**Unformatted text preview: **Additional Session Material
TA: Wonmun Shin
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December 17, Saturday Chapter 3 Robinson Crusoe Economy (Consumption-Leisure Choice)
Robinson Crusoe with constant wage: w ^ SE / WE / TE Robinson Crusoe with concave production function: A ^ SE / WE / TE A. Exercise 1: A Tax on Robinson (2012 Final, Recitation 6)
In class we assumed that Robinson receives a constant wage. This is a realistic assumption if there are no diminishing returns to his work (that is, if the amount of coconuts he gets for working one hour is the
same regardless of the amount of hours he works). More realistically, he faces diminishing returns as he probably gets the easy to get coconuts rst so the more he works, the harder it gets to get additional coconuts. Imagine that his budget constraint is √
C = A L where L is the amount of work and C is consumption. (a) Plot the budget constraint in the C-L space. Imagine that Robinson's preferences are neoclassical (that is, increasing in C and leisure and concave). (b) Plot the indierence curves in the C-L space (note: recall that L is labor, not leisure).
(c) Find graphically the optimal amount of work eort and consumption.
(d) Imagine that Robinson's wins the lottery. That is, without having to work, he can now enjoy 10,000
cookies for free. Display Robinson's new budget constraint and his new likely behavior. Make sure you explain
Robinson's behavior in terms of wealth and substitution eects.
(e) Imagine instead that Robinson's economy experiences a positive productivity shock (the term A in
the production function increases). Plot the new budget constraint and describe the new optimal choice for
Robinson. Make sure you explain Robinson's behavior in terms of wealth and substitution eects.
(f ) What are the dierences between your answers in (d) and (e)? Explain.
(g) Imagine now that a government levies an output tax at rate √
C = (1 − τ )A L. τ so that the new budget constraint is What are the eects on work eort and consumption of an increase in 1 τ? B. Exercise 2: Taxing Robinson (2014 Final, Recitation 6) Chapter 4 Intertemporal Choice and Consumption Theory
DBC and IBC (two period/ no money)
Intertemporal choice model r
^ : Saver (SE/ WE/ TE) | Borrower (SE/ WE/ TE) | Agg.Economy (SE/ WE/ TE) Income ^ : Temporary shock | Permanent shock | Anticipated shock Classical consumption theory (LCH and PIH)
Keynesian consumption theory (LCC)
Aggregate demand (only consumption) / Aggregate supply
Goods market equilibrium Temporary increase in A Permanent increase in A Anticipated increase in A A. Exercise 1: Short speech (2012, 2014 Final)
If the economy as a whole is open and is indebted (as it is the case for the USA today), an increase in interest
rates leads to lower consumption unambiguously. Do you agree? If so, why? B. Exercise 2: Should I go to school? (2013 Final, Recitation 9)
C. Exercise 3: Capital income tax (2014 Final, Recitation 9)
Imagine a consumer that lives for two periods, receives some income
borrow and save by buying or selling bonds B1 Y1 today and Y2 from a cookie bank at the interest rate tomorrow, and can r. He has to decide how much to consume today and tomorrow. This person is a professional athlete so that his
and his Y2 Y1 is very high is very low. (a) Will the consumer choose to save or to borrow? What is the key intuition for this result?
(b) What is his budget constraint in each period? What is his inter-temporal budget constraint?
(c) Draw on a graph his income point, his budget line and his optimal consumption point. Make sure you
are consistent with (a). τ > 0. That is,
B1 +rB1 , he receives only: B1 +(1−τ )rB1 Consider the case now in which the government taxes the net income from savings at rate B1 in bonds, tomorrow instead of receiving:
(rB1 ) to the government). when the consumer holds
(since he is giving: τ Ö 2 (d) What is the new budget constraint in each period? What is the new inter-temporal budget constraint?
Draw on a graph his new budget line and optimal consumption point.
(e) How does the consumer react to an increase in τ ? Make sure to decompose the total eect between wealth eect and substitution eect.
(f ) Which of these two eects would still be here for a neutral guy who is neither saving nor borrowing?
How would he react to an increase in τ ? (g) Knowing that the macroeconomy as a whole behaves like the neutral guy, what does (f ) tell you about
the aggregate consumption demand function C d (r, P DV (Y ), τ ) ? Does it shift when τ increases? How? (h) Consider a simple classical model with only consumption on the demand side. What are the eects of
a temporary increase in τ on the cookie market? What happens on the money market? Chapter 5 Money (and Money Market)
Real vs. nominal interest rate
Money demand (Baumol-Tobin model)
Money market equilibrium Chapter 6 General Equilibrium (in Classical Model)
Walras' Law
GE analysis [step1] Draw two diagram (Real, Money) [step2] Consider shift of curves! (one by one) *
* Real market: demand curve? supply curve?
