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 Venndiagram [L2II, …g. 6]! J. Lagerlöf (U of Copenhagen) Microeconomics (MikØk) 3: L2II Spring ‘
11 12 / 29 Fully NonLinear Tari¤: Analytical solution (4/9)
Step 1
Claim: If IRL and ICH are satis…ed, so is IRH.
Proof:
By ICH θ u (q ) t θu q > t θu q By θ >θ t 0
By IRL Step 2
Guess that ICL 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: L2II Spring ‘
11 13 / 29 Fully NonLinear 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 (IRL) and
θ u (q ) t θu q t. (ICH) 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: L2II Spring ‘
11 14 / 29 Fully NonLinear Tari¤: Analytical solution (6/9)
Since IRL and ICH 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.
 Spring '11
 KlausSchmidt

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