Flexprice_Model_and_IS_Curve-Review_and_Problems.ipynb

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    "# <font color=\"880000\">Flexprice Model and IS Curve: Review and Problems</font>\n",
    "\n",
    "<https://www.icloud.com/keynote/0ijR6uZ6ikrKf8JzrJlJhuujg> | <http://nbviewer.jupyter.org/github/braddelong/LSF18E101B/blob/master/Flexprice_Model_and_IS_Curve-Review_and_Problems.ipynb>\n",
    "\n",
    "GSI's have read me the riot act...\n",
    "\n",
    "* Reading the Riot Act: <https://en.wikipedia.org/wiki/Riot_Act>\n",
    "\n",
    "We have gone too far too fast, and it is time to pause and do some examples...\n",
    "\n",
    "The examples I will do start one of the things I am thinking about these days—the one-year anniversary of the Trump-McConnell-Ryan corporate tax cut...\n",
    "\n",
    "* The Trump tax cut, and its non-effect on investment spending...\n",
    "\n",
    "&nbsp;"
   ]
  },
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    "### <font color=\"000088\">Investment as a Share of Potential GDP</font.\n",
    "\n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c9571d00970b-pi\" alt=\"Investment as a Share of Potential GDP\" title=\"Gross_Private_Domestic_Investment___FRED___St__Louis_Fed.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "This is _nominal_ investment spending as a share of potential GDP\n",
    "\n",
    "* In our simple macro model, this is I/Y* \n",
    "\n",
    "This is the principal driver of the business cycle\n",
    "\n",
    "> $ I = I_o - I_rr $\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### Trump Administration Claims\n",
    "\n",
    "The Trump administration and their... I guess I have to call them \"tame\", or something less polite... economists insisted that the passage of the 2017 corporate tax cut would produce a substantial jump in investment spending, and a substantial acceleration of economic growth.\n",
    "\n",
    "For example: Robert Barro in December 2017 <https://www.project-syndicate.org/onpoint/how-us-corporate-tax-reform-will-boost-growth-by-robert-j--barro-2017-12>...\n",
    "\n",
    "Preview: \"Listen up! It's just not happening!\" in the words of [P!NK](https://www.youtube.com/watch?v=YUtHjOvPKT0):\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"https://delong.typepad.com/.a/6a00e551f080038834022ad39f14d7200d-pi\" alt=\"Lecture Investment Savings Review and Problems Macro MRE key\" title=\"Lecture-_Investment-Savings-_Review_and_Problems__Macro__MRE_key.png\" border=\"0\" width=\"600\" height=\"535\" />\n",
    "\n",
    "&nbsp;"
   ]
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    "### <font color=\"000088\">How US Corporate-Tax Reform Will Boost Growth</font>\n",
    "\n",
    "Robert Barro, Paul M. Warburg Professor, Harvard University <https://www.project-syndicate.org/onpoint/how-us-corporate-tax-reform-will-boost-growth-by-robert-j--barro-2017-12> \n",
    "\n",
    "Barro is going through a Solow Growth Model calculation of the effects of last December's 2 trillion wealth transfer that was last December's corporate tax cut:\n",
    "\n",
    ">Barro: Once we know the change in the capital-labor ratio, it is straightforward to estimate the long-run change in real (inflation-adjusted) per capita GDP. The short-run effects can then be inferred by using previous estimates of convergence rates associated with economic growth….\n",
    "\n",
    ">The tax changes raise long-run capital-labor ratios by 25% for non-residential corporate structures and 17% for corporate equipment… [a] long-run level effect… 7%…. If one assumes a capital share of income [α] of 40%, the convergence rate in the neoclassical growth model would be around 5% per year… the growth rate rises in the short run by 0.34% per year…\n",
    "\n",
    "&nbsp;"
   ]
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    "### <font color=\"000088\">Let's Do the Math...</font>\n",