Money market: demand curve? supply curve? [step3] Find new equilibrium in the real market [step4] Eect of the real market on the money market [step5] Result 1. Temporary productivity shock
2. Permanent productivity shock
3. Money supply shock
4. Money demand shock 3 Chapter 7 Investment Theory (and General Equilibrium)
(Neoclassical) Investment theory
GE analysis 1. Temporary productivity shock
2. Permanent productivity shock
3. Money supply shock A. Exercise 1: Installation Costs (2013 Final, Reciation 10)
B. Exercise 2: A Tax on MPK (2012 Final)
In this question we consider a tax on the marginal product of capital. Let us imagine that the neoclassical
rms discussed in class (with a one-period time-to-build technology) have to pay a tax equivalent a fraction τ of the revenues obtained every year. The tax is levied on the sales of output but not on the sales of (depre- ciated) machinery or capital. Consider rst the investment decision of a rm that uses its own cash to nance its investment.
(a) Explain intuitively how rms will make the decision to invest comparing revenues and expenditures
today and tomorrow.
(b) How does the desired capital stock at time t and the investment demand function depend on the interest rate, on the level of productivity, A, and the tax rate, τ ? Provide your economic intuition. (c) What interest rate aects the investment decision: nominal or real? Explain intuitively.
(d) What productivity parameter(s) aect the investment decision: today's or tomorrow's? Explain intuitively.
(e) What tax rate(s), τ, aect the investment decision: today's or tomorrow's? Explain intuitively. Consider now the investment decision when, in order to nance its investment, a rm needs to borrow
money from the bank at the nominal interest rate R.
(f ) How do your answers (a) through (e) change? Why? Explain
(g) Imagine that, when the government sees that the economy is in a recession at time t, it reduces the
tax rate, τ, temporarily. That is, it reduces τt but it leaves τt+1 and all future tax rates unchanged. How will this tax policy aect the macroeconomy in a classical general equilibrium world?
(h) How will the temporary tax cut aect the macroeconomy in a Keynesian world?
(i) Imagine now that the government cuts the tax rate permanently. That is, it reduces τt and all future taxes. What are the macroeconomic eects of this policy in the classical world?
(j) What are the macro implications of a permanent tax cut in the Keynesian world? 4 as well as τt+1 Chapter 8 Keynesian Model
Key assumptions in Keynesian world
IS-LM model [step1] Draw diagram (IS (C [step2] Consider shift of curves! (one by one) *
*
*Y d , I d ), LM, Y S) IS :
LM : s : [step3] SR result (IS-LM) [step4] MR result (4P s
[step5] LR result (IS-LM-Y ) =λ Yd−Ys ) 1. Change in money supply
2. Change in price level Sticky price A. Exercise 1: More Short Speeches (2012 Final, 2014 Final)
(a) What are the eects of an increase in the cost of going to the bank (what in class we labeled with the
Greek letter ψ) in the classical model of the business cycle? (b) What are the eects of an increase in the cost of going to the bank (what in class we labeled with
the Greek letter ψ) in the Keynesian model of the business cycle? (c) In the long run, the Keynesian model shows that an increase in money supply leads to ination and
no real eects in GDP. Do you agree? If so, why? B. Exercise 2: Productivity Shocks (2013 Final)
(a) Suppose an economy without Investment. Using the classical model, what is the eect of a permanent
increase in productivity on Output, Consumption and Price level? Show graphically and explain.
(b) How would your answer to a) change if consumers were liquidity constrained? Explain.
(c) What is the eect of a permanent increase in productivity in the Keynesian Model, with sticky prices?
Is your answer dierent to part a? If so, explain why. Make sure that you discuss the short, the medium and
the long run, and that you show graphs.
(d) Suppose that the Federal Reserve wants to keep the interest rate constant immediately after they
observe the productivity shock. In the Keynesian Model, what should the Fed do? Analyze the eect of this
policy in the short, medium and long run. 5 C. Exercise 3: Seen in the news (2014 Final)
Last week, oil prices plunged to their lowest level in 5 years. There is an ongoing debate on the impact it will
have on the US economy. Let's see how you guys can contribute to it! The Obama administration says that
it is good news because it is going to boost supply - that is for the same amount of inputs, we will get more
output since fewer resources will have to be used to pay for oil. (a) Consider a simple classical model with only consumption on the demand side. By interpreting the drop in oil prices as a permanent increase in productivity, explain why they might be right. What happens
to the equilibrium levels of output and interest rate? What happens to the price level? Draw a graph and
explain your answer. However, the Fed is worried that in the short-run, it could create deationary pressures that would hurt
the economy that is, since the cost of one key input, energy, is lower, rms will charge lower prices overall
in the future. To understand, we are going to modify a little bit the simple Keynesian model (IS-LM) that we
saw in class, by incorporating expectations of consumers. Recall that the real interest rate is given (approximately) by: r = R − πe * ( ), where R is the nominal interest rate, and πe is the expected ination between today and tomorrow (prices today are sticky so they do not move anyway). Since the money market has to R= clear, we also know that: * ** (b) Combine ( ) and ( ** ψ
(
2(M s /P ∗ )2 ). ) to express r as a function of market with aggregate demand Y d ψ, M s, P ∗, Y and πe. Draw a graph of the cookie and this modied LM curve. What is the dierence with what we saw in class?
