TEST BANK FOR Advanced Macroeconomics By David Romer Converted

(a) Since the growth rate of a variable equals the time derivative of its log, as shown by equation (1.10) in the text, we can write (1)  ( )   ( ) Z t ln ( ) ln ( ) ( ) Z t d Z t dt d X t Y t dt   . Since the log of the product of two variables equals the sum of their logs, we have (2)  ( )   ( ) Z t ln ( ) ln ( ) ln ( ) ln ( ) Z t d X t Y t dt d X t dt d Y t dt     , or simply (3)  ( ) ( )  ( ) ( )  ( ) ( ) Z t Z ...