Slides 4

For the Final Exam

Homework A

• Budget line stays the same due to unchanged • Indifference curve stays the same due to

unchanged preference• Optimum stays the same• P doubles• Monetary policy has no effect on optimum

since income and price both double

Intertemporal Budget Constraint (IBC)

• Idea: no one borrows or saves forever• Before she dies, • Dividing on both sides gives

(IBC)So what really matters is permanent income, not current income. Exercise: what happens if rises?

Preference

• Intertemporal (Total) Utility: • Instantaneous (Each Period) Utility: • Two properties: • For example,

Dynamic Optimization

• Constraint optimization• Can be transformed to an unconstraint

optimization problem by substituting into the utility function

• Then take derivative of with respect to and let

Calculus

• Consider where are both functions of • Then

+• For our problem

Calculus Two

+++

Euler Equation (First Order Condition)

This looks similar to

marginal rate of substitution equals relative price at optimum.

Interpretation

• • So at optimum a person is indifferent between

two options: (I) consume one more unit now; (II) save that one unit and consume later. At optimum the two options yield the same change in utility.

Log Utility Function

• For log utility function the Euler equation is

or

This shows the dynamic path of consumption

Solution of Dynamic Optimization

• Plugging the Euler Equation into the IBC gives

and we have the solution

where denotes permanent income.

Exercise

• What if falls?• What if rises?• So whether a person saves or borrows in the

first period does not matter. Kind of counter-intuitive

Ricardian Equivalence

• Consider the effect of temporary tax cut. The permanent after-tax income is

• Temporary tax cut has no effect on as long as the present value of tax stays the same (so stays the same), i.e., as long as a current tax cut will be followed by a future tax hike.

Smooth Consumption

• Let then Euler equation implies that

So the optimum is smooth consumption. The reason is diminishing marginal utility.

Random Walk

• Let’s add randomness to Euler equation

This shows that consumption follows random walk (RW). • RW has the property that its change is

unpredictable, i.e.,

New-Keynesian Theory I

• Use micro foundation• IBC assumes no borrowing constraint. If

borrowing constraint (market imperfection) exists, then for poor people the budget constraint is

(IBC2)• Now current income matters again. Tax cut will

be very effective in stimulating expenditure.

New-Keynesian Theory II

• Consider doubling money supply• But assume prices of some markets are

flexible, others sticky (market imperfection)• Then will change disproportionally. • Then optimum will change since budget line

shifts. • Monetary policy can be very effective.

Let’s Summarize

• http://www.youtube.com/watch?v=GTQnarzmTOc

• http://www.youtube.com/watch?v=3u2qRXb4xCU

History of Macroeconomics

• Classical model (Adam Smith, David Ricardo, Thomas Malthus)

• Markets clear by themselves• Key assumption: prices are flexible• Policies (and government) are not needed• Policies can create inefficiency, e.g., tax,

minimum wage, tariff

What’s Wrong?

Great Depression

• Widespread and sustained unemployment (surplus in labor market)

• Signal for market failure• Classical model cannot explain • Here comes Keynesian theory which focuses

on insufficient demand (after stock market crash)

Model of Sticky Prices

• Keynes believes that one reason for unemployment is sticky nominal wage

• Keynes believes more spending is needed to raise the price level and lower real wage

• Can you draw a graph?

World War II

• Keynes believes WWII cut short of great depreciation

• Government expenditures rises• Through multiplier effect, income rises more

than the increase in G• So broken window can be good. In long run

we are all dead.

Phillips Curve

• Keynes ignores the role of expectation• Therefore he believes in a negative relation

between inflation and unemployment, i.e., a fixed Phillips curve

• Can you draw a graph?• Then here comes stagflation in 1970s

What’s Wrong?

Stagflation

• In 1970 both unemployment rate and inflation rate rose

• can be explained by expectation-augmented Phillips curve

• Lucas critique: econometrics cannot be used to estimate Phillips curve because we cannot assume fixed expectation

Micro Foundation

• Hayek and Lucas emphasize the microeconomic foundation for macroeconomics, Keynes does not.

• The basic model is a two-period utility maximization problem

New Classical Theory

• Permanent income hypothesis• Random walk hypothesis for consumption• Ricardian equivalence• Smooth consumption• The new classical theory indicates very small

multiplier effect.

Real Business Cycle Theory

• is built upon the new classical theory• Emphasizes that markets clear by themselves,

economy can be self-correcting• Unemployment (intertemporal labor

substitution) is voluntary• Fluctuation in income (business cycle) is a

Pareto Efficient. Government had better do nothing.

Dynamic Stochastic General Equilibrium (DSGE) models

• The simple two-period model can be generalized

• Multiple periods• Random variables• General equilibrium• To much for this course

New Keynesian Theory

• Keynesian school is fighting back• Micro foundation is used• Market can still fail due to various reasons• Borrowing constraints, sticky prices, etc• So policy is needed to fix market failure

Who are they?

• Classical approach: Friedrich Hayek*, Robert Lucas*, Robert Barro, Edward Prescott*

• Keynesian approach: John Keynes, Paul Krugman*, Larry Summers, Ben Bernanke, Joseph Stiglitz*, Gregory Mankiw

• Extreme Keynesian approach: ?

Yeah. It’s Me!

Marxian Economics

• People are greedy• Income gap and social instability are inevitable• Widespread market failure (e.g., no health

insurance market for the poor, great depression)

• Government needs to do everything (planned economy)

• Fatal drawback: incentives are ignored

(Most) People are Thin

• in Planned Economy• http://

www.youtube.com/watch?v=UMLtkp4AFkc

Truth?

• Somewhere in middle.• Macroeconomics is still a growing baby. • There are many unsettled issues• For example, introduce game theory to

Macro?