(c) By interpreting the drop in oil prices as an exogenous decrease in ination expectation πe, explain what eect this will have on the cookie market in the short run. What happens to the equilibrium level of
output and interest rate? Draw a graph and explain your answer.
(d) What could the Fed do to keep the same equilibrium level of output instead?
explain your answer. What would happen to the equilibrium level of interest rate? Chapter 9 Government
Government Budget Constraint
Government spending in Classical model Temporary increase in G Permanent increase in G Government spending in Keynesian model
Budget Decit Classical view: Ricardian Equivalence Keynesian view 6 Draw a graph and A. Exercise 1: Government and the Cycle (2012 Final)
Consider the model with government spending discussed in class. Remember that we assumed that gov- ernment spending was useless (in the sense of not being productive nor aecting utility) but it nevertheless
aected aggregate demand. (a) If the government can borrow and lend and print money, what is the government budget constraint?
Discuss each of the elements.
(b) If the government does not have access to nancial borrowing or printing money, what is the budget
constraint? Imagine that the only tax available to the government is a lump-sum tax. (c) Why do economists say that the lump-sum tax is non-distortionary? Explain.
(d) Imagine that the government increases spending temporarily. What are the eects on GDP, the real
interest rate, the price level, consumption and investment? Explain
(e) Imagine that the government increases spending permanently. What are the eects on GDP, the real
interest rate, the price level, consumption and investment? Explain
(f ) In the light of your answer to (e), when government spending is useless, is it a good idea to expand the
size of government? Why or why not? Why do you think countries all over the world increase government
spending continuously? Imagine now that, on top of aecting aggregate demand, government spending aects the productivity of
private capital (more roads make cars more productive). But imagine that does not aect supply during the
period in which the spending is made (maybe because roads take time to build). Consider a world in which
prices are exible so they move to clear all the markets all the time. Again, using the classical world, answer
the following questions: (g) Imagine that the government increases this type of spending temporarily. What are the eects on GDP, the real interest rate, the price level, consumption and investment? Explain
(h) Imagine that the government increases spending permanently. What are the eects on GDP, the real
interest rate, the price level, consumption and investment? Explain B. Exercise 2: Government Decits (2013 Final)
Assume that you live in an economy that lasts for two periods. Suppose that the government reduces taxes
in the economy by 1 million in the rst period, and that government spending remains unchanged both in
period 1 and 2. In order to nance this tax cut and in order to continue the same spending, the government
will have to borrow and increase taxes in period 2. Imagine taxes are lump sum. (a) By how much will the government have to increase taxes in period 2?
(b) Consider the Classical Model. What is the eect of this tax cut on Output, Consumption, Private
Savings, Investment, the interest rate and the price level? Explain. 7 (c) Consider now the case where all consumers are liquidity constrained (Keynesian Model). What is the
eect of the tax reduction on Output, Consumption, Private Savings, Investment, the interest rate and the
price level? Explain. Imagine now that the government implements the tax cut in the rst period, but that the decit will be
nanced entirely by a reduction in government spending. (d) If the tax cut in period 1 is nanced with a reduction in G in period 1, by how much will government
spending have to be cut in period 1?
(e) What will be the eect of all this on output, consumption, investment and the interest rate in the
Keynesian Model? Explain.
(f ) What will be the eect of all this on output, consumption, investment and the interest rate in the
Classical Model? Explain.
(g) If the tax cut in period 1 is nanced with a reduction in G in period 2, by how much will government
spending have to be cut in period 2?
(h) What will be the eect of this on output, consumption, investment and the interest rate in the
Keynesian Model? Explain.
(i) What will be the eect of all this on output, consumption, investment and the interest rate in the
Classical Model? Explain. NOTE: In this problem, even in the Keynesian Model, we have exible prices. The only dierence is that
consumers are liquidity constrained. Also, you need to show graphically your results. 8 ...

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