Consider a family that ranks combinations of household production time (N) and purchased goods and services (Y) according to the formula: U=NY. Suppose the maximum time available in a day is 16 hours and currently a spouse devotes 7 hours to market work (H) at a wage of $5 per hour. Suppose the family also receives $10 per day in non-labor income (i.e. food stamps).
a. What is the level of utility associated with the current mix of market work and household production?
b. Assume that a recession occurs and the worker is laid o from his or her job. What is the level of utility at the new mix of market work and household production?
c. Suppose the probability of nding a comparable job during this recession is . What is the return of taking an hour away from household production activities to look for a job?
d. Assuming = 0:5, would an hour spent in the labor force searching for a job make this person better o or worse o ? Would the worker continue to be a member of the labor force under these conditions? If not, how would he/she be categorized?
e. Suppose that if the worker were willing to accept a job paying only $2 per hour, the probability of finding a job would be = 1=3. Would the worker continue to be a member of the labor force?