Matthias Doepke - Marcroeconomics - Chapter 1 docx

... under continuous compound- ing 0 Initial value of the investment Table 1. 1: Notation for Chapter 1 Year Mar Jun Sep Dec 19 96 15 5.7 15 6.7 15 7.8 15 8.6 19 97 16 0.0 16 0.3 16 1.2 16 1.3 What is the growth ... between 19 92 and 19 93 is given by in equation (1. 1). Starting GDP is , ending GDP is ( ), and is one year. Plugging all the numbers in, we get: $13 5 =( )( $13 0...

Ngày tải lên: 04/07/2014, 10:20

... example, under ( )=ln( )+ln (1 )and ( )= , equation (2.5) becomes: 1 = 1 1 1 ( ) 1 or equivalently: = (1 )( ) 1 Now we plug in the budget equation = to get: ( ) = (1 )( ) 1 After some canceling and ... three-dimensional rendering of this function for particular values of and . 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 product (y) labor (l) capital (k) Fi...

Ngày tải lên: 04/07/2014, 10:20

... of with respect to : ( )= 1 1 (1 ) 1 1 (1 ) 1 1 = 1 1 (1 ) 1 1 1 1 = 1 1 (1 ) 1 1 1 1 1 Notice immediately that the derivative ( ) has the same sign as the term: 1 1 1 since the term outside of ... output (GDP) of an increase in : = + = + = 1 1 1 1 1 1 We divide by ,tofindthat 0 if and only if: 1 1 1 1 1 1 0 or: 1 1 1 + 1 1 1 0 or: 1 1 1...

Ngày tải lên: 04/07/2014, 10:20

... that 1 ( )=0.Wehad: 1 ( )= 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 ... is: = =1 1 ( )+ =1 ( ) (1 + ) 1 The first-order condition with respect to is: 1 ( )+ ( 1) (1 + ) 1 =0(FOC ) Rotating this forward and dividing the FOC by the...

Ngày tải lên: 04/07/2014, 10:20

... consumptions in the al- location 1 2 =1 in the first place. Summing equation (5.4) over all consumers and rearranging yields: =1 =1 ¯ =1 =1 =1 =1 ¯ =1 =1 =1 =1 ¯ =1 =1 so: =1 =1 ¯ =1 0 We assumed that ... pure-exchange case. 5.3 Walras’ Law 43 good is also satisfied. Summing the budget constraints over all consumers yields: =1 =1 = =1 =1 Rearranging gives: =1 =1...

Ngày tải lên: 04/07/2014, 10:20

... 1 )+ ( 2 2 )+ 1 [ ( 1 ) 1 1 ]+ 2 [ ( 2 )+ 1 (1 + ) 2 ] There are seven first-order conditions: 1 ( 1 1 )+ 1 [ ]=0(FOC 1 ) 1 ( 2 2 )+ 2 [ ]=0(FOC 2 ) 2 ( 1 1 )+ 1 [ ( 1 )] = 0(FOC 1 ) 2 ( 2 2 )+ 2 [ ... where the house- hold’s supply equals the household’s demand. Accordingly, we set = and call the resulting wage : 1 2 1 2 1 1 = 1 1 We gather like terms to g...

Ngày tải lên: 04/07/2014, 10:20

... as: 1+ = +1 (8.2) Taking the ratio of equation (8 .1) for two consecutive years, we get: +1 = +1 +1 We know from equation (8.2) that +1 equals 1+ ,andthe terms cancel, so we have: 1+ = +1 +1 (8.3) We ... eliminate the multipliers from equation (8 .11 ): 1 (1 ) = 1 +1 From the goods market-clearing constraint, we know that = . Therefore we get: +1 = 1 The left-hand s...

Ngày tải lên: 04/07/2014, 10:20

... with respect to is: = 1 1 2 1 1 1 1 2 1 1 + (1 ) 1 1 and for investment we get: = 1 2 1 1 1 2 1 1 (1 ) 1 1 It turns out that the relative change in investment is larger. A one-percent increase in leads ... difference between output and investment. Using equation (9.4) for yields: = = 1 1 + (1 ) 1 = 1 1 + (1 ) 1 1 2 1 1 = 1 1 2 1 1 + (1 ) 1 (9.5) Aggre...

Ngày tải lên: 04/07/2014, 10:20

... labor: (1 + ) (1 + ) = (1 ) 1 + or: (1 + ) (1 + )= (1 ) 1 + (11 .6) Finally, investment is determined by: = = 1 1 (11 .7) Plugging equation (11 .7) into the law of motion in equation (11 .6) yields: (1 + ) (1 ... 11 .3 in terms of output per worker. The first step is to divide the production function in equation (11 .11 ) by the number of workers , which yields: = ( ) 1 1...

Ngày tải lên: 04/07/2014, 10:20

... steady-state capital stock is: SS = 1 1 so the derivative of the steady-state capital stock with respect to is: SS = 1 1 1 1 1 Plugging in yields: SS = 1 1 1 1 1 + = 1 1 + 1 1 = 1 1 + SS (12 .10 ) ... .So: 1 (1 ) + 1+ + =0 We cross-multiply to find: (1 + ) (1 ) = + [ 2 (1 + )][ (1 ) ]= + [ 2 (1 + )] (1 ) = [1+ 2 (1 + )] and: 2 (1 + ) [1 + 2 (1 + )] =...

Ngày tải lên: 04/07/2014, 10:20