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Unformatted text preview: Macroeconomic Policy Class Notes Macroeconomic Measurement 2: Value production and distribution Revised: September 27, 2011 Latest version available at www.fperri.net/teaching/macropolicyf11.htm Production So far we have discussed what GDP is and how GDP is spent. Now we will briefly discuss how to measure the factors of production. In macro it is helpful to introduce the concept of aggregate production function which is a useful way to think about the relation between product/value and the factors that are used to produce it. The aggregate production of value can be described by the following relation: Y = AF ( K,L ) Capital and labor are the factors of production, while A denotes the so called Total Factor Productivity (TFP). We will now briefly discuss how to measure K and L while we will talk about TFP in later classes. The capital stock The capital stock of a country represents the amount of physical, productive assets present in that country. Note that the US capital stock is not the same thing as US wealth as US wealth represents the total assets owned by US nationals. The capital stock today is the result of two forces, investment and depreciation. The accumulation of capital stock of a certain type of capital is described through: K t = I t + (1- ) K t- 1 where represents the depreciation rate. Suppose that at the beginning of time the capital stock was K and that the depreciation rate is constant. Using the above Value production and distribution 2 equation repeatedly we get K 1 = (1- ) K + I 1 K 2 = (1- ) K 1 + I 2 = (1- ) 2 K + (1- ) I 1 + I 2 ... K t = I t + (1- ) I t- 1 + ... (1- ) t- 1 I 1 + (1- ) t K so the current capital stock is given by a weighted sum of all past investments, where the weights are decreasing with time. Investment far back in time have a smaller weight because they are more depreciated. Different capital goods have different capital depreciation rates, as shown in the table below: Type of good Annual depreciation rate Computers (after 78) .31 Computers (before 78) .27 Trucks .12 Ships .06 Industrial buildings .03 Residential housings .01 Figure 1 shows the depreciation profile for an investment of 100 dollars in equipment for various goods. Note that here we attempt to measure physical depreciation that is not necessarily connected with the fiscal depreciation (i.e. how much depreciation of your capital you can write off as a business expense). By summing up the value of the capital stock of all different goods we get the total capital stock of the US economy. In the table below we can see the composition of the US capital stock in 2001: Composition of the US capital stock in 2010 Total Fixed private Fixed Govt Cons Dur....
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