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nomy is 10 for the year what is real gdp well we already really know the answer it s 10 cans of budweiser real gdp is measured in real units that s obvious in this example because the real units are obvious cans of bud to do this more formally we find real gdp by dividing nominal gdp by a price index in this case the price index is easy to figure out it s 1 per can of bud so real gdp is 10 1 per can of bud 10 cans of bud one confusion with real gdp is that the bea and economic textbooks insist on talking about it in terms of dollars that is because the price index they use is not something like 1 per can but is something like 1 37 per 1 of output in 2005 so real gdp is 10 1 37 per 2005 dollar 7 3 units of 2005 dollars which would be reported as 7 3 2005 dollars but despite being reported in terms of dollars real gdp has nothing to do with money i sometimes think that we should save our effort at coming up with good price indices and just use something like the price of a can of bud or a pair of levi 501 jeans as the price deflator in national accounts because then real gdp would be reported in real tangible units and would save us from confusing it with a nominal number for example if the price of a can of bud was 0 50 then real gdp in the us for 2014 would be 17 615 billion 0 50 per can on bud 35 230 cans of bud nominal gdp through q3 2015 is 18 060 so that s real gdp of 36 120 cans of bud a 2 5 increase in real gdp from 2014 i m laboring this point because when it comes to explaining how growth works this confusion between nominal and real concepts becomes a problem let s go back to our simple 10 can economy with a price per can of 1 and see how growth works growth through expanding production of existing products this is the easiest to explain something happens at anheuser busch that lets them produce even more cans of bud with their given inputs perhaps they water it down even more than it already is whatever the reason the economy produces 12 cans of bud this year we know that real gdp went up from 10 cans to 12 cans but let s walk through how to do this calculation using nominal gdp and a price index think of two possibilities nominal gdp stays constant that is nominal gdp is still 10 then it must be that the price of a bud fell to 0 83 the supply curve of bud shifted out and hence the quantity of bud went up and the price of bud went down real gdp is 10 0 83 per can 12 cans of bud for the given flow of money through the economy which does not have any necessary relationship to real gdp the price of a can of bud must adjust to make supply equal demand the price of bud stays constant let each can still be 1 the it must be that nominal gdp is 12 and real gdp is 12 1 per can 12 cans of bud here the supply curve of bud has shifted out but apparently the demand curve shifted out as well leaving the price unchanged and the quantity higher why would this happen who knows and who cares it s possible for a given flow of money through the economy the price of a can of bud must adjust to make supply equal to demand note that it is irrelevant whether nominal gdp goes up or stays constant it could even fall whether nominal gdp rises or not is completely irrelevant to whether real gdp goes up if we could observe the real quantity of cans consumed we wouldn t need nominal gdp at all but we don t actually observe the number of cans of bud consumed all we observe is nominal gdp and the price of a can of bud so when the bea reports a nominal gdp of 10 and a price of 0 83 per can we divide and infer that real gdp is 12 cans of bud if your question now is where people get the extra money to afford 12 cans of bud when their price stays at 1 take a moment to meditate on the equation we ll come back to that in a few paragraphs growth through addition of new products this one will stretch the mind a little more but the same principles are going to hold rather than bud watering down their beer even further we re going to introduce a new beer into the market someone and god bless them invents real ale coffee porter in response people with functioning taste buds buy 5 cans of coffee porter and everyone else still buys 5 cans of bud so we ve still only got 10 cans of beer being sold is this economic growth meaning that real gdp is higher it depends on relative prices if those cans of coffee porter are more expensive than cans of bud then this represents real economic growth why because if the relative price of coffee porter is higher than that of bud then the relative marginal utility of coffee porter is higher than that of bud assuming that utility for both has typical properties declining mu then we know the mu of the 5th can of bud is higher than the 10th can and since coffee porter has a higher mu than that it follows that we are better off in utility terms more intuitively if we weren t better off then why were we willing to substitute away from bud even though coffee porter costs more which suggests that if