Problem_Set 2_solutions_to_problems_from watson_solutions

Problem_Set 2_solutions_to_problems_from watson_solutions -...

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18 Bargaining Problems 1. (a) v =50 , 000; u J = u R =25 , 000; t =15 , 000. (b) Solving max x 60 , 000 x 2 + 800 x yields x =400 . Th isimp l ies v = 220 , 000, u J = u R =110 , 000, v J = 100 , 000, and v R = 320 , 000. Thus, t = 210 , 000. (c) From above, x = 400 and v =220 , 000. u J =40 , 000 + (220 , 000 40 , 000 20 , 000) / 4=80 , 000 and u R =20 , 000+(3 / 4)(220 , 000 60 , 000) = 140 , 000. This implies t = 180 , 000. 2. (a) The surplus with John working as a programmer is 90 , 000 w .Th e surplus with him working as a manager is x 40 , 000 w> 110 , 000 w . Thus, the maximal joint value is attained by John working as a manager. John’s overall payo f is w + π J [ x 40 , 000] which is equal to (1 π J ) w + π J [ x 40 , 000]. The f rm’s payo f is π F [ x 40 , 000 w ]. Knowing that John’s payo f must equal t 40 , 000, we f nd that t =[1 π J ][ w 40 , 000]+ π j x . (b) John should undertake the activity that has the most impact on t ,and hence his overall payo f , per time/cost. A one-unit increase in x will raise t by π J . A one unit increase in w raises t by 1 π J .A s sum ingtha t x and w can be increased at the same cost, John should increase x if π j > 1 / 2; otherwise, he should increase w . 3. (a) x ,t =0 , and u 1 = u 2 . u 1 u 2
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This note was uploaded on 08/20/2011 for the course ECON 101 taught by Professor Etw during the Spring '11 term at Università di Bologna.

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Problem_Set 2_solutions_to_problems_from watson_solutions -...

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