for increasing riches in the future? And why is the world today so unequal as we look across countries? Macroeconomists study these questions in their standard way. Ruthless simplification, followed by specifying aggregate behavioral relationships and equilibrium conditions, and then analyzing the consequences of their assumptions and trying to map their conclusions onto the world. Economists make an intellectual bet: that an exact solution to a grossly oversimplified model that approximates the most important features of the world will be a reasonably good approximation to what is actually going on in the world. Basics: The Production Function So, begin by assuming that four things are important: labor L, capital K, technology and organization E, and diminishing returns to scale. We begin with a production function: Y = K ( EL ) 1 with a parameter between 0 and 1, governing diminishing returns to scale. 2 We are going to want to work with rates of change, and with log rates of changewhich are the same thing as proportional rates of growth: d ln( x ) dt = 1 x dx dt So lets take logs and then the time derivative of our production function: ln( Y ) = ln( K ) + (1 )ln( L ) + (1 )ln( E ) d ln( Y ) dt = d ln( K ) dt + (1 ) d ln( L ) dt + (1 ) d ln( E ) dt 1 Y dY dt = 1 K dK dt + (1 ) 1 L dL dt + (1 ) 1 E dE dt Basics: The Capital-Output Ratio...
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20060830_econ_101b_lecture_notes - 1 Lecture Notes: Econ...

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