Question

consider a guy who works in the CN tower. he lives next to thr CN tower. he is very energetic so his potential maximum work hours are 24 hours per day. his wage rate is 20 dollars per hour. he receives 100 dollars of non labor income everyday. he now has ro make labor supply decidions for tomorrow.

1. what is his income if he doesnt go to work

2. what is his income if he works to his full potential

3.draw a graph to show his budget constraint. label all points

4. what is the slope of his budget constraint

5. draw a graph to dhow hid reservation wage

Answer 1

1) If the individual doesn't go to work, then he will only be able to earn from the non labour income, therefore, his income would be only $100 that he receives as non Labour income.

2)If he works to his full potential, then as given in the question, he would be able to work 24 hours a day. Therefore, at wage rate of $20 per hour, his maximum income will be 24×20 = $480.

3) The following diagram shows the Budget Constraint ABC faced by the consumer, on x -axis we have talen leisure from left to right and labour from right to left. The consumer has total of 24hours to work , therefore point C on X-axis is the maximum number of hours he can work or choose to consume it in leisure.

If he performs no labor and only chooses leisure for 24hours, then he will atleast have the non-labour income given by point B.

On Y- axis we have composite good , which is taken to be a numeraire for the sake of simplicity; if entire income earned is spent on composite good, then he will be able to consume 100+480 = 580 units of each good, given by point A . Hence ABC is budget line.

​​​​​​4) Slope of budget Constraint is equal to -(wage rate) = -20.

The slope of budget line is given by price of commodity x divided by proce of commodity y. Here price of commodity y is 1 ( composite good is numeraire) and price of good x is the opportunity cost of leisure i.e. The wage rate. (slope is negative because it is downward sloping)

5) The wage at which the individual values leisure time exactly as much as the market values leisure is the reservation wage. At this wage rate, the individual is just indifferent between working and not working.
Put another way, the “reservation wage” is equal to the slope of the individuals indifference curve at zero hours of work.

Here, since the utility function is not given, the two possibilities are shown :

IC1 : If indifference curve is such that the slope of IC i.e. reservation wage is greater than the slope of budget line i.e market wage then, the individual will not choose to work.

IC2 : If the reservation wage is lesser than market wage as shown by IC2 slope, then he will choose to work.