▁claim ▁that ▁it ▁allows ▁the ▁form ulation ▁of ▁theoretical ▁relationships ▁with ▁rig or , ▁general ity , ▁and ▁simplicity . ▁ ▁Mathemat ics ▁allows ▁econom ists ▁to ▁form ▁meaning ful , ▁test able ▁propos itions ▁about ▁ ▁wide - r anging ▁and ▁complex ▁subjects ▁which ▁could ▁less ▁easily ▁ ▁be ▁expressed ▁inform ally . ▁Further , ▁the ▁language ▁of ▁mathematics ▁allows ▁econom ists ▁to ▁make ▁specific , ▁positive ▁claims ▁about ▁controvers ial ▁or ▁content ious ▁subjects ▁that ▁would ▁be ▁impossible ▁without ▁mathematics . ▁Much ▁of ▁economic ▁theory ▁is ▁currently ▁presented ▁in ▁terms ▁of ▁mathematical ▁economic ▁models , ▁a ▁set ▁of ▁st yl ized ▁and ▁simplified ▁mathematical ▁relationships ▁assert ed ▁to ▁clarify ▁assumptions ▁and ▁imp lications . ▁ ▁Broad ▁applications ▁include : ▁ ▁optimization ▁problems ▁as ▁to ▁goal ▁equilibrium , ▁whether ▁of ▁a ▁household , ▁business ▁firm , ▁or ▁policy ▁mak er ▁ ▁static ▁( or ▁equilibrium ) ▁analysis ▁in ▁which ▁the ▁economic ▁unit ▁( such ▁as ▁a ▁household ) ▁or ▁economic ▁system ▁( such ▁as ▁a ▁market ▁or ▁the ▁economy ) ▁is ▁mode led ▁as ▁not ▁changing ▁ ▁compar ative ▁stat ics ▁as ▁to ▁a ▁change ▁from ▁one ▁equilibrium ▁to ▁another ▁induced ▁by ▁a ▁change ▁in ▁one ▁or ▁more ▁factors ▁▁ ▁dynamic ▁analysis , ▁trac ing ▁changes ▁in ▁an ▁economic ▁system ▁over ▁time , ▁for ▁example ▁from ▁economic ▁growth . ▁ ▁F ormal ▁economic ▁model ing ▁began ▁in ▁the ▁ 1 9 th ▁century ▁with ▁the ▁use ▁of ▁differential ▁calculus ▁to ▁ ▁represent ▁and ▁explain ▁economic ▁behavior , ▁such ▁as ▁utility ▁maxim ization