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soln6 - W.L.O.G Let w 3 =0 and w 1>=0 w 2>=0 Sales...

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1 Solutions to Problem Set No. 6 1. The Military Draft. All register! When called, as long as no one earlier failed to register, they will register. 2. Entry Deterence. (a), (b) Entrant – In; Incumbent – Accommodate. (c) Entrant – Out; Incumbent – Retaliate. Since given “Out”, The Incumbent’s EU(Accommodate)=EU(Retaliate)=100. 3. Alternative Offers. Notice that prices must be in whole dollar amounts. (a) The seller posts $10 or $9. The buyer accepts at $9, and is indifferent at $10. (b) The buyer bids $1. The seller accepts. The seller will always accept a positive price for the good. (c) Seller posts $1 or more. The buyer rejects any price over $1 and bids $1. The buyer will accepts $1. (d) Buyer bids $9 or less. Seller accepts bid of $9 or more and rejects all other bids. Buyer accepts any posted price not greater than $9 and rejects $10. 4. Incentive for Sales Personnel.
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Unformatted text preview: W.L.O.G, Let w 3 =0, and w 1 >=0, w 2 >=0. Sales Person: If he accepts the offer, he will compare the EUs to decide on the effort level: EU agent (E H )=.5(w 1-E H )+.5(w 2-E H )=.5(w 1 +w 2 )-E H EU agent (E L )=.5w 2 Therefore, he will carry out high effort if w 1 >=2E H ; low effort otherwise. If it’s the case that w 1 >=2E H , he will compare the EU of rejecting the offer, i.e. 0, with the EU of accepting the offer and carrying out high level effort. If .5(w 1 +w 2 )-E H >0, he will accept the offer. Otherwise, reject. Similarly if w 1 <2E H , he will accept the offer if w 2 >0. Otherwise, reject. Abe: If w 1 >=2E H , EU Abe (w 1 ,w 2 )=.5(s 1-w 1 )+.5(s 2-w 2 ) If w 1 <2E H , EU Abe (w 1 ,w 2 )=.5(s 2-w 2 ) Given s 1 >2E H , it is optimal for him to set w 1 =2E H and w 2 =0. Therefore, (w 1 ,w 2 ,w 3 )=(2E H ,0,0)....
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