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# Joey Derives IS/LM

 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 12:31:56 PMPosted: 2 years agoSo, this is a function (a) of me being bored and (b) wanting to see if I actually remember how to derive IS/LM without cheating.Disclaimer: I hate this model, and you all should as well.Without further ado...IS CurveY = Yp = Ip + C + I + G + NXIp = I-bar + b (r + f)C = C-bar + mpc * (Y-bar-T-bar) + crG = G-barNX = NX-bar + xrwhereby b, c, and x are parameters and the notation "bar" indicates that the variable is autonomous or in the case of Y, T, and G, exogenous.Expanding this:Y = Yp = I-bar + b (r + f) + C-bar + mpc * (Y-T) + cr + G-bar + NX-bar + xrI should end up with some y-intercept - which in this case I'll just call B - minus some constant (slope coefficient of the IS curve) multiplied by the level of output.Y = I-bar + br + bf + C-bar + mpcY - mpcT + cr + G-bar + Nx-bar + xrY = I-bar + C-bar + G-bar + NX-bar + r(b+c+x) + bf + mpcY - mpcT-r(b+c+x) = I-bar +C-bar + G-bar + NX-bar + bf + mpcY - mpcT - Y-r = (I-bar + C-bar + G-bar + NX-bar + bf + mpcY - mpcT - y)/ (b + c + x)r = - [(I-bar + C-bar + G-bar + NX-bar + bf + mpcY - mpcT - y)/ (b + c + x)]Then distribute the negative sign....r = (-I-bar - C-bar - G-bar - NX-bar - bf - mpcY + mpcT + Y) / (b + c + x)Realistically I could set this all equal to Y, but I'm too lazy.Since I'm not using numbers I'm going to use a cute trick. My only things actually being varied within the framework of a model of some economy is r and Y - i.e., per some given level of C, G, NX, and I, the IS curve gives us some combination of Y and r that equates planned spending with actual spending, with the difference being unplanned inventory investment. Thus, I can set everything else equal to some arbitrary constant, which will obviously shift the function up and down, but for the sake of argument we'll assume is fixed.So let's rewrite this mess of an equation as such:r = (-I-bar - C-bar - G-bar - NX-bar - bf - mpcY + mpcT + Y) / (b + c + x)is the same as:r = [(-I-bar - C-bar - G-bar - NX-bar - bf - mpcY + mpcT) / (b + c + x)] + Y/(b + c + x)Therefore, [(-I-bar - C-bar - G-bar - NX-bar - bf - mpcY + mpcT) / (b + c + x)] is our y-intercept, which I'll call B, and [1/(b+ c + x)] is the slope of the IS curve, which I'll call M.Therefore,r = B - MYWe have our IS curve!LM CurveSo we start with an equation of money demand predicated on liquidity preference, whereby income is a parameter which shifts the curve up and down and changes in the riskless interest rate move us along the curve.In other words, the demand for real money balances can be written as follows:(M/P) = Y - brwhere, again, b is a parameter > 0, and the slope of the Md curve.Since the LM curve gives us combinations of income and the riskless interest rate where financial markets are in equilibrium, the next step is obviously to equate Md with Ms (i.e., money demand with money supply).The real money supply, we know, is equal to M/P, whereas real money demand is Y - br.Therefore,Y - br = M/PThus,Y = M/P + brAnd let's write this, much like our IS curve, in terms of Y:br = M/P - Yr = [(M/P - Y) / (b)]And then go through the same steps as above:r = [(M/P)/(b)] - [(y)/(b)][(M/P)/(b)] is thus our y-intercept whereas (-1/b) is our slope coefficient.And...... done!I probably screwed up somewhere, but that's IS/LM, lol.~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 4:17:18 PMPosted: 2 years agoEh, I can keep going I guess.AD CurveFrom above, IS Curve:r = (-I-bar - C-bar - G-bar - NX-bar - bf - mpcY + mpcT + Y) / (b + c + x) (1)Then we define the MP Curve :r = r-bar + lambda * pi (2)where:r = riskless policy rate (real)r-bar = autonomous changes to monetary policylambda > 0 = slope coefficient denoting how aggressively central banks respond to increases in inflation, and via the Taylor Principle must be greater than 0 such that nominal interest rates rise by more than the increase in inflationpi = inflationThen, to get the AD curve, we need only substitute the MP curve into the IS curve, or (2) into (1), and solve for pi.Therefore:r-bar + lambda * pi = [(-I-bar - C-bar - G-bar - NX-bar - bf - mpcY + mpcT + Y) / (b + c + x)] (3)pi = [(-I-bar - C-bar - G-bar - NX-bar - bf - mpcY + mpcT + Y) / (b + c + x)] / (lambda) (3)Again... super messy, but we can fix that.pi = [(-I-bar - C-bar - G-bar - NX-bar - bf - mpcY + mpcT + Y) / (b + c + x)] / (lambda)pi = [(-I-bar - C-bar - G-bar - NX-bar - bf - mpcY + mpcT + Y) / [lambda * (b + c + x)]pi = [[(-I-bar - C-bar - G-bar - NX-bar - bf - mpcY + mpcT)]/ [lambda * (b + c + x)]] + [(Y)/ [lambda * (b + c + x)]]The first term, thus, is the y-intercept, which I'll label D, and 1/(lambda * (b+c+x)) is the slope of the AD curve, which I'll call T.Therefore:pi = D - TYwhere pi is inflation, and D and T are constants > 0.