Question

3. Consider a consumer who has well-behaved preferences over leisure (L) and consumption (x) They have nonlabor income m and have 24 hours in the day that must be divided between leisure and working. They are initially paid a wage w for each hour of work. The price of x is 1 (a) Suppose they optimally choose to work 8 hours. Draw the consumer's budget set and an indifference curve showing this situation. (b) Now suppose that they are paid an overtime wage that is higher than w for each hour worked in excess of 8 hours. (The wage is w per hour for the first 8 hours of work and greater than w for any additional time.) Draw the new budget set and explain any impact this has on their choice of hours worked

Answer 1

The labour -leisure choice in front of the consumer can be depicted on the leisure- commodity space. The horizontal axis shows number of hours devoted to leisure increasing from left to right. And hence from right to left are the number of hours in labour. Since M is the non labour income, the consumer can spend it all in consumption of other goods, and also it will not affect the total number of hours available to him , hence there is a kink on the budget line ABC at B .

Overtime wages alters the choice of the consumer. But it depends on the level at which it is fixed. If it is fixed at initial choice of leisure , the consumer definitely has the required incentive to switch away from leisure towards labour and be on a higher indifference curve IC' on the new budget line A'BC.

Non labou Ino me Виce ad | wage Constraint is enc Pudget Mt 24u Tota! NO. a Houu availalle a day 24) Mt24w иosles fy 8 Rousus If cannumun eisue hen ни 24-8 16 a ourtime M C Дciane 24 laout

i paid at Pudget Pis initial Choiu oшкиiти итy If leisune then the dingam overtime wiu lu an Lihu as Chown new thi in wonkfa Consumr the is perid to in come and teisuu, 'n Hours torgen Guuen betueen traoll 4а eriie ountue eiure the He onaumu maki to order Hence the Some Should ошенiтe иде expands availaule to the choices CconUmun the Sine it initial chau af leiaune Рouoptale Hi teisue, bu ng i proded at and to fncl wiu consumls оjiиng Indierunce fo longe Hours нighes сише at a