    "\n",
    "Let's do the math and unpack what is going on here. And let's move into the flexprice model, because the U.S. economy is near full employment, so we are not talking about a cyclical recovery boosting short-run growth by putting lots of unemployed people to work:\n",
    "\n",
    "* $ \\frac{K}{Y} = 4 $\n",
    "* $ α = 0.4 $\n",
    "* $Y = K^α(EL)^{1-α} $\n",
    "\n",
    "To Your iClickers: What is dY/dK?\n",
    "\n",
    "1. 25%\n",
    "2. 40%\n",
    "3. 10%\n",
    "4. 16%\n",
    "5. None of the above\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "⟹ dY/dK = α(Y/K) = 10%\n",
    "\n",
    "* Boost growth by 0.34%/year\n",
    "* GDP of 20 trillion dollars\n",
    "* What is ΔY?\n",
    "\n",
    "1. 340 billion\n",
    "2. 680 billion\n",
    "3. 170 billion\n",
    "4. 34 billion\n",
    "5. None of the above\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "⟹ ΔY = 20 trillion x 0.34% = 70 billion\n",
    "\n",
    "What is ΔI?\n",
    "\n",
    "1. 700 billion\n",
    "2. 200 billion\n",
    "3. 340 billion\n",
    "4. 900 billion\n",
    "5. None of the above\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "⟹ ΔI = 70 billion/10% = 700 billion\n",
    "\n",
    "* I/Y = 16%\n",
    "    * ⟹ ΔI/Y = 3.5%\n",
    "    * ⟹ ΔI/I = 22%\n",
    "\n",
    "&nbsp;"
   ]
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    "### <font color=\"000088\">The OECD Does Not See It…</font>\n",
    "\n",
    "<img src=\"https://delong.typepad.com/.a/6a00e551f080038834022ad39ef65d200d-pi\" alt=\"OECD Investment Forecast https data oecd org gdp investment forecast htm\" title=\"OECD_Investment_Forecast_https___data_oecd_org_gdp_investment-forecast_htm.png\" border=\"0\" width=\"600\" height=\"381\" />\n",
    "\n",
    "What the OECD is...\n",
    "\n",
    "&nbsp;"
   ]
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    "### <font color=\"000088\">I Do Not See It...</font>\n",
    "\n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c9571d00970b-pi\" alt=\"Investment as a Share of Potential GDP\" title=\"Gross_Private_Domestic_Investment___FRED___St__Louis_Fed.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "I am not surprised not to see it. \n",
    "\n",
    "Why not? Because we are talking about a 15 percentage point—temporary—reduction in the taxes on investment. dY/dK = 10%. That is shared between investors, middlemen, workers with market power, managers, and the government. So figure that 15 percentage point is a change in after-tax r of between 0.75 and 1.5 percentage points for your return on investment. And that is simply not large enough to drive such a huge rapid leap in investment spending...\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">But There Has Been an Appreciation of the Dollar...</font>\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"https://delong.typepad.com/.a/6a00e551f080038834022ad3bed828200b-pi\" alt=\"Value of Foreign Currency https fred stlouisfed org graph id DTWEXB 0\" title=\"Value_of_Foreign_Currency__https___fred_stlouisfed_org_graph__id_DTWEXB__0.png\" border=\"0\" width=\"600\" height=\"467\" />\n",
    "\n",
    "* About 10%—consistent with investment incentives that raise the rate of return on investment in the U.S. by 1%-point for ten years...\n",
    "\n",
    "* And this will drive an increase in foreign savings that will drive some—not a lot—of increased investment in America.\n",
    "    * Offset by the decrease in government savings that comes about because of the higher deficit...\n",
    "\n",
    "&nbsp;"
   ]
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    "### <font color=\"000088\">Why Are We Not Surprised Not to See It?</font>\n",
    "\n",
    "* As I said before, flexprice model...\n",
    "\n",
    "* Investment needs to be looked at from both the supply and the demand side:\n",
