The Labor Supply Model

Liz and Jenna each earn $75 per day in non-labor income. If they choose to participate in the labor force, they will each earn a wage rate of $10 per hour. They each have 16 hours available in the day to divide between home and market time.

Liz has relatively strong preferences for market goods over leisure time. She is also very willing to substitute market goods such as take-out for home-produced goods such as cooking.

Jenna has relatively strong preferences for home time. She enjoys some types of home production, such as cooking, as leisure and is not very willing to substitute prepared foods.

Question 1: Draw separate figures for Liz and Jenna showing 1) the budget constraint 2) example indifference curves and 3) the optimal choice of dividing time between home and work. Hint: one of Jenna or Liz does participate in the labor force, and one does not.

Question 2: Suppose that the government decides to incentivize the use of public transportation for commuting by providing a transit card to all individuals with the value of $25 per day, regardless of whether the individual participates in the labor force. Explain how this subsidy is likely to affect the participation (at both the extensive and intensive margin) of both Liz and Jenna. You may explain your answers graphically or verbally. Assume that both Liz and Jenna will use the full value of the transit card.

Question 3: Suppose instead that the government now allocates the subsidy as a tax credit of $3 per hour worked to workers commuting via public transportation. Explain how this version of the subsidy is likely to affect the participation (at both the extensive and intensive margin) of both Liz and Jenna. You may explain your answers graphically or verbally. Again, assume that both Liz and Jenna will commute by public transit if they work.

Question 4: Finally, suppose that the government decides to administer the policy by providing a $25 per day transit card, but only to individuals who actually work. Explain how this version of the subsidy is likely to affect the participation (at both the extensive and intensive margin) of both Liz and Jenna. You may explain your answers graphically or verbally. Again, assume that both Liz and Jenna will commute by public transit if they work. Hint: for the purposes of this question, it may be useful to think of Jenna and Liz's choice to work as a choice over discrete hours of work (that is, they cannot choose to work exactly 5 minutes, but instead choose 0 hours, 1 hour, etc.). Think about what is the effective wage for the first hour of work, and how this is likely to compare to the reservation wage.