Lecture 3_1 is attached below. 1. Consider the labor supply problem in Lecture 3_1.pdf. Suppose instead of

  
 
 
 

Lecture 3_1 is attached below.

 

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1. Consider the labor supply problem in Lecture 3_1.pdf. Suppose instead of having an income target, the worker's reference point essentially says that "I expect to work 8 hours per day." The worker evaluates income in a standard way (see the first half of Lecture 3_1.pdf), but the cost of effort now is reference dependent. Of course, the worker is happier (in the gain region) if she works less than 8 hours per day, and vice versa. To summarize, the worker's utility function is U(h) cs(h): = wh wh + (2(h-8))² 16 (h-8)² 16 " " if h > 8, if h < 8. As usual, the additional coefficient "2" in the cost of effort when h≥ 8 captures loss aversion. (a) What is the worker's utility if she works 8 hours; that is, what is the value of U(8) - C8 (8)? (b) Assume that w > 1. Suppose the worker works h hours and h < 8. Is the worker's utility higher than U(8) - cs(8) or lower, or it depends? (Hint: check the derivative of U(h) - cs(h) when h< 8.) (c) Assume that w > 1. What can you conclude about the optimal h based on your answer in question 1.b? Do you think it is possible that sometimes when w increases, the optimal h decreases? 1. Consider the labor supply problem in Lecture 3_1.pdf. Suppose instead of having an income target, the worker's reference point essentially says that "I expect to work 8 hours per day." The worker evaluates income in a standard way (see the first half of Lecture 3_1.pdf), but the cost of effort now is reference dependent. Of course, the worker is happier (in the gain region) if she works less than 8 hours per day, and vice versa. To summarize, the worker's utility function is U(h) cs(h): = wh wh + (2(h-8))² 16 (h-8)² 16 " " if h > 8, if h < 8. As usual, the additional coefficient "2" in the cost of effort when h≥ 8 captures loss aversion. (a) What is the worker's utility if she works 8 hours; that is, what is the value of U(8) - C8 (8)? (b) Assume that w > 1. Suppose the worker works h hours and h < 8. Is the worker's utility higher than U(8) - cs(8) or lower, or it depends? (Hint: check the derivative of U(h) - cs(h) when h< 8.) (c) Assume that w > 1. What can you conclude about the optimal h based on your answer in question 1.b? Do you think it is possible that sometimes when w increases, the optimal h decreases?

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