Download - Slides 4
![Page 1: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/1.jpg)
Slides 4
For the Final Exam
![Page 2: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/2.jpg)
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
![Page 3: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/3.jpg)
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?
![Page 4: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/4.jpg)
Preference
• Intertemporal (Total) Utility: • Instantaneous (Each Period) Utility: • Two properties: • For example,
![Page 5: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/5.jpg)
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
![Page 6: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/6.jpg)
Calculus
• Consider where are both functions of • Then
+• For our problem
![Page 7: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/7.jpg)
Calculus Two
+++
![Page 8: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/8.jpg)
Euler Equation (First Order Condition)
This looks similar to
marginal rate of substitution equals relative price at optimum.
![Page 9: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/9.jpg)
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.
![Page 10: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/10.jpg)
Log Utility Function
• For log utility function the Euler equation is
or
This shows the dynamic path of consumption
![Page 11: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/11.jpg)
Solution of Dynamic Optimization
• Plugging the Euler Equation into the IBC gives
and we have the solution
where denotes permanent income.
![Page 12: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/12.jpg)
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
![Page 13: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/13.jpg)
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.
![Page 14: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/14.jpg)
Smooth Consumption
• Let then Euler equation implies that
So the optimum is smooth consumption. The reason is diminishing marginal utility.
![Page 15: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/15.jpg)
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.,
![Page 16: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/16.jpg)
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.
![Page 17: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/17.jpg)
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.
![Page 18: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/18.jpg)
Let’s Summarize
• http://www.youtube.com/watch?v=GTQnarzmTOc
• http://www.youtube.com/watch?v=3u2qRXb4xCU
![Page 19: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/19.jpg)
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
![Page 20: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/20.jpg)
What’s Wrong?
![Page 21: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/21.jpg)
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)
![Page 22: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/22.jpg)
![Page 23: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/23.jpg)
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?
![Page 24: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/24.jpg)
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.
![Page 25: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/25.jpg)
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
![Page 26: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/26.jpg)
What’s Wrong?
![Page 27: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/27.jpg)
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
![Page 28: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/28.jpg)
Micro Foundation
• Hayek and Lucas emphasize the microeconomic foundation for macroeconomics, Keynes does not.
• The basic model is a two-period utility maximization problem
![Page 29: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/29.jpg)
New Classical Theory
• Permanent income hypothesis• Random walk hypothesis for consumption• Ricardian equivalence• Smooth consumption• The new classical theory indicates very small
multiplier effect.
![Page 30: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/30.jpg)
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.
![Page 31: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/31.jpg)
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
![Page 32: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/32.jpg)
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
![Page 33: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/33.jpg)
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: ?
![Page 34: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/34.jpg)
Yeah. It’s Me!
![Page 35: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/35.jpg)
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
![Page 36: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/36.jpg)
(Most) People are Thin
• in Planned Economy• http://
www.youtube.com/watch?v=UMLtkp4AFkc
![Page 37: Slides 4](https://reader035.vdocument.in/reader035/viewer/2022081520/5681689a550346895ddf28fc/html5/thumbnails/37.jpg)
Truth?
• Somewhere in middle.• Macroeconomics is still a growing baby. • There are many unsettled issues• For example, introduce game theory to
Macro?