    "    * $ I = I_o - I_rr = (T - G) + (IM - GX) + (1 - [c_o + c_y(1-t)])Y $ \n",
    "    * $ I = I_o - I_rr = (tY - G) + (im_yY - x_fY_f - - x_εε_o - x_εε_rr^f + x_εε_rr) + (1 - [c_o + c_y(1-t)])Y $\n",
    "    * $ ΔI = ΔI_o - I_rΔr = (1-c_y)YΔt + x_εε_rΔr - YΔc_o $\n",
    "        * With a tax cut, $ (1-c_y)YΔt $ goes the wrong way\n",
    "        * $ YΔc_o $ simply does not happen\n",
    "\n",
    "And so we are left, on the supply side, with:\n",
    "\n",
    "> $ΔI = x_εΔε = x_εε_rΔr  $\n",
    "\n",
    "What's going on here? The higher interest rates will induce people to stop buying U.S. exports. People who then earn dollars by selling us imports will have no choice but to invest that money in the United States—and that increased foreign saving will drive higher investment.\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "> $ ΔI = x_εε_rΔr x_ε = 500 ε_r = 10 $\n",
    "\n",
    "By how much would r have to go up to make $ ΔI = 700 $?\n",
    "\n",
    "1. 14%\n",
    "2. 7%\n",
    "3. 1.4%\n",
    "4. 3.5%\n",
    "5. None of the above\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "By a lot: A 14% rise in r? A 140% rise in the value of foreign currency?\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">How Do They Justify Writing This?</font>\n",
    "\n",
    "* Robert Barro (2017): crickets\n",
    "* Kevin Hassett (2003): “The U.S. is an open economy the borrows in an international capital market, hence... little or no impact on interest rates…”\n",
    "* Greg Mankiw (2017): “An open economy has the production function y = f(k), where y is output per worker and k is capital per worker. The capital stock adjusts so that the after-tax marginal product of capital equals the exogenously given world interest rate r…”\n",
    "\n",
    "What does this mean? This means: $ r = r^f $\n",
    "\n",
    "* Why does $ r = r^f$? We know that:\n",
    "    * $ (r = r^f) ⟹ (ε = ε_o) $\n",
    "    * $ Δr = 0 and Δε = 0 $\n",
    "    * $ ΔI = x_εΔε = x_εε_rΔr $\n",
    "\n",
    "What must be going on for both of these things to be true? What are they assuming behind the curtain?\n",
    "\n",
    "1. $ x_ε = 0 $\n",
    "2. $ ε_rΔr $\n",
    "3. $ x_ε = ∞ $\n",
    "4. None of the above\n",
    "\n",
    "⟹ xεΔ = ∞\n",
    "\n",
    "* Often heard (especially from Hassett): “The U.S. is an open economy the borrows in an international capital market, hence [policy change X] will have little of no impact on interest rates…”\n",
    "    * This misses the fact that international capital mobility requires international imbalances in trade…\n",
    "    * And that requires movements in exchange rates\n",
    "    * Which then support differences in interest rates across countries…\n",
    "\n",
    "&nbsp;"
   ]
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    "### <font color=\"000088\">Using a Long-Run Model to Analyze a Short-Run Problem</font>\n",
    "\n",
    "* What Joseph Schumpeter called “the Ricardian vice…”\n",
    "    * Somewhat different is what Schumpeter called “the Keynesian vice”: using a model too simple for the problem—“the happy times of Mrs. Marcet, when every schoolgirl by learning the use of a few simple concepts acquired competence to judge of all the ins and outs of the infinitely complex mechanisms of capitalist society…”\n",
    "    * Yes, this is a family course. But the misogyny you think you hear in Schumpeter—plus the feminization of Keynesians—and the echo of _le vice anglais_ you hear are there: Schumpeter was a... colorful personality...\n",
    "* Curiously enough, Keynes put the “Ricardian vice” best…\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Keynes Put the “Ricardian Vice” Best</font>\n",
    "\n",
