Matthias Doepke - Marcroeconomics - Chapter 5 pptx

... proportionality factor Table 5. 1: Notation for Chapter 5 Exercises Exercise 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 consumer is: max =1 ( 1 2 )subjectto: (5. 1) =1 = =1 We will also need a market-clearing constraint for each of the goods. The ma...

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... 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- ing 0 Initial value of the investment Table 1.1: Notation for Chapter 1 Year Mar Jun Sep Dec 1996 155 .7 156 .7 157 .8 158 .6 1997 160.0 160.3 161.2...

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... 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. Above we derived: = 1+ There is no on the right-hand side, so when we take the partial derivative with respect to , the right-hand side is just a constant. Accordingly, = 0, i.e., Cruso...

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... second-period income increases, then does too. Conversely, if second-period in- come decreases, then does too. This makes intuitive sense. If 2 goes down, households will 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 Model 23 3.2 A Two-Period Model We begin this sect...

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... )+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: = 1 1 1 52 The Labor Market Plugging the utility function into equation (6 .5) yields: 2 1 = (1 + ) just like in Chapter 3. All the analysis from that chapter carries...

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... 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-run consequences of expected inflation, while Chapter ... inflation that we will pick up later in this book. Chapter 18 is concerned with the coordination of monetary 8.3 A Cash-in-Advance Economy 61 8.3 A Cash-in-Advance Economy In this section...

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... single shock has long-run effects, and investment goes through a full cycle in response to this shock. Response to a Single Shock -0 .01 -0 .0 05 0 0.0 05 0.01 0.0 15 0.02 0.0 25 123 456 78 Periods Deviation ... the original value: D1=C1. For the next value, we apply the smooth- ing formula. We recommend that you set to .5: D2= .5* D1+ .5* C1. In the same way, you can get the other...

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... 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 capital stock exceeds the steady-state level: capital per unit of effective labor will shrink, until the steady state is reached. 0 0. 05 0.1 0. 15 0.2 0. 25 k 0.37 0.77 delta*k f(...

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... 12.1 Permanent Changes in Government Spending 121 0 5 10 15 20 25 30 35 40 0 0 .5 1 1 .5 2 2 .5 Capital Stock time t K(t) Figure 12.1: Evolution of capital stock. The solid ... output as in equation (BC2) and the dotted line as- suming they affect output as in equa- tion (BC1). 0 5 10 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0 .5 0.6 0.7 Consumption time t C(t) Figure 12.2: ... pur...

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... 0.1 0.2 0.3 0.4 0 .5 0.6 0.7 0.8 0.9 1 0 0. 05 0.1 0. 15 0.2 0. 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 Tax Now let ... function of . The government’s period-by-period revenue function ( ) is now simply: ( )= ( SS SS ) where SS is the steady-state investment level (which is tax-exempt). We can find SS by solv...

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