Georgetown University ECON 551 Assignment-1-551-solutions-verified by experts 2021

Econ  551 Assignment  1:  Solutions Due:  Thursday,  September  18,  2014,  5pm 1a.  A  consumer  is  considering  how  much  to  work  (each  week).  She  c ...

Econ  551 Assignment  1:  Solutions Due:  Thursday,  September  18,  2014,  5pm 1a.  A  consumer  is  considering  how  much  to  work  (each  week).  She  can  work  a  maximum  of  80  hours   per  week.  Each  hour  she  doesn’t  work  is  an  hour of  leisure,  l.  For  each  hour  she  works,  she  gets  paid   a  wage  w.  With  the  money  she  earns,  she  can  buy  a  single  consumption  good,  c,  whose  price  is  set   equal  to  one. (i)  Draw  this  consumer’s  budget  set  in  (l;  c)-­‐space  (l  is  measured  on  the horizontal  axis, c  on  the   vertical  axis).  Mark  the  slope  of  the  budget  line,  and  the  intercepts  on  both  axes. (ii)  On  the  same  …gure,  draw  the  budget  set  of  a  second  worker  who,  having  more  education,  earns  a   higher  hourly  wage  rate,  w’. (iii)  For  the  original  worker,  denote  the  income  she  earns  by  working  h  hours  by  y  =  wh.  Now  draw   her  budget  set  in  (y;  c)-­‐space  (y  on  the  horizontal  axis). (iv)  Finally,  consider  the  following  income  tax  system.  Individuals  who  earn  less  than  a  threshold   amount  y  receive  an  earned  income  credit  (EIC)  of  20%.  That  is,  for  each  dollar  earned  up  to  y,  the   worker  makes  $1.20.  Any  income  above  the  threshold  is  taxed  at  a  rate  of  25%.  Draw  the  consumer’s   budget constraint  in  (y;  c)-­‐space.Let  us  now  assume  that  the  wage  is  $1  per  hour,  and  that  the  consumer  only  likes  an  hour  of  leisure   when  she  has  something  to  consume  during  that  hour.  That  is,  an  extra  hour  is  worthless,  unless   complemented  with  an  extra  unit  of  the  consumption  good.  Similarly,  an  extra  unit  of  the   consumption  good  is  useless  unless  she  has  time  to  consume  it. (v)  Draw  and  label  the  consumer’s  budget  constraint  in  (l;  c)-­‐space,  and  on the  same  picture  draw  her   indifference  curves.  How  much  leisure  does  the  consumer  choose,  how  much  of  the  consumption   good  does  she  buy,  and  how  many  hours  per  week  does  she  work?When  she  has  a  wage  of  $1  per  hour,  she  chooses  point  A,  at  which  she  enjoys  40  hours  of  leisure  (l  =   40),  and  consumes  40  units  of  the  consumption  good.  She  works  40  hours  per  week. (vi)  Now  suppose  this  person  becomes  educated  and  her  wage  increases  to  $3  per  hour.  On  the  same   diagram,  draw  and  label  the  consumer’s  new  budget constraint.  What  are  her  optimal  choices  of   leisure  and  the  consumption  good  now? Answer  (vi):  With  the  higher  wage,  the  consumer  chooses  point  B  in  the  diagram.  Here  she  enjoys   more  leisure  than  before  -­‐ 60  hours  per  week,  and  she  works  only  20  hours  per  week.  But  her   consumption  of  the  consumption  good  also  increases,  to  60  units. To  see  how  to  get  these  numbers,  note  that  if  the  consumer  worked  as  much  as  she  could  (80  hours),   she  would  have  $240.  Each  hour  of  leisure  she  chooses  reduces  her  income  by  $3,  so  we  can  think  of   her  as  facing  a  "price  of  leisure"  of  $3.  The  price  of  the  consumption  good  is  $1.  We  know  she  will   purchase  equal quantities  of  leisure  and  the  consumption  good  -­‐ that  is,  l  =  c.  Her  budget  constraint   is  then  just  c  +  3l  =  240  or  4c  =  240:  But  this  means  c  =  60,  and  hence  l  =  60. 1b.  Consider  a  consumer  with  total  income  of  $200  signing  up  for  new  internet  service.  He  has  the   choice  between  standard  and  premium  service  packages.  Under  the  sta