    "Keynes: “Now ‘in the long run’ this is probably true. If, after the American Civil War, that American dollar had been stabilized and defined by law at 10 per cent below its present value, it would be safe to assume that n and p would now be just 10 per cent greater than they actually are and that the present values of k, r, and k' would be entirely unaffected. But this long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is past the ocean is flat again…”\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Why Do They Make This Mistake?</font>\n",
    "\n",
    "Keynes on how hard it is to be a good economist:\n",
    "\n",
    "* The study of economics does not seem to require any specialised gifts of an unusually high order. Is it not, intellectually regarded, a very easy subject compared with the higher branches of philosophy and pure science? Yet good, or even competent, economists are the rarest of birds. \n",
    "* An easy subject, at which very few excel! \n",
    "* The paradox finds its explanation, perhaps, in that the master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician, historian, statesman, philosopher—in some degree. He must understand symbols and speak in words. He must contemplate the particular in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light of the past for the purposes of the future. No part of man's nature or his institutions must lie entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood…\n",
    "\n",
    "But there is more: motivated reasoning, and a failure to take _any_ steps to mark their beliefs to market...\n",
    "\n",
    "* Why no circling around to figure out why it hasn’t worked?\n",
    "* Back when we Clinton types were forecasting the effects of our economic policies, we did later on circle around—and found that things had worked.\n",
    "* Why don’t they?\n",
    "\n",
    "&nbsp;"
   ]
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    "### <font color=\"000088\">Effects of Dollar Swings</font>\n",
    "\n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09fa61da970d-pi\" alt=\"Real Exchange Rate Value of Foreign Currency Goods\" title=\"Real_Exchange_Rate__Value_of_Foreign_Currency_Goods_.png\" border=\"0\" width=\"600\" /> \n",
    "\n",
    "* 40% increase in the exchange rate—the value of foreign currency—from 1985 to 1988\n",
    "    * About half a reduction in interest rate differentials…\n",
    "    * About half a shift in beliefs (Reagan boom disappointingly weak—not really “Morning in America” after all)\n",
    "* Flexprice model\n",
    "\n",
    "----\n",
    "\n",
    "* What is going to happen to the economy?\n",
    "    * $ r^f $ ⇑ 2%\n",
    "    * $ ε_o $ ⇑ 20%\n",
    "* Our framework:\n",
    "    * $ I = I_o - I_rr = S^g + S^f + S^p $\n",
    "    * $ I = I_o - I_rr = (tY - G) + (im_yY - x_fY_f - x_εε_rr^f + x_εε_rr) + (1 - [c_o + c_y(1-t)])Y $\n",
    "    * $ ΔI = - I_rΔr = - x_εΔε_o - x_εε_rΔr^f + x_εε_rΔr $\n",
    "    \n",
    "> $ Δr = \\frac{x_εΔε_o + x_εε_rΔr^f}{I_r + x_εε_r} $\n",
    "\n",
    "* $ x_ε = 500 $\n",
    "* $ ε_r = 10 $\n",
    "* $ I_r = 20000 $\n",
    "\n",
    "> $ Δr = \\frac{(500)(0.20) + (500)(10)(.02)}{20000 + (500)(10)} $\n",
    "\n",
    "> $ Δr = \\frac{200}{25000} = 0.008 $\n",
    "\n",
    "> $ ΔI = -(20000)(0.008) = -160 $\n",
    "\n",
    "> $ ΔGX = x_εΔε = (500)(0.2 + 10(.02-.008)) = + 160 $\n",
    "\n",
    "Export manufacturing production recovers...\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Effects of Capital Inflows</font>\n",
    "\n",
    "Reference: **Olivier Blanchard, Jonathan D. Ostry, Atish R. Ghosh, and Marcos Chamon** (2015): _[Expansionary or contractionary effects of capital inflows: It depends what kind](https://voxeu.org/article/macro-effects-capital-inflows-capital-type-matters)_: \"Some scholars view capital inflows as contractionary, but many policymakers view them as expansionary. Evidence supports the policymakers.... For a given policy rate, bond inflows lead to currency appreciation and are contractionary, while non-bond inflows lead to an appreciation but also to a decrease in the cost of borrowing, and thus may be expansionary...\"\n",
