Find the tallest person male or female in denmark

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Unformatted text preview: we allowed to guess that a constraint is satis…ed? Suppose the problem is to …nd the tallest person in Denmark, subject to the requirement that this person is male. A valid way of doing this is to: 1 2 3 Ignore the requirement. Find the tallest person (male or female) in Denmark. Check if this person is male. If the answer at (3) is yes, then we have found the solution; otherwise, however, we have not found the solution. See also Venn-diagram [L2-II, …g. 6]! J. Lagerlöf (U of Copenhagen) Microeconomics (MikØk) 3: L2-II Spring ‘ 11 12 / 29 Fully Non-Linear Tari¤: Analytical solution (4/9) Step 1 Claim: If IR-L and IC-H are satis…ed, so is IR-H. Proof: By IC-H θ u (q ) t θu q > t θu q By θ >θ t 0 By IR-L Step 2 Guess that IC-L is satis…ed. Step 3 Inspect the problem and note that the two remaining constraints must bind, so we can plug them into the objective function. I See next slide! J. Lagerlöf (U of Copenhagen) Microeconomics (MikØk) 3: L2-II Spring ‘ 11 13 / 29 Fully Non-Linear Tari¤: Analytical solution (5/9) The simpli…ed problem: choose q, q, t , and t so as to maximize V q, q, t , t = ν t c q + (1 ν ) (t c q) , (1) subject to θu q t 0 (IR-L) and θ u (q ) t θu q t. (IC-H) Since V is increasing in t and t , both constraints must bind at the optimum. I In the Appendix this is shown more carefully. J. Lagerlöf (U of Copenhagen) Microeconomics (MikØk) 3: L2-II Spring ‘ 11 14 / 29 Fully Non-Linear Tari¤: Analytical solution (6/9) Since IR-L and IC-H bind, we have t = θu q (2) and t = θ u (q ) = θ u (q ) θu q + t θu q + θu q = θ u (q ) θ θuq. (3) By plugging (2) and (3) into the objective function (1), we get V q, q = ν θu q + (1 cq ν ) θ u (q ) θ θuq cq . The ne...
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This note was uploaded on 03/31/2013 for the course CENG 216 taught by Professor Klausschmidt during the Spring '11 term at Uni. Copenhagen.

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