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The US Social Security system provides an old-age benefit. Although the actual system is complicated, a simplified version of the system works as follows. Every dollar of earnings a worker earns (earnj ) at age j is taxed at the combined employee-employer rate of OASI = .106, provided earnings are below the maximum taxable earnings. When a worker earns an extra dollar in a year this increases the workers average lifetime earnings and old-age benefits increase as a workers average lifetime earnings increases.
Answer questions (a) and (b) below. Present your calculations in the form of a graph plotting age against the marginal tax rate. Explain the logic of your calculation. (a) Calculate the marginal tax rate on earnings at every age j between 23 and 64 for a worker whose average lifetime earnings is forecasted to be beyond the "first bendpoint but not beyond the "second bendpoint? (b) Calculate the marginal tax rate on earnings at every age j between 23 and 64 for a worker whose average lifetime earnings is forecasted to be beyond the "second bendpoint? Critical Extra Information: 1. Interest rate r = .04 2. Demographics: a worker works from age 23-64, retires at age 65 and lives to age 80 and then dies. 3. In retirement a worker receives an old-age benefit governed by the for- mulas below. The first formula holds for an individual with lifetime earnings greater than the "first bendpoint level bend but less than the second bend- point bend2. The second formula holds for an individual with lifetime earnings beyond the "second bendpoint. b(lifetime earnings) .9 * bend +.35 * (lifetime earnings bend) b(lifetime earnings) = .9*bendi+.35*(benda-bend)+.15*(li fetime earnings-benda) 64 j=23 earn; lifetime earnings 64 - 23+1 Answer questions (a) and (b) below. Present your calculations in the form of a graph plotting age against the marginal tax rate. Explain the logic of your calculation. (a) Calculate the marginal tax rate on earnings at every age j between 23 and 64 for a worker whose average lifetime earnings is forecasted to be beyond the "first bendpoint but not beyond the "second bendpoint? (b) Calculate the marginal tax rate on earnings at every age j between 23 and 64 for a worker whose average lifetime earnings is forecasted to be beyond the "second bendpoint? Critical Extra Information: 1. Interest rate r = .04 2. Demographics: a worker works from age 23-64, retires at age 65 and lives to age 80 and then dies. 3. In retirement a worker receives an old-age benefit governed by the for- mulas below. The first formula holds for an individual with lifetime earnings greater than the "first bendpoint level bend but less than the second bend- point bend2. The second formula holds for an individual with lifetime earnings beyond the "second bendpoint. b(lifetime earnings) .9 * bend +.35 * (lifetime earnings bend) b(lifetime earnings) = .9*bendi+.35*(benda-bend)+.15*(li fetime earnings-benda) 64 j=23 earn; lifetime earnings 64 - 23+1
