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hello in this video we're gonna do a little macroeconomics looking at some identities among private saving national saving public saving investment and the real interest rate we'll start with a closed economy so there are no exports or imports in a closed economy why GDP equals C consumption plus I investment plus G government purchases let's assume that we're given the following values GDP is 10,000 C consumption to 7,000 we here we have an investment function 2000 - 200 R where R is - real interest rate G is government expenditures of 2000 and T as taxes or some might call it nut taxes and that equals 1000 we want to find the real interest rate the level of investment national saving public saving and private saving and I'm giving you the equations for national saving public saving and private saving also note down here national saving will equal investment in equilibrium and investment or national saving is equal to public saving plus private saving all right so first thing I'm gonna do is I'm gonna substitute everything that we know into our closed economy expression so why is 10,000 C is 7,000 I is 2,000 minus 200 R and G is 2,000 we got one equation and one unknown so we're gonna just solve this for R the real interest rate so 10,000 equals 11,000 minus 200 are subtracting 11,000 from both sides and cancelling the minus signs out on both sides are the real interest rate equals 5 which represents 5% define the level of investment spending in equilibrium take this five and plug it into the investment function so the total level of investment spending is 1000 we can simply find national saving right now by saying national saving equals investment so investments 1,000 national saving is 1000 we could alternatively back in the National saving as Y minus C minus G doing that we get 1000 to find public saving just taxes - government expenditures - 1000 to find private saving y - t - C and that equals 2,000 so 2004 private saving and over here I'm just gonna add up public saving and private saving to show us another way of deriving national saving and we get 1000 for that alright I hope you found this video helpful