Computing Equilibrium Prices in Exchange Economies with Tax Distortions

Market Equilibrium with Transaction Costs

“…We maintain I3 and I5 until the end of the algorithm whence we merge the two price tiers. This may lead to some goods being undersold, but we prove that equation (7) still holds. Also note that invariant I4 holds for any allocations, whether at the higher or lower price tier.…”

“…An ǫ-approximate market equilibrium is characterized by relaxing the market clearing condition (Equation (3)) and optimal allocation condition (Equation (4)). Refer to equations (7) and (8) in table B. A: Market Equilibrium…”

“…An alternate model is to let the transaction cost be a fixed fraction of the price. Such costs can be interpreted as taxes and have been studied by Codenotti et al [7]. Taxes could be uniform, that is, depend only on the good, or non-uniform, that is, depend on the good and the buyer.…”

“…Invariant 3 then implies that z j = 0 at the end of the last round. From definition of x ij , x ij ≥ h ij + y ij /(1 + ǫ) ≥ (h ij + y ij )/(1 + ǫ) for all i and j. Summing over i, this gives equation (7).…”

“…(As in Equation ( 8)) I5: A good j is allocated at price either p j or p j /(1 + ǫ) where p j is the current price. Invariant I3 is a tighter version of equation (7). We maintain I3 and I5 until the end of the algorithm whence we merge the two price tiers.…”