    "\n",
    "----\n",
    "\n",
    "A _bond inflow_ is: a $ {\\Delta}{\\epsilon}_o < 0 $\n",
    "\n",
    "A _non-bond inflow_ (DFI) is:\n",
    "\n",
    "* a $ {\\Delta}{\\epsilon}_o < 0 $\n",
    "* a $ {\\Delta}{\\rho} < 0 $\n",
    "    * where $ r = i + \\rho - \\pi $\n",
    "\n",
    "So holding i constant:\n",
    "\n",
    "> $ {\\Delta}Y = {\\mu}(x_{\\epsilon}{\\Delta}{\\epsilon}_o - (I_r + x_{\\epsilon}{\\epsilon}_r){\\Delta}{\\rho}) $\n",
    "\n",
    "The key question is: when capital flows in, does it just come by itself or does it bring an increased supply of risk-bearing capacity along with it?\n",
    "\n",
    "----\n",
    "\n",
    "Reference: Basic Model:\n",
    "\n",
    "> $ Y = C + I + G + NX $\n",
    "\n",
    "> $ C = c_o + c_y(1-t)Y $\n",
    "\n",
    "> $ I = I_o - I_rr $\n",
    "\n",
    "> $ G $\n",
    "\n",
    "> $ NX = GX - IM $\n",
    "\n",
    "> $ IM = im_y $\n",
    "\n",
    "> $ GX = x_fY^f + x_{\\epsilon}{\\epsilon} $\n",
    "\n",
    "> $ {\\epsilon} = {\\epsilon}_o + {\\epsilon}_r(r^f - r) $\n",
    "\n",
    "> $ r = i + {\\rho} - {\\pi} $\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "> $ MPE = c_y(1-t) - im_y $\n",
    "\n",
    "> $ \\mu = \\frac{1}{1 - MPE} $\n",
    "\n",
    "> $ A_o = [c_o + I_o + G] + [x_fY^f + x_{\\epsilon}{\\epsilon}_o + x_{\\epsilon}{\\epsilon}_rr^f] $\n",
    "\n",
    "> $ Y = \\mu(A_o - (I_r + x_{\\epsilon}{\\epsilon}_r)r) $\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "### <font color=\"000088\">Effects of Capital Outflows</font>\n",
    "\n",
    "The reverse of the effects of capital inflows:\n",
    "\n",
    "A _bond outflow_ is: a $ {\\Delta}{\\epsilon}_o > 0 $\n",
    "\n",
    "A _non-bond outflow_ is:\n",
    "\n",
    "* a $ {\\Delta}{\\epsilon}_o > 0 $\n",
    "* a $ {\\Delta}{\\rho} > 0 $\n",
    "    * where $ r = i + \\rho - \\pi $\n",
    "\n",
    "So holding i constant:\n",
    "\n",
    "> $ {\\Delta}Y = {\\mu}(x_{\\epsilon}{\\Delta}{\\epsilon}_o - (I_r + x_{\\epsilon}{\\epsilon}_r){\\Delta}{\\rho}) $\n",
    "\n",
    "The key question is: when capital flows out, does it just leave by itself or does it carry risk-bearing capacity away with it?\n",
    "\n",
    "&nbsp;"
   ]
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    "# calibrating the flexprice model to the U.S. economy today\n",
    "# consensus parameter values...\n",
    "\n",
    "Y = 20000\n",
    "C = 13500\n",
    "I = 3250\n",
    "G = 3750\n",
    "GX = 2500\n",
    "IM = 3000\n",
    "NX = GX-IM\n",
    "\n",
    "I_0 = 3650\n",
    "I_r = 20000\n",
    "e_r = 10\n",
    "x_e = 500\n",
    "t = 0.15\n",
    "c_0 = 750\n",
    "c_y = 0.75\n",
    "\n",
    "im_y = 0.15\n",
    "x_f = 0.10\n",
    "Y_f = 25000\n",
    "\n",
    "e = 0\n",
    "r = 0.02\n",
    "\n",
    "C_calc = c_0 + c_y*(1-t)*Y\n",
    "I_calc = I_0 - I_r*r\n",
    "GX_calc = x_f*Y_f + x_e*e_r*e\n",
    "\n",
    "GX_calc"
   ]
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    "<img src=\"https://tinyurl.com/20181029a-delong\" width=\"300\" style=\"float:right\" />\n",
    "\n",
    "## Catch Our Breath\n",
    "\n",
    "* Ask me two questions…\n",
    "* Make two comments…\n",
    "* Further reading…\n",
    "\n",
    "<br clear=\"all\" />\n",
    "\n",
    "----\n",
    "\n",
    "Lecture Support: <http://nbviewer.jupyter.org/github/braddelong/LSF18E101B/blob/master/Flexprice_Model_and_IS_Curve-Review_and_Problems.ipynb>   \n",
    "Keynote File: <https://www.icloud.com/keynote/0ijR6uZ6ikrKf8JzrJlJhuujg>\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "----"
   ]
  },
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    "## <font color=\"000088\">Appendix: National Income and Components</font>\n",