*drops mic*~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 4:25:00 PMPosted: 2 years agoEh, somehow I forgot to subtract r-bar. Bleh. The proof would be a little different, but it's a constant so I'd end up tossing it out eventually anyway.~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 14,314 Add as FriendChallenge to a DebateSend a Message 6/21/2015 4:46:27 PMPosted: 2 years agoo.o .....Want to debate? Pick a topic and hit me up! - http://www.debate.org...
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 4:50:39 PMPosted: 2 years agoAt 6/21/2015 4:46:27 PM, Zaradi wrote:o.o .....lol~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 6,898 Add as FriendChallenge to a DebateSend a Message 6/21/2015 4:56:46 PMPosted: 2 years agoI don't know how to speak Asian.Empress of DDO (also Poll and Forum "Maintenance" Moderator) "The two most important days in your life is the day you were born, and the day you find out why." ~Mark Twain "Wow" -Doge "Don't believe everything you read on the internet just because there's a picture with a quote next to it." ~Abraham Lincoln Guide to the Polls Section: http://www.debate.org...
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 4:57:21 PMPosted: 2 years agoAt 6/21/2015 4:56:46 PM, PetersSmith wrote:I don't know how to speak Asian.lol~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 14,314 Add as FriendChallenge to a DebateSend a Message 6/21/2015 5:00:21 PMPosted: 2 years agoAt 6/21/2015 4:57:21 PM, ResponsiblyIrresponsible wrote:At 6/21/2015 4:56:46 PM, PetersSmith wrote:I don't know how to speak Asian.lolRev's Asian right? Go ask him to translate this for me? ^_^Want to debate? Pick a topic and hit me up! - http://www.debate.org...
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 5:00:59 PMPosted: 2 years agoAt 6/21/2015 5:00:21 PM, Zaradi wrote:At 6/21/2015 4:57:21 PM, ResponsiblyIrresponsible wrote:At 6/21/2015 4:56:46 PM, PetersSmith wrote:I don't know how to speak Asian.lolRev's Asian right? Go ask him to translate this for me? ^_^I'm pretty sure Rev actively taunts me for being an "econ nerd." I doubt he'll understand this, lol~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 5:02:04 PMPosted: 2 years agoIf anyone wants a graphical derivation - via screenshots from Twiddla or something - I may be willing to accommodate your request.~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 13,835 Add as FriendChallenge to a DebateSend a Message 6/21/2015 5:04:40 PMPosted: 2 years agoAt 6/21/2015 5:00:21 PM, Zaradi wrote:At 6/21/2015 4:57:21 PM, ResponsiblyIrresponsible wrote:At 6/21/2015 4:56:46 PM, PetersSmith wrote:I don't know how to speak Asian.lolRev's Asian right? Go ask him to translate this for me? ^_^I'm only half, so only the math part looks somewhat intelligible.
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 5:05:18 PMPosted: 2 years agoFack, another mistake:"C = C-bar + mpc * (Y-bar-T-bar) + cr"That's..... wrong. I should be subtracting cr from the consumption function.#oops~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 5:07:30 PMPosted: 2 years agoYuck, that... mucks up a lot.I also should be subtracting the "r" term from the investment and NX functions, lol.~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 14,314 Add as FriendChallenge to a DebateSend a Message 6/21/2015 5:43:46 PMPosted: 2 years agoAt 6/21/2015 5:07:30 PM, ResponsiblyIrresponsible wrote:Yuck, that... mucks up a lot.I also should be subtracting the "r" term from the investment and NX functions, lol.Wow the Econ nerd can't even do Econ....One of us! One of us! One of us!Want to debate? Pick a topic and hit me up! - http://www.debate.org...
