Class+13+Partial+Equilbrium+III+_Second+Welfare+Theorem%2C+Taxes%2C+Monopoly_

Class+13+Partial+Equilbrium+III+_Second+Welfare+Theorem%2C+Taxes%2C+Monopoly_

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Partial Equilibrium III: Taxes, Second Welfare Theorem, Monopoly
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Allocations: Good? Feasible? Competitive? Allocation An allocation x=[q s ,q d , ,m] . Allocations: what we care about. Feasible Allocation An allocation x= [q s d , ,m] is feasible if: (i) q s q d All limes are produced (ii) Y–c(q s ) +m Money (endowment) is used to produce the limes, c(q s ), to pay profit, , and to consume m . Preferences Consumer and firm have preferences over allocations. Firm: The more money ( profit ) the better. Consumer: Whatever maximizes U=m + v(q)
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Allocations: Good? Feasible? Competitive? Competitive Allocation An allocation x * = [q * , q * , * ,m*] is competitive if there is some price p* s.t. (i) Q D (p*) = Q S (p*) = q* “Demand =Supply” (ii) m* = Y - p*q* (iii) * = p*q* - c (q*) Pareto Efficiency An allocation x is Pareto efficient if there is no other feasible allocation x’ such that no one is worse off under and either the firm or the consumer is strictly better off. First Welfare Theorem (for quasilinear economies): Every competitive allocation is Pareto efficient. There does not exist any allocation that both, the firm and the consumer, prefer to the competitive allocation. Observe: A feasible allocation X = [q s , q d , ,m] is Pareto Efficient if and only if 1) m+ =Y–c(q s ) (No money is wasted) 2) q s =q d (The good is not wasted) 3) v’(q s )=c ’(q d ) (There is not too much nor too little production.)
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Taxes
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0 1 2 0 1 2 3 4 ( ) 0.853 2.706 D P = ( ) ( ) 5 2 1 0.853 2 DS Pq t qq q =+ = () 5 2 D q = ( ) 2 S Pq q = ( ) 2 S Pq t qt + Competitive Allocations: A Specific Tax p* q * Example: Economy given by Y=10 U(m,q) = m + 5 q c(q)= q 2 Specific tax on seller: t=1 Competitive Allocation with a specific Tax t Competitive price and quantity: p*= 2.706, q*= 0.853 Competitive Allocation: m* = Y - p*q* = 10 – 2.7(0.85) = 7.69 * = p*q* - c (q*) – tq* = 2.7(0.85) – (0.85) 2 - 0.85(1)= 0.728 T = tq* = 0.85 The competitive allocation with a tax is [q * , q * , * ,m*], T = [0.85, 0.85, 0.728, 7.69 ], 0.85 Price quantity Equilibrium?
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This note was uploaded on 12/08/2010 for the course PYSCH 111 taught by Professor Malley during the Spring '08 term at University of Michigan.

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Class+13+Partial+Equilbrium+III+_Second+Welfare+Theorem%2C+Taxes%2C+Monopoly_

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