 # ug_labor_17_final.pdf - Final Examination Labor Economics...

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Final ExaminationLabor EconomicsFall 2017Name: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. Clearlyindicate your final response to each answer.1.(9 points)Two individuals inhabit a household. Both have a utility function given byui= 3li+c, i= 1,2,whereliis the leisure of individualiandcis total household consumption, which is equal toc=w1h1+w2h2+y,wherewiis the wage of individualiandyis the non-labor income of thehousehold. The time endowment of each household member isT= 20,so thatT=hi+li,i= 1,2,wherehiis the labor supply of individuali.(a) Ifw1= 5,w2= 2,andy= 100,how much does each individual work if labor supplyis determined in Nash equilibrium?What is the total amount of consumption in thehousehold?(b) If the household maximizesu1(l1, c) +u2(l2, 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)?1
2.(9 points)A monopsonist produces a good only using labor, with a production function givenbyq= 2H,whereHis the total amount of hours supplied to the monopsonist. There areNindividuals in the labor market that are one of two types. One-half of the individuals(N/2)have a utility function given byu= 4l+cand one-half(N/2)have a utility function given byu= 2l+c,wherelis the individual’s leisure andcis their goods consumption. Their time constraintisT=h+l,wherehis the individual’s amount of time supplied to the labor market. Anindividual’s budget constraint isc=wh+y,whereyis their nonlabor income. The values ofN, T,andyare not required to answer the questions.(a) If the price of the monopsonist’s output isp= 1.5,what is her profit-maximizing wageo§er? At this wage, how much labor is supplied by each type of person?(b) If the price of the monopsonist’s output isp= 3,what is her profit-maximizing wageo§er? At this wage, how much labor is supplied by each type of person?(c) If the government imposed a minimum wage ofm= 6,what would be the smallestoutput pricepat which the monopsonist would produce any output?2

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