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 5:50:09 PMPosted: 2 years agoAt 6/21/2015 5:43:46 PM, Zaradi wrote:At 6/21/2015 5:07:30 PM, ResponsiblyIrresponsible wrote:Yuck, that... mucks up a lot.I also should be subtracting the "r" term from the investment and NX functions, lol.Wow the Econ nerd can't even do Econ....Just for that, I'm going to redo all of this sh1t and post it to your wall - in tiny, miniature chunks - just to increase your suffering.One of us! One of us! One of us!Oh, it's on.~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 14,314 Add as FriendChallenge to a DebateSend a Message 6/21/2015 6:09:28 PMPosted: 2 years agoAt 6/21/2015 5:50:09 PM, ResponsiblyIrresponsible wrote:At 6/21/2015 5:43:46 PM, Zaradi wrote:At 6/21/2015 5:07:30 PM, ResponsiblyIrresponsible wrote:Yuck, that... mucks up a lot.I also should be subtracting the "r" term from the investment and NX functions, lol.Wow the Econ nerd can't even do Econ....Just for that, I'm going to redo all of this sh1t and post it to your wall - in tiny, miniature chunks - just to increase your suffering.One of us! One of us! One of us!Oh, it's on.;)Want to debate? Pick a topic and hit me up! - http://www.debate.org...
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 6:19:08 PMPosted: 2 years agoAt 6/21/2015 6:09:28 PM, Zaradi wrote:At 6/21/2015 5:50:09 PM, ResponsiblyIrresponsible wrote:At 6/21/2015 5:43:46 PM, Zaradi wrote:At 6/21/2015 5:07:30 PM, ResponsiblyIrresponsible wrote:Yuck, that... mucks up a lot.I also should be subtracting the "r" term from the investment and NX functions, lol.Wow the Econ nerd can't even do Econ....Just for that, I'm going to redo all of this sh1t and post it to your wall - in tiny, miniature chunks - just to increase your suffering.One of us! One of us! One of us!Oh, it's on.;)Make your comments public, and expect some notification spam within the next hour, lmfao~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 12,398 Add as FriendChallenge to a DebateSend a Message 6/21/2015 6:37:02 PMPosted: 2 years agoIS CurveY = Yp = Ip + C + I + G + NXIp = I-bar - b (r + f)C = C-bar + mpc * (Y-bar-T-bar) - crG = G-barNX = NX-bar - xrY = I-bar - b (r + f) + C-bar + mpc * (Y-bar-T-bar) - cr + G-bar + NX-bar - xrY = I-bar - br - bf + C-bar + mpc * Y-bar - mpc * T-bar - cr + G-bar + NX-bar - xrY = I-bar + C-bar + G-bar + Nx-bar + mpc * Y-bar - mpc * T-bar - bf - r (b + c + x)r (b + c + x) = I-bar + C-bar + G-bar + Nx-bar + mpc * Y-bar - mpc * T-bar - bf - Yr = [(I-bar + C-bar + G-bar + Nx-bar + mpc * Y-bar - mpc * T-bar - bf - Y) / (b + c + x)]^^ That's simplified enough, lol.~ResponsiblyIrresponsible DDO's Economics Messiah
 Posts: 14,314 Add as FriendChallenge to a DebateSend a Message 6/21/2015 6:46:21 PMPosted: 2 years agoAt 6/21/2015 6:19:08 PM, ResponsiblyIrresponsible wrote:At 6/21/2015 6:09:28 PM, Zaradi wrote:At 6/21/2015 5:50:09 PM, ResponsiblyIrresponsible wrote:At 6/21/2015 5:43:46 PM, Zaradi wrote:At 6/21/2015 5:07:30 PM, ResponsiblyIrresponsible wrote:Yuck, that... mucks up a lot.I also should be subtracting the "r" term from the investment and NX functions, lol.Wow the Econ nerd can't even do Econ....Just for that, I'm going to redo all of this sh1t and post it to your wall - in tiny, miniature chunks - just to increase your suffering.One of us! One of us! One of us!Oh, it's on.;)Make your comments public, and expect some notification spam within the next hour, lmfaoMake my comments public? But I thought you knew what you were doing! ;)Want to debate? Pick a topic and hit me up! - http://www.debate.org...