3. Non-linear Income Tax (12 points) In the realm of Asgard, residents' monthly labor incomes are taxed based on the following schedule: Bracket 1: Any pre-tax earnings (that is, earnings before accounting for taxes and subsidies) between $0 and $160 are subsidized at a rate of 50% Bracket 2: Any pre-tax earnings above $160 and below $320 are taxed at a rate of 0% Bracket 3: For any pre-tax earnings above $320, the subsidy is reduced at a rate of 25% Bracket 4: Earnings are not taxed after the subsidy falls to $0 (a) Suppose the wage in Asgard is $20 for all workers. (i) What is the minimum number of hours a worker could work and still receive the maximum subsidy? (1 point) (ii) After how many hours of work would the subsidy phase out entirely? (2 points) (b) For every tax/subsidy bracket, determine the sign of the substitution effect, income effect and total effect compared to a baseline with no taxes or subsidies at all, and fill in that determination on the following table. Use to indicate if the effect incentivizes work, if it disincentives work, 0 is there is no effect, and ? if the effect is uncertain. (6 points) Bracket 1 Bracket 2 Bracket 3 Income effect Substitution effect Total effect 3. Non-linear Income Tax (12 points) In the realm of Asgard, residents' monthly labor incomes are taxed based on the following schedule: Bracket 1: Any pre-tax earnings (that is, earnings before accounting for taxes and subsidies) between $0 and $160 are subsidized at a rate of 50% Bracket 2: Any pre-tax earnings above $160 and below $320 are taxed at a rate of 0% Bracket 3: For any pre-tax earnings above $320, the subsidy is reduced at a rate of 25% Bracket 4: Earnings are not taxed after the subsidy falls to $0 (a) Suppose the wage in Asgard is $20 for all workers. (i) What is the minimum number of hours a worker could work and still receive the maximum subsidy? (1 point) (ii) After how many hours of work would the subsidy phase out entirely? (2 points) (b) For every tax/subsidy bracket, determine the sign of the substitution effect, income effect and total effect compared to a baseline with no taxes or subsidies at all, and fill in that determination on the following table. Use to indicate if the effect incentivizes work, if it disincentives work, 0 is there is no effect, and ? if the effect is uncertain. (6 points) Bracket 1 Bracket 2 Bracket 3 Income effect Substitution effect Total effect