coffee porter and bud sold for the same amount then we aren t any better off in this case it s a perfect substitute and the choice of 5 of each is just random it s the difference in relative prices that a new product introduces that defines it s contribution of real growth so eocnomic growth is just about things getting more expensive no note that i didn t say anything about the absolute price of bud or coffee porter because that is irrelevant for real gdp so long as coffee porter is more expensive than bud we ve experienced real growth that holds if porter costs 2 to bud s 1 or 20 to bud s 10 or 0 02 to bud s 0 01 once we ve established that there is a relative price difference then the same questions about nominal gdp from before come up let s say that we observe that coffee porter costs twice as much as bud how do we calculate real gdp nominal gdp stays constant it must be that bud costs 0 67 and the porter is 1 33 so nominal gdp is 10 multiply it out and you can see it what is real gdp in this case sticking with our standard of using the price of bud real gdp is 10 0 67 per can of bud 15 cans of bud it is as if our economy produced 15 cans of bud where before it only produced 10 there is real gdp growth due to the introduction of coffee porter even though all coffee porter does is replace consumption of bud and total beer drinking stays constant at 10 cans the price of bud stays constant if bud still costs 1 then the porter is 2 so nominal gdp is 15 again just multiply it out what is real gdp 15 1 per can of bud 15 cans of bud real gdp has gone up it is irrelevant what the nominal price of bud is we observe real gdp growth because the introduction of coffee porter introduced a relative price difference notice that if all the bea reports to me is nominal gdp and the price of bud i can infer real gdp regardless of what exactly happens our bud based measure of real gdp goes up to 15 i don t actually have to observe the number of cans purchased this example of adding a new product brings up one issue with price indices which is product replacement if as would be logical if people tasted them the introduction of coffee porter completely eliminated bud from the market then we cannot calculate real gdp there will be no price of bud to divide nominal gdp by and we can t just use the price of coffee porter because yesterday all we had was bud and there was no price for coffee porter one of the reasons we use more sophisticated price indices that combine the price of bud and coffee porter in some way is so that we always have a price index to use but that sophisticated price index by putting things in 2005 dollars or something like that creates confusion between real gdp and nominal gdp always think of real gdp as being cans of bud rather than in dollar terms now if you are still wondering where people get the extra money to buy the coffee porter in this example then the next section is for you where does the extra money come from nowhere there is no extra money nominal gdp is not a measure of how much money we have nominal gdp is the flow of dollars through the economy the stock of money is well a stock in all the examples above what is the stock of money you can t answer that question because i never said anything about it let s say that this economy has a stock of 4 one dollar bills here s the transactions flow in this economy in the initial stage with only 10 can of bud consumed person a starts with the 4 nominal gdp is zero person a buys 4 buds for 4 from person b nominal gdp is 4 person b buys 4 buds for 4 from person c nominal gdp is now 8 person c buys 2 buds for 2 from person d nominal gdp is now 10 person d ends up with 2 and person c with 2 final nominal gdp is 10 then next period we start again only now c and d hold the money stock the money stock is always 4 and it gets turned over and over resulting in 10 of nominal transactions or gdp no it doesn t matter that the circle isn t closed here with different people ending up with the actual dollars real gdp is 10 cans of bud if we have the case where coffee porter gets introduced things look like this person a starts with the 4 nominal gdp is zero person a buys 2 porters for 4 from person b nominal gdp is 4 person b buys 4 buds for 4 from person c nominal gdp is now 8 person c buys 2 porters for 4 from person d nominal gdp is now 12 person d buys 1 bud for 1 and 1 porter for 2 from person e nominal gdp is now 15 person d ends up with 1 and person e with 3 final nominal gdp is 15 no new money is necessary real gdp is 15 cans of bud the same 4 gets recycled over and over again this time used to purchase both buds and porters different people end up with money stock at the end we could easily write out an example where the growth occurred because of just an increase in the number of buds and if you prefer that nominal gdp not increase you can easily go back and work out the same set of transactions lower the absolute prices and get nominal gdp to come out to exactly 10 and yes i made up these