Consider Meltzer and Richards (1981) model with only two types of income: yp (poor) and yr...

 

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Consider Meltzer and Richards (1981) model with only two types of income: yp (poor) and yr (rich). Normalize population to 1 with the share of rich being 8 < 0.5. Average income is "y. To focus on inequality and distributional conflict, we add inequality into the model directly: Denote by 8 the share of the total income directed onto the rich, i.e., yr = 0'y 8 (income per rich person) and yp = (1-0) y 1-8 (income per poor person). So an increase in 0 represents an increase in inequality. Also we must have 8 > 8 (so yp <y< yr). The government is going to use income tax rate t and taxation is costly as before with DWL 0.5t2 per person. (a) Suppose the tax collected from the population is distributed as a lump-sum subsidy to everyone. What is the bliss point for the rich? for the poor? (b) Who represents the median voter in this model? What will be the tax? How does it depend on 0? (c) Define the burden of taxation as the net redistribution away from the rich. How does it depend on 8? (d) Now suppose the collected revenue is distributed as lump-sum only to the poor. What will be the tax? Compare it with the previous case without targeted transfers. How does the tax depend on 8? (e) Find the burden with the targeted transfer. How does it compare with the case without the targeted transfer? Which of the situations has greater degree of conflict in the society? Consider Meltzer and Richards (1981) model with only two types of income: yp (poor) and yr (rich). Normalize population to 1 with the share of rich being 8 < 0.5. Average income is "y. To focus on inequality and distributional conflict, we add inequality into the model directly: Denote by 8 the share of the total income directed onto the rich, i.e., yr = 0'y 8 (income per rich person) and yp = (1-0) y 1-8 (income per poor person). So an increase in 0 represents an increase in inequality. Also we must have 8 > 8 (so yp <y< yr). The government is going to use income tax rate t and taxation is costly as before with DWL 0.5t2 per person. (a) Suppose the tax collected from the population is distributed as a lump-sum subsidy to everyone. What is the bliss point for the rich? for the poor? (b) Who represents the median voter in this model? What will be the tax? How does it depend on 0? (c) Define the burden of taxation as the net redistribution away from the rich. How does it depend on 8? (d) Now suppose the collected revenue is distributed as lump-sum only to the poor. What will be the tax? Compare it with the previous case without targeted transfers. How does the tax depend on 8? (e) Find the burden with the targeted transfer. How does it compare with the case without the targeted transfer? Which of the situations has greater degree of conflict in the society?

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a The richs bliss point is the income level at which their utility is maximized Assuming the rich have a utility function given by uyr yp yr yp their ... View the full answer