Section notes for ECON 402, Intermediate Macroeconomics, with Professor Chris House

Part I

1 A too short introduction

Plotting, two-period budget constraints, comparative statics with the intertemporal budget constraint, agents can always consume their endowment, not being allowed to borrow, indifference curves, derivatives, optimization

2 Intertemporal choice, the saving supply function, dynamic general equilibrium

Here are the notes for section 2. A few take-aways:

  • Intertemporal choice lead to the consumption Euler equation: \(\text{MU}(c_1) = (1+r) \text{MU}(c_2)\).
  • The saving supply function: \(s_1(r,y) := y_1 - c_1(r,y)\). We plotted the saving supply function for both
    • log utility and
    • linear utility.
  • Dynamic general equilibrium. Definition 2.2 defines our notion of equilibrium, which is important—see slide 17 of Lecture 4_handouts. From national accounting, we saw that \(Y = C\) for the endowment economies we explored. Therefore aggregate saving was \(0\). This equilibrium market-clearing condition provides a procedure for computing equilibrium levels of consumption and the equilibrium interest rate:
    1. Compute the demand functions, \(c(r,y)\). Since income is exogenous, these are simply functions of the interest rate.
    2. Using the demand functions, calculate the saving functions.
    3. In equilibrium, the interest rate (price) must adjust so that aggregate saving is \(0\). With the interest rate in hand, equilibrium levels of consumption and saving can be read off of items 1. and 2.

3 Saving supply and saving demand

Saving supply and saving demand determine the equilibrium rate of interest. Shifters of supply and demand are discussed. National accounting requires that \(Y_1 = C_1 + I_1\), so \(S_1 > 0\).

4 Summing up

Valuing a job, valuing a job with wage growth, valuing a job with a finite work horizon, PIH with permanent and transitory fluctuations, neoclassical production, valuing a unit of capitl.

Part II

5 Choice under Uncertainty

Precautionary saving in the face of uncertainty, computing expected values, expection, St. Petersburg paradox, concavity and risk aversion, an expanded answer to problem 5 on Midterm Exam 1

6 Introduction to the Solow model of economic growth

Neoclassical production, returns to scale, the final-good-producing firm makes no profits in equilibrium, the Solow model as a dynamic general-equilibrium model, Solow dynamics with population growth, growth rates of capital per worker.

You may also find this slidedeck on the fundamentals of asset pricing helpful.

7 Economic growth continued

The AK model, the AK model with diminishing returns: each new unit of capital added to the economy is slightly less productive than the last—eventually investment falls to the level of depreciation, the Solow model with population growth and technological change: \[ \begin{align*} g_K = g_Y = g_C = g_I = (1+g_A)(1+n), \end{align*}\] enter through the narrow gate; for the gate is wide and the road is easy that leads to destruction—the golden rule: in steady state where \(K_{t+1} = K_t = K\), \[ \begin{align*} K &= (1-\delta)K + I = (1-\delta)K + Y - C = (1-\delta)K + AK^{\alpha} - C \\ \therefore C &= \delta K + AK^{\alpha} \\ \therefore \frac{\partial C}{\partial K} &= 0 \implies \delta = \text{MPK}, \end{align*} \] Solow with human capital from section 12.2 of the House Lecture notes

8 Midterm Exam II Review

Steady-state \(K^{\star}\) with taxes, potential for tax policy to explain cross-country differences in output, wages when \(N_t = 1\), wages after a tax cut, influx of immigrants

Part III

9 IS–LM

Investment function, \(I(r)\); deriving the IS curve; how fiscal policy shifts the IS curve; supply and demand of real balances; deriving the LM curve; how monetary policy shifts the LM curve; IS–LM as a theory of aggregate demand; expansionary monetary policy; expansionary fiscal policy

10 IS–LM continued, Open Economy Macroeconomics

Updward-sloping short-run aggregate supply, adjustment of output via the short-run aggregate supply function, the effects of a monetary expansion in the IS–LM/AD–AS framework, the effects of an increase in \(G\) in the IS–LM/AD–AS framework, \(Y = C + I + G + NX\), \(S = I + NX\), opening trade with an economy featuring low \(K\), borrowing from abroad, increase in \(G\)

\(\star\) The notes for section 10 were updated 4/14/2018.

11 Mundell–Fleming

Monetary neutrality, \(r = r^{\star}\) in a small open economy, the goods and services market and the IS\(^{\star}\) curve, the nominal exchange rate, the money market and the LM\(^{\star}\) curve, fixed vs floating exchange rates, example: monetary policy and floating exchange rates, the monetary transmission mechanism under floating exchange rates, example: fiscal expansion under floating exchange rates, example: trade policy under floating exchange rates, example: fixed exchange rates and fiscal policy, example: a monetary expansion under fixed exchange rates, devaluation, thanks

Slide deck for final review

Here is the slide deck presented in the review session on 4/20, which corrected a few typos and added a few slides on the second midterm

Figures for the minimum-wage question on the practice final

Selected suggested solutions to homeworks

  • H1.2: A proportional increase to all prices means the implicit price deflator and CPI are the same. The algebra is on the last page.
  • H2: Impatient consumers and the interest rate, the elasticity of intertemporal substitution, and capital taxation and the user cost
  • E1: Extra credit: A cool example of intertemporal choice
  • E2: Extra credit: Time-varying prices of capital
  • E3: Extra credit: R&D in a basic Solow model and a linear IS–LM system

Answers to questions people have asked

  • The difference between ex ante and ex post interest rates
  • Interpreting differences in logs as a percentage change
  • Are the 10 people who run their own business counted in the establishment survey? It depends.
  • A cool figure that illustrates the effects of economic growth. (By the way, I made that with R Shiny, which is pretty cool.)
  • On two-period endowment economics with government