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# 332mid08 - UNIVERSITY OF TORONTO Joseph L Rotman School of...

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UNIVERSITY OF TORONTO Joseph L. Rotman School of Management Oct. 21, 2008 Ezer/Kan/Florence RSM332 MID-TERM EXAMINATION Pomorski/Zhou DURATION - 2 hours Aid Allowed: Silent electronic calculator and one 1-sided 8 1 2 × 11” crib sheet Name: Student Number: Circle the section that you are registered in: Ezer Zhou Florence (10a.m.–12p.m.) Florence (12p.m.–2p.m.) Kan (Mon.) Kan (Tue. 9a.m.–11a.m.) Kan (Tue. 1p.m.–3p.m.) Pomorski (Tue.) Pomorski (Wed. 2p.m.–4p.m.) Pomorski (Wed. 4p.m.–6p.m.) Instructions 1. Write all your answers on the examination paper. 2. Answer five out of six questions. Each question is worth 20 marks. Do not answer all six questions! In the table below, cross out the question that you choose not to answer. Question Marks 1 2 3 4 5 6 Total 1

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1. Consider two consumers, Mr. C. E. Oh and Mrs. O. Ner. Mr. Oh’s utility function is U O ( C 0 , C 1 ) = C 1 2 0 C 1 2 1 and Mrs. Ner’s utility function is U N ( C 0 , C 1 ) = C 1 4 0 C 3 4 1 . They each receive labor income of \$1,000 today and nothing next period. Moreover, there is a factory: a production opportunity that transforms input invested today, I 0 , into the output of f ( I 0 ) = 30 I 1 2 0 next period. A capital market is not available. (a) Mr. Oh is managing the factory. What is the optimal investment implied by his own utility function and income? (5 points) (b) Mrs. Ner is the owner of the factory. If she invests exactly as what Mr. Oh suggested in part (a), what will be her utility from consumption today and next period? (2 points) (c) If Mrs. Ner instead chose the optimal level of investment according to her own utility function and income, how much would she invest? What would be her utility? (4 points) (d) We want to compensate Mrs. Ner for having to separate ownership and control. Suppose that Mrs. Ner lets Mr. Oh tell her how much to invest (as in part (a)). By how much would her consumption today, C 0 , need to go up (keeping C 1 at the same level as in part (b)) so that her utility is the same as in part (c)? (4 points) (e) Now suppose that there is a capital market that Mr. Oh and Mrs. Ner can lend
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332mid08 - UNIVERSITY OF TORONTO Joseph L Rotman School of...

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