Intermediate Macroeconomics
Juan Rubio-Ram´ırez
Problem Set 1 – Suggested Solutions
Math Review
1. Show that the following expressions can be written as log-polynomials.
For this question, we would need to apply di↵erent formulae of logarithms.
(a) Z=BM↵N1−↵.
ln Z=ln �BM↵N1−↵�
=ln B+ln (M↵)+ln �N1−↵�
=ln B+↵ln M+(1−↵)ln N.
(b) M=✓eµA⌧
eµD!.
ln M=ln �✓eµA⌧
eµD!�
=ln (✓eµA⌧)−ln �eµD!�
=ln ✓+ln (eµ)+ln A⌧−ln �eµ�−ln D!
=ln ✓+µ+⌧ln A−µ−!ln D
=ln ✓+(−)µ+⌧ln A−!ln D.
2. Show that the growth rate of variable x,gx, can be approximated as the di↵erence of the log-level of the
variable.
Let gx
tbe the growth of variable xat time t. We have
gx
t=xt−xt−1
