Solow+Growth - Solow Growth o Condensing the production...

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Solow Growth o Condensing the production function: we’re going to use a production function of y = output per worker ($ made per worker) k = capital per worker (# of machines per worker) T = technology (how efficiently your capital can be turned into $) o f(k) has several main properties f(k) is increasing in k—more capital is always better f(k) is increasing at a decreasing rate—your first unit of capital gives you a greater benefit than your second, which gives you a greater benefit than your third, etc. o Two other variables of interest: savings rate You need to figure out how much of your output to eat and how much to invest. Generally we will tell you that you save a certain percentage of output (say, 10%) and re-invest it That amount gets added to your capital stock next period. So saving means less to eat now, but gives you more output next period o Two other variables of interest: depreciation Machines break Generally we will tell you that a certain percentage of your machines break each period That amount gets subtracted from your capital stock next period So high depreciation means less to eat next period o Important assumption: we will not be looking at population growth on its own. So for now, assume that population is held constant. o How to put all of these together Step 0: Setup. You’re given k 1 , f(k), s, and d. Step 1: Production. Plug k1 into f(k) and get a value for y1. Step 2: Some of your equipment breaks. Subtract depreciation from k1. Step 3: You re-invest. Figure out how much you save, and add that to k1 Step 4: You now have k2, which is your capital value for next year. Return to step 1. So the formula for next period’s capital is First term = leftover machines after breakage Second term = new machines after re-investment You may also be asked about consumption. That’s (1-s)*y. Why? o It often helps to set up a table with k 1 , y, and k 2 . Solving for steady-state
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This note was uploaded on 11/28/2011 for the course ECON 102 taught by Professor Rossana during the Winter '08 term at University of Michigan.

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Solow+Growth - Solow Growth o Condensing the production...

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