Macro Summary

All models are wrong, some are useful. So much more true about Macroeconomics. Macro can’t be just a bunch of equations, it is highly contextual and talks about mainly one economy we have, the actual numbers, their magnitudes and the history which provides evidence are just as important for the beginners semi-empirical model.

This summary tries to anchor on algebra.

The tools with Fed are Monetary Base (or Money supply) which is more of a classical method, nominal interest rates (\(i\)), and measured value of inflation (\(\pi\)) because the real tool is the real interest rate \(r = i - \pi.\) Modern policy primarily uses \(r\).

The goal of this summary is to call out empirical rules, intuitive linear models, and separate algebraic facts. Analysis can follow Algebra.

Classical Theory

Before 1930s Macro went with a simplistic theory that basically said if we doubled the money in the economy all prices and wages will adjust to 2x fairly quickly. This is called the classical dichotomy: the use of money does not affect the real exchange of goods and services, so long as prices can adjust. For example, iPhone cost in Yen vs USD, money is seen as just a measuring tool. This theory leads to the Quantity Theory of Money.

Real GDP is \(Y\). By definition, \[ Y = C + I + G + NX, \] where \(C\) = Consumption, \(I\) = Investment, \(G\) = Government spending, and \(NX\) = Net Exports. This identity is often rearranged for various purposes.

We often think of output \(Y\) in the long run as coming from a production function that depends on capital \(K\), labor \(L\), and technology \(A\). A classic example is Cobb–Douglas: \[ Y = A \, K^\alpha \, L^{1-\alpha}. \] When \(\alpha = 0.3\), we get \(Y = A\,K^{0.3}\,L^{0.7}\). This model shows diminishing marginal products of capital and labor, e.g. \(\frac{\partial Y}{\partial K} = 0.3 \frac{Y}{K},\ \frac{\partial Y}{\partial L} = 0.7 \frac{Y}{L}.\) As \(K\) or \(L\) increases, its marginal contribution falls.

Quantity Theory of Money
In its simplest form: \[ P \cdot Y = M \cdot V, \] where \(M\) = money supply, \(V\) = velocity of money, \(P\) = price level, and \(Y\) = real GDP. Taking logs and small changes, \[ dP + dY = dM + dV \quad\Rightarrow\quad \pi = dP = dM + dV - dY. \] A classical assumption is \(dV=0\) in the long run, giving \(\pi = dM - dY.\) However, in reality \(dV\) can be non-zero, so the theory is less reliable in the short run, as evidenced in the 1970s.

Keynesian Theory

Classical theory can over-simplify, assuming prices and wages adjust rapidly to balance markets. Keynesian theory helps analyze the short run, where prices are “sticky.” Short-run output is determined by Aggregate Demand, or Planned Expenditure: \[ Y_{pe} = C + I + G + NX. \]

The IS Curve

To see how \(Y\) depends on the real interest rate \(r\), we break down each component. For example: \[ C = \bar{C} + \mathrm{mpc}\,(Y - T) - c\,r, \] where \(\bar{C}\) is exogenous consumption, \(\mathrm{mpc}\) is the marginal propensity to consume out of disposable income \((Y-T)\), and \(-c\,r\) captures that higher real interest rates reduce consumption.

Similarly, \[ I = \bar{I} - d\,(r + \bar{f}), \quad NX = \overline{NX} - x\,r. \] Higher \(r\) dampens both investment (since the cost of borrowing is higher) and net exports (via a stronger currency).

Equilibrium occurs when actual output \(Y\) = planned expenditure \(Y_{pe}\). Summing up \(C, I, G, NX\) and isolating \(Y\), we arrive at the IS Curve: \[ Y = \frac{\bar{C} + \bar{I} - d\,\bar{f} + \bar{G} + \overline{NX} - \mathrm{mpc}\,\bar{T}}{1 - \mathrm{mpc}} \;-\; \frac{c + d + x}{1 - \mathrm{mpc}}\; r. \]

Notice that this is structurally \(Y = b - m\,r\), i.e. \(y = mx + b\) but with \(r\) as the “x.” - The intercept (analogous to \(b\)) is: \[ \underbrace{ \frac{\bar{C} + \bar{I} - d\,\bar{f} + \bar{G} + \overline{NX} - \mathrm{mpc}\,\bar{T}}{1 - \mathrm{mpc}} }_{\text{all exogenous lumps}} \] - The slope (analogous to \(m\)) is: \[ \underbrace{ \frac{c + d + x}{1 - \mathrm{mpc}} }_{\text{positive, so final slope is negative}} \] but it carries a minus sign, so \(\Delta r \up\) leads to \(\Delta Y \down\).
This is the essential shape of the IS curve: downward sloping in \((r, Y)\) space.

Monetary Policy Curve

The Fed's policy can be thought of as a rule linking \(r\) to \(\pi\). A simple version is: \[ r = \bar{r} + \lambda\, \pi. \] If \(\pi\) rises, the Fed raises \(i\) enough so that real rates go up. Without such a response, an increase in \(\pi\) would lower \(r\), spurring excess demand and more inflation.

Short Run Aggregate Supply Curve

The Phillips curve relates unemployment \((U)\) to wage/inflation: \[ \pi = \pi_e - \omega\,(U - U_n), \] meaning if unemployment is below the natural rate \(U_n\), inflation rises above expectations \(\pi_e\). Using Okun's Law, \((U - U_n) = -0.5\,(Y - Y_p)\), we rewrite as: \[ \pi = \pi_e + \gamma\,(Y - Y_p), \] giving us a Short Run Aggregate Supply (SRAS) curve. When actual output \(Y\) exceeds potential \(Y_p\), inflation climbs.

The Aggregate Demand and Supply Model

In the short run, equilibrium requires Aggregate Demand = Short-Run Aggregate Supply. - AD comes from the IS curve plus the monetary policy rule \(r(\pi)\). - SRAS is \(\pi = \pi_e + \gamma\,(Y - Y_p)\).
Solving simultaneously gives equilibrium \((Y^*, \pi^*)\). Over time, if \(Y \neq Y_p\), inflation expectations adjust, shifting the SRAS until the economy returns to its long-run level \(Y_p\).

Links

One reason the Quantity Theory can fail in the short run is price stickiness. However, during the pandemic, businesses were able to raise prices quickly ("shrinkflation", "greedflation"), suggesting less stickiness in certain contexts. Some commentary hints at a revival of the Quantity Theory:
Sep 2022 article about the Quantity Theory
July 2023 article about the Quantity Theory

In the short run, \(\pi = \pi_{e} + \gamma\,(Y - Y_p)\). This WSJ article discusses how measured \(\pi\) can differ by region or political orientation. Also, see this WSJ article on Phillips curve validity.