PS5sol

PS5sol - EEP101/ECON125 Spring 99 Prof D. Zilberman TA's:...

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EEP101/ECON125 Spring 99 Prof D. Zilberman TA's: Malick/Marceau Suggested Solutions to Problem Set 5 * 1. The rule for a single rotation is to choose the cropping age T when ) ( ) ( ' T rQ T Q = . (a) In this exercise, the change in growth is : T T T T e e e e T Q 87 . 0 2 87 . 0 87 . 0 2 87 . 0 ) 8 . 0 1 ( 264 . 6 ) 87 . 0 )( 8 . 0 ( ) 8 . 0 1 ( 9 ) ( ' - - - - - = - - - = The right hand side of the optimal condition is: 3 87 . 0 3 87 . 0 ) 8 . 0 1 ( 3 . 0 ) 8 . 0 1 ( 3 1 . 0 ) ( T T e e T rQ - - - = - × = Our condition becomes: ) ( ) 8 . 0 1 ( 3 . 0 ) 8 . 0 1 ( 264 . 6 ) ( ' 3 87 . 0 87 . 0 2 87 . 0 T rQ e e e T Q T T T = - = - = - - - Dividing both sides by 0.3 and by 2 87 . 0 ) 8 . 0 1 ( T e - - gives: T T e e 87 . 0 87 . 0 8 . 0 1 88 . 20 - - - = Collecting terms in e gives 0461 . 0 68 . 21 1 87 . 0 = = - T e . Taking the natural logarithm of each side yields: years T T 536 . 3 87 . 0 0764 . 3 ) 0461 . 0 ln( = - = - = and the conclusion that a rhino’s horn should be cut off after three and half years of growth. (b.i) Factors that can reduce the rotation period include Higher interest rates Cropping more than once, i.e., regrowth Anticipated future sales restrictions (Why let something grow until nest year if you won’t have a market in which to sell it.) Note: There is a possibility that the animal dies while under anesthetic during the horn-removal operation. This will lengthen the optimal rotation time. (That is, uncertainty will affect when something is cut.) * Solutions provided by S. Marceau.
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EEP101/ECON125 Spring 99 Prof D. Zilberman TA's: Malick/Marceau (b.ii) Factors that may explain more frequent dehorning in reality include Real higher interest rates (e.g., 30% rather than 10%)
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PS5sol - EEP101/ECON125 Spring 99 Prof D. Zilberman TA's:...

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