Matthias Doepke - Marcroeconomics - Chapter 5 pptx

... proportionality factorTable 5. 1: Notation for Chapter 5 ExercisesExercise 5. 1 (Easy)Show that Walras’ law holds for the credit-market economy that we discussed in Chapter 3.2. That is, use the ... selling the endow-ment. Mathematically, the problem of consumeris:max=1(1 2)subjectto: (5. 1)=1==1We will also need a market-clearing constraint for each of the goods. The market-clearingcondition ... pure-exchange economy, assume that the bud-get constraints for each of theconsumers and the market-clearing constraints for the ﬁrst1 goods are satisﬁed. We want to show that the last market-clearing...

Matthias Doepke - Marcroeconomics - Chapter 1 docx

... is two years.$1 35 =2($100 ) so:= [ln($1 35 ) ln($100 )](0 5) 0 150 052 30 = 15 150 052 30%Economists generally prefer to use continuous compounding, for two reasons. First, un-der continuous ... after years under continuous compound-ing0Initial value of the investmentTable 1.1: Notation for Chapter 1Year Mar Jun Sep Dec1996 155 .7 156 .7 157 .8 158 .61997 160.0 160.3 161.2 161.3What ... income of these two countries at that date?Exercises 5 024680 5 10 15 20 25 Year (n)V(n)Figure 1.1: Exponential Growth0120 5 10 15 20 25 Year (n)ln[V(n)]Figure 1.2: Log of Exp GrowthThe...

Matthias Doepke - Marcroeconomics - Chapter 2 docx

... problems of constrain-ed maximization when it is either difﬁcult or impossible to solve the constraints for indi-vidual variables. At ﬁrst we treat the method as a cook-book recipe. After we ... even easier. Abovewe derived:=1+There is no on the right-hand side, so when we take the partial derivative with respectto, the right-hand side is just a constant. Accordingly, = 0, i.e., Crusoe’s ... Consumption=1,forsome between zero and one. This particular Cobb-Douglas functionexhibits constant returns to scale, since (1)+( ) = 1. Figure 2.1 is a three-dimensionalrendering of this function for particular...

Matthias Doepke - Marcroeconomics - Chapter 3 ppsx

... second-period income increases, then does too. Conversely, if second-period in-come decreases, thendoes too. This makes intuitive sense. If2goes down, householdswill try to invest first-period ... )=1[2+1(1 + )](1 + )(1 + )so we set the left-hand side to zero and solve for :1=[2+1(1 + )](1 + )(1 + )(3.11)3.2 A Two-Period Model233.2 A Two-Period ModelWe begin this section with ... termson the right-hand side:( )(+1)=(1 + )(3.16)If you compare equation (3.16) to equation (3.7), you will find the Euler equations are thesame in the two-period and infinite-period models....

Matthias Doepke - Marcroeconomics - Chapter 6,7 doc

... )+ln(24 )where is the household’s consumption. Production on type- farms is given by:=( )0 5 and that on type- farms is:=2( )0 5 We are going to solve for the wage that clears the market. In ... each household is:=111 52 The Labor MarketPlugging the utility function into equation (6 .5) yields:21= (1 + )just like in Chapter 3. All the analysis from that chapter carries forward. ... interest rate in-creases. That means that the right-hand side increases, so the left-hand side must increasein order to maintain the equality. There are two ways that the left-hand side can...

Matthias Doepke - Marcroeconomics - Chapter 8 pdf

... assets, Chapter 19 turns to the issue of expected versus un-expected inflation. You can think of the cash-in-advance model as describing the long-runconsequences of expected inflation, while Chapter ... inflation that wewill pick up later in this book. Chapter 18 is concerned with the coordination of monetary8.3 A Cash-in-Advance Economy618.3 A Cash-in-Advance EconomyIn this section we derive the ... and in Chapter 19 we will return to the question of optimal monetary pol-icy. While the prime emphasis of the cash-in-advance model is the inefficiency of holdingcash instead of interest-bearing...

Matthias Doepke - Marcroeconomics - Chapter 9 doc

... single shock has long-run effects, and investment goes through a full cycle inresponse to this shock.Response to a Single Shock -0 .01 -0 .0 05 00.0 05 0.010.0 15 0.020.0 25 123 456 78PeriodsDeviation ... the original value: D1=C1. For the next value, we apply the smooth-ing formula. We recommend that you setto .5: D2= .5* D1+ .5* C1. In the same way,you can get the other smoothed growth rates. ... yeartwo on the formula is therefore:Trend+1=(1+ˆ)(0 5) Trend +( 05) GDPIn terms of the spreadsheet, this translates into E2=(1+D1)*( .5* E1+ .5* B1), and so on.This completes the computation of the...

Matthias Doepke - Marcroeconomics - Chapter 11 pot

... production function equa-tion (11.1) exhibits constant returns to scale, which means that if we double both inputs,output also doubles. Our choice of a constant-returns-to-scale production function ... initial capitalstock exceeds the steady-state level: capital per unit of effective labor will shrink, until thesteady state is reached.00. 05 0.10. 15 0.20. 25 k 0.37 0.77delta*kf(k)s*f(k)Figure ... with1See Chapter 1 for a discussion of growth rates and how to compute them. Chapter 11Economic GrowthThis chapter examines the determinants of economic growth. A startling fact about eco-nomic...

Matthias Doepke - Marcroeconomics - Chapter 12 pdf

... 12.1 Permanent Changes in Government Spending1210 5 10 15 20 25 30 35 4000 .5 11 .5 22 .5 Capital Stocktime t K(t)Figure 12.1: Evolution of capital stock.The solid ... output as inequation (BC2) and the dotted line as-suming they affect output as in equa-tion (BC1).0 5 10 15 20 25 30 35 4000.10.20.30.40 .5 0.60.7Consumptiontime t C(t)Figure 12.2: ... purchases affect output as inequation (BC2) and the dotted line as-suming they affect output as in equa-tion (BC1).0 5 10 15 20 25 30 35 4000.20.40.60.811.21.41.6Interest ratetime t r(t)Figure...

Matthias Doepke - Marcroeconomics - Chapter 13 docx

... 0.1 0.2 0.3 0.4 0 .5 0.6 0.7 0.8 0.9 100. 05 0.10. 15 0.20. 25 Tax revenue when γ=0 .5 τ T(τ)Figure 13.1: A government revenue func-tion that exhibits a Laffer curve.A Lump-sum TaxNow let ... function of .The government’s period-by-period revenue function( ) is now simply:( )= (SS SS)whereSSis the steady-state investment level (which is tax-exempt). We can ﬁndSSbysolving ... signi - cantly in their characteristics. Consider the jobs available to Ph.D. economists: they rangefrom Wall Street ﬁnancial wizard, big-time university research professor, to small-time col-lege...

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