Consider the consumption-savings model from the notes, with one change: the government imposes a proportional tax...

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Consider the consumption-savings model from the notes, with one change: the government imposes a proportional tax on asset returns. That is, the government applies a tax rate of on the returns households receive at t = 2: specifically, the househol d pays the government a2(1+r) at t = 2 if a2 > 0, whereas it pays 0 if a2 0. (a) Illustrate, in a properly labelled diagram, the household budget constraint for this problem. Explain what happens to this budget constraint when the tax increases. (b) Under the assumption that the household chooses to be a borrower (i.e., a 2 < 0), derive the Euler equation for this problem. Explain how it differs from the Euler equation without the tax from the notes, and illustrate this situation in a properly labelled diagram. (c) Under the assumption that the household chooses to be a saver (i.e., a 2 > 0), derive the Euler equation for this problem. Explain how it differs from the Euler equation without the tax from the notes, and illustrate this situation in a properly labelled diagram. (d) Use a properly labelled diagram to illustrate a situation in which an Euler equation would be an inappropriate method for describing the household's optimal consumption and savings decisions. Explain why this is the case. (e) Evaluate the following claim: "An increase in the tax on asset returns will cause savings to decrease" Consider the consumption-savings model from the notes, with one change: the government imposes a proportional tax on asset returns. That is, the government applies a tax rate of on the returns households receive at t = 2: specifically, the househol d pays the government a2(1+r) at t = 2 if a2 > 0, whereas it pays 0 if a2 0. (a) Illustrate, in a properly labelled diagram, the household budget constraint for this problem. Explain what happens to this budget constraint when the tax increases. (b) Under the assumption that the household chooses to be a borrower (i.e., a 2 < 0), derive the Euler equation for this problem. Explain how it differs from the Euler equation without the tax from the notes, and illustrate this situation in a properly labelled diagram. (c) Under the assumption that the household chooses to be a saver (i.e., a 2 > 0), derive the Euler equation for this problem. Explain how it differs from the Euler equation without the tax from the notes, and illustrate this situation in a properly labelled diagram. (d) Use a properly labelled diagram to illustrate a situation in which an Euler equation would be an inappropriate method for describing the household's optimal consumption and savings decisions. Explain why this is the case. (e) Evaluate the following claim: "An increase in the tax on asset returns will cause savings to decrease"