The consumer chooses consumption cand leisure I to maximize utility u(cl) subject to his budget constraint: c= (1 TN)(b 1)+(1 TT -T where TnN is the proportional tax rate on labor income, Ti is the tax rate on firm profits, T is a lump-sum tax, w is the market wage, h is the consumer's total endowment of time, and are the profits of the firm. We make the usual assumptions about the utility function, and we assume (as usual) that the consumer takes wages, the tax rate, and firm profits as given. The firm has a simple constant returns to scale production function: D y = an + bk and chooses nD to maximize profits: =y-wn An equilibrium is simply a set of allocations and prices such that the consumer and firm solve their respective problems and labor demand no equals labor supply ns = h - 1. The government collects tax revenue and uses it to finance an exogenous level of spending G 9= Tnwn +TI+T. a. Find equilibrium w and a. b. Initially, the government collects all taxes in lump-sum form (i.e., TN = T10, T = G). Now suppose that it reduces T and raises Tu by enough to keep total tax revenue unchanged. What is the impact of this change (up, down, no change, or ambiguous) on consumption, labor input, total output, and consumer's utility? You may use diagrams to support your answer. c. Suppose instead that the government reduces T and raises Tn by enough to keep total tax revenue un- changed. What is the impact of this change on consumption, labor input, total output, and consumer's utility? d. If lump-sum taxation is unavailable, should the government in this model use taxes on corporate profitste Wi taxes on labor income, or a little of both? Briefly (one paragraph will do explain why. You may use diagrams to support your answer. Go to Settings to e. Identify one unrealistic feature of the model that plays an important role in your answer to (d). The consumer chooses consumption cand leisure I to maximize utility u(cl) subject to his budget constraint: c= (1 TN)(b 1)+(1 TT -T where TnN is the proportional tax rate on labor income, Ti is the tax rate on firm profits, T is a lump-sum tax, w is the market wage, h is the consumer's total endowment of time, and are the profits of the firm. We make the usual assumptions about the utility function, and we assume (as usual) that the consumer takes wages, the tax rate, and firm profits as given. The firm has a simple constant returns to scale production function: D y = an + bk and chooses nD to maximize profits: =y-wn An equilibrium is simply a set of allocations and prices such that the consumer and firm solve their respective problems and labor demand no equals labor supply ns = h - 1. The government collects tax revenue and uses it to finance an exogenous level of spending G 9= Tnwn +TI+T. a. Find equilibrium w and a. b. Initially, the government collects all taxes in lump-sum form (i.e., TN = T10, T = G). Now suppose that it reduces T and raises Tu by enough to keep total tax revenue unchanged. What is the impact of this change (up, down, no change, or ambiguous) on consumption, labor input, total output, and consumer's utility? You may use diagrams to support your answer. c. Suppose instead that the government reduces T and raises Tn by enough to keep total tax revenue un- changed. What is the impact of this change on consumption, labor input, total output, and consumer's utility? d. If lump-sum taxation is unavailable, should the government in this model use taxes on corporate profitste Wi taxes on labor income, or a little of both? Briefly (one paragraph will do explain why. You may use diagrams to support your answer. Go to Settings to e. Identify one unrealistic feature of the model that plays an important role in your answer to (d)