examples but i just need to show you that it is possible to get economic growth even though there is no new money in the economy economic growth occurs either because we produce more of existing things or because we introduce new things that that are more valuable than the old things we produced which shows up in relative price differences the level of absolute prices is irrelevant the level of nominal spending is irrelevant the stock of money is irrelevant for any modern economy it is effectively impossible for there to be not enough money to let growth occur the economy as a whole can always turn over the money stock faster to allow for the extra transactions if necessary whether that turnover involves you and means that you can afford to buy some coffee porter is a different question and involves your own productivity and or ownership of a bud or coffee porter producing machine share this share on x opens in new window x share on facebook opens in new window facebook share on reddit opens in new window reddit email a link to a friend opens in new window email like loading posted in uncategorized 20 replies calculating growth rates posted on january 13 2016 by dvollrath 8 note the growth economics blog has moved sites click here to find this post at the new site i m prepping for my undergraduate growth course this semester which uses an awesome book by the way we don t require calc from our econ majors at uh so i have to ease them into a few things during the course one of those is using logs to both visualize and then analyze economic growth this post is some notes i started working on to help introduce students to the concepts if you re teaching this might come in handy if you re interested in growth but a little shy about math this might be helpful if you literally have nothing better to do it will kill about 10 minutes and or help put you to sleep we re interested in living standards as measured by real gdp per capita we don t concern ourselves a lot with the absolute value of real gdp per capita as that number depends on exactly how we construct price indices base years etc what we care about is how fast economies grow this is like saying that we don t care whether you start at 150 pounds or 68 kilograms but if your weight grows by 5 per year we know you are going to get fat to visualize those growth rates and to do some crude analysis we invariably plot real gdp per capita in logs when i say log i mean the natural log there are lots of cool explanations of how natural logs work but this post is not one of them for now we re going to take it on faith that natural logs work the way i say they do take the natural log of gdp per capita in each year and graph it against the year itself the figure below for india is an example where real gdp per capita is plotted using the grey line natural logs have a few great properties for our purposes using them means that every step up the y axis is an identical percent change in real gdp per capita going from 7 0 to 7 5 for example is a 65 increase in real gdp per capita going from 7 5 to 8 0 is also a 65 increase in real gdp per capita this is true even though from 7 0 to 7 5 is going from 1 096 to 1 800 in gdp per capita and going from 7 5 to 8 0 is going from 1 800 to 2 980 by plotting things in natural logs we can see the percent increases rather than the absolute increases even more fun is that because of this property we can pick off the average growth rate between two years relatively easily the average growth rate between two years is just the slope of the straight line connecting the two end points in the figure for india i ve overlaid the calculation of the growth rate for several sub periods as well as the average growth rate from 1950 to 2010 from 1950 to 2010 as an example connect the two end points and find the slope of the line you could do this mathematically as follows for the other sub periods you do the same thing just using the end points from those time periods so from 1950 to 1975 growth average 2 0 from 1975 to 1985 if average 3 0 and from 1985 to 2010 it averaged 5 2 why those particular sub periods and not others solely because they looked like obvious break points there is no formula for deciding what sub periods to calculate it just seems intuitive that something different happened around 1985 for example that sets that period apart from the others but you could calculate the growth rate from 1972 to 2003 if you wanted to you want to argue with me that the 1985 to 2010 period should be broken up again into pre 2003 and post 2003 sub periods okay i can t tell you you re wrong the three sub periods i did calculate have the feature that their average growth seems very close to the actual growth that is the actual path of gdp per capita doesn t stray very far from the straight line we used to calculate the average growth from 1950 to 1975 for example what do i mean by very far nothing technical just eye balling it compa...
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