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Consider a family that ranks combinations of household production time (N) and purchased goods and services (Y) according to the formula: U=NY.

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?
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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 nding a job would be  = 1=3. Would the worker continue to be a member of the labor
force?

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