Question

Answer the following questions using the standard leisure-work choice model

a)Draw a budget constraint for a worker has a job which pays a wage of $10.00 per hour. Draw an indifference map for typical worker. Assume that the worker is able to choose any number of hours of work and this worker’s optimal position is to work 8 hours a day. Show this point on your graph.

b)Suppose the worker now receives $60 per day non-labor income. On your graph (from part a) draw another budget constraint to illustrate this non-labor income. Show the new optimal position for the worker. Briefly, explain your new position and any change in the number of hours worked per day.

c)Using the information above, re-draw an indifference map for a worker who decides not to work after receiving the $60 per day non-labor income. Show the optimal position on your graph. Briefly explain why this individual is or is not rational by choosing not to work.

Answer 1

Let C denote the consumption of other goods. Let the price of consumption goods be p2 (for simplicity this is taken to be 1). Wage rate is the opportunity cost of leisure. If the person enjoys one hour of leisure then he will have to sacrifice $10 (the amount that he could have received if he chooses to work for 1 hour). Price of leisure = $10. The hours available to him are 24 hours in a day.

If he works for entire 24 hours, then he earns 24*$10 = $240

Buget equation:

Price of consumption * units of consumption + price of leisure * units of leisure = income

p2 * C + 10*L = 240

C+ 10L = 240

This is the original budget line. FIgure 1 shows the graph when the individual decided to work for 8 hours in a day. This means that he enjoys (24-8) = 16 hours of leisure. He earns $10*8 = $80 as income. Point A depicts the point when the consumer decides to work for 8 hours.

Figure 1

b) Now, he recieves $60 per day as non-labour income. This means that even if he does not work at all and enjoys 24 hours of leisure, he still has $60 to spend. His new budget equation is plotted in figure 2 in red color

When the income rises, the new optimal position for the worker is depicted as point B. As the non-labour income has increased, the consumers decides to work less as compared to before because he can consume more than what he was consuming before (C1) while at the same time increasing the hours of leisure as well.

Figure 2

c)  a worker who decides not to work after receiving the $60 per day non-labor income, then he just gets the non-labour income as depicted in figure 3.

Figure 3

The consumer is not rational because now he is consuming on a lower IC when he decides to do leisure for 24 hours because in optimal he would have increased the number of hours worked as in part b.