# What we have not yet concluded this graphical

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Unformatted text preview: …rm must give up either allocative e¢ ciency or some rents (or a combination of those things). It is never optimal to give up only rents and to keep the …rst-best production levels for both types. What we have not yet concluded This graphical analysis didn’ tell us exactly how the optimal, t feasible solution looks like. I I Are both types’production levels distorted? Does any one of the types (or both of them) get any rents? J. Lagerlöf (U of Copenhagen) Microeconomics (MikØk) 3: L2-II Spring ‘ 11 9 / 29 Fully Non-Linear Tari¤: Analytical solution (1/9) The …rm chooses q, q, t , t so as to max. its expected pro…t, V q, q, t , t = ν t c q + (1 ν ) (t c q) , subject to four constraints: I Low types must prefer their bundle to no bundle at all: θu q I (IR-L) t 0. (IR-H) Low types must prefer their bundle to the high types’bundle: θu q I 0. High types must prefer their bundle to no bundle at all: θ u (q ) I t t θ u (q ) t. (IC-L) High types must prefer their bundle to the low types’bundle: θ u (q ) J. Lagerlöf (U of Copenhagen) t θu q Microeconomics (MikØk) 3: L2-II t. (IC-H) Spring ‘ 11 10 / 29 Fully Non-Linear Tari¤: Analytical solution (2/9) How to Solve the Problem: A Five-Step Recipe 1 2 3 4 5 Show that IR-L and IC-H imply IR-H, so we can ignore IR-H. Guess that IC-L doesn’ bind. t Inspect the problem and note that the two remaining constraints must bind. Therefore we can plug them into the objective function. Solve the resulting unconstrained problem. Verify that the solution satis…es IC-L (i.e., that the guess at (2) was correct). J. Lagerlöf (U of Copenhagen) Microeconomics (MikØk) 3: L2-II Spring ‘ 11 11 / 29 Fully Non-Linear Tari¤: Analytical solution (3/9) Why are...
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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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