    "\n",
    "**Real GDP**:   \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09fa5e71970d-pi\" alt=\"Real GDP\" title=\"Real_GDP.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "**Real GDP per Worker**:   \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09fa624b970d-pi\" alt=\"Real GDP per Worker\" title=\"Real_Gross_Domestic_Product___FRED___St__Louis_Fed.png\" border=\"0\" width=\"600\" /> \n",
    "\n",
    "**Investment as a Share of Potential GDP**:   \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c9571d00970b-pi\" alt=\"Investment as a Share of Potential GDP\" title=\"Gross_Private_Domestic_Investment___FRED___St__Louis_Fed.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "**Consumption as a Share of Potential GDP**:   \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401b8d2e16931970c-pi\" alt=\"Consumption as a Share of Potential GDP\" title=\"Consumption_as_a_Share_of_Potential_GDP.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "**Gross Exports as a Share of Potential GDP**:   \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09fa626c970d-pi\" alt=\"Gross Exports as a Share of Potential GDP\" title=\"Gross_Exports_as_a_Share_of_Potential_GDP.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "**Imports as a Share of Potential GDP**:   \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c9571b68970b-pi\" alt=\"Gross Imports as a Share of Potential GDP\" title=\"Gross_Imports_as_a_Share_of_Potential_GDP.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "**Net Exports as a Share of Potential GDP**:   \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401b8d2e16752970c-pi\" alt=\"Net Exports as a Share of Potential GDP\" title=\"Net_Exports__as_a_Share_of_Potential_GDP.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "## <font color=\"000088\">Monetary</font>\n",
    "\n",
    "**Price Level**:   \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09fa6155970d-pi\" alt=\"Price Level\" title=\"Price_Level.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "**Inflation Rate**:   \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401b8d2e167e8970c-pi\" alt=\"Inflation Rate\" title=\"Inflation_Rate.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "## <font color=\"000088\">Interest and Exchange Rates</font>\n",
    "\n",
    "**Nominal Short-Term Safe Rate**:    \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09fa61a3970d-pi\" alt=\"Short Term Safe Nominal Interest Rate\" title=\"Short-Term_Safe_Nominal_Interest_Rate.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "**Long-Term Real Safe Rate**:    \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c9571c5b970b-pi\" alt=\"Long Term Real Risky Interest Rate\" title=\"Long-Term_Real_Risky_Interest_Rate.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "**Long-Term Risky Real Rate**:     \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401b7c957415e970b-pi\" alt=\"Long Term Risky Real Rate\" title=\"Long-Term_Risky_Real_Rate.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "**Real Exchange Rate** (Value of Foreign Goods/Currency):   \n",
    "<img src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09fa61da970d-pi\" alt=\"Real Exchange Rate Value of Foreign Currency Goods\" title=\"Real_Exchange_Rate__Value_of_Foreign_Currency_Goods_.png\" border=\"0\" width=\"600\" /> \n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;\n",
    "\n",
    "## <font color=\"000088\">The Output Gap</font>\n",
    "\n",
    "<img style=\"display:block; margin-left:auto; margin-right:auto;\" src=\"http://delong.typepad.com/.a/6a00e551f08003883401bb09fbb872970d-pi\" alt=\"The Output Gap\" title=\"The_Output_Gap.png\" border=\"0\" width=\"600\" />\n",
    "\n",
    "----\n",
    "\n",
    "&nbsp;"
   ]
  }
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