ug_labor_17_final.pdf - Final Examination Labor Economics...

Final Examination
Labor Economics
Fall 2017
Name:
Carefully read each question before answering. If a question seems ambiguous, state your interpre-
tation of it before answering. Show all intermediate steps used in arriving at a conclusion. Clearly
indicate your final response to each answer.
1. (9 points) Two individuals inhabit a household. Both have a utility function given by
u
i
= 3 l
i
+ c, i = 1 , 2 ,
where l
i
is the leisure of individual i and c is total household consumption, which is equal to
c = w
1
h
1
+ w
2
h
2
+ y, where w
i
is the wage of individual i and y is the non-labor income of the
household. The time endowment of each household member is T = 20 , so that T = h
i
+ l
i
,
i = 1 , 2 , where h
i
is the labor supply of individual i.
(a) If w
1
= 5 , w
2
= 2 , and y = 100 , how much does each individual work if labor supply
is determined in Nash equilibrium? What is the total amount of consumption in the
household?
(b) If the household maximizes u
1
( l
1
, c ) + u
2
( l
2
, c ) , determine the labor supply of each indi-
vidual. What is total consumption in this case?
(c) Are both individuals better o § in the “cooperative” solution (i.e., the second case)?
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2. (9 points) A monopsonist produces a good only using labor, with a production function given
by q = 2 H, where H is the total amount of hours supplied to the monopsonist. There are N
individuals in the labor market that are one of two types. One-half of the individuals ( N/ 2)
have a utility function given by
u = 4 l + c
and one-half ( N/ 2) have a utility function given by
u = 2 l + c,
where l is the individual’s leisure and c is their goods consumption. Their time constraint
is T = h + l, where h is the individual’s amount of time supplied to the labor market. An
individual’s budget constraint is c = wh + y, where y is their nonlabor income. The values of
N, T, and y are not required to answer the questions.
(a) If the price of the monopsonist’s output is p = 1 . 5 , what is her profit-maximizing wage
o § er? At this wage, how much labor is supplied by each type of person?
(b) If the price of the monopsonist’s output is p = 3 , what is her profit-maximizing wage
o § er? At this wage, how much labor is supplied by each type of person?
(c) If the government imposed a minimum wage of m = 6 , what would be the smallest
output price p at which the monopsonist would produce any output?
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