Consider the Two-Period Consumption model covered in class and assume that preferences are given by u(C,...

 

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Consider the Two-Period Consumption model covered in class and assume that preferences are given by u(C₁, C₂, g) = 1-o - 0 + B 1-0 C2 1-0 + In (g) The endowment profile of the representative household is e₁ for the first period and is e₂ for the second one. Finally, to transfer resources from period 1 to period 2, the agent has access to savings. The return on savings is r. Assume that a government now imposes linear taxes (i.e, proportional taxes equal to t) on endowments. The resulting tax revenues are used to produce some form of public good, g, which contributes to the agents' utility as illustrated by the previous description of the utility function. a) Write down the two constraints that the agent faces during the two periods. b) Write down the government budget constraint? When answering the following questions make sure you provide all the relevant derivations and steps to obtain full marks. c) What are the optimal consumptions c₁ and c₂? d) What is the optimal savings? e) What is the impact of a change in tax rates on optimal first and second period consumption? f) What is the impact of a change in the interest rate on optimal savings? g) How would your answers in b), c) and d) change if the government now taxes only consumption (sales taxes)? h) Assuming that there are only sales taxes, how would your answers in c) and d) change if G=0.5? i) What type of tax scheme impacts the most the savings behaviour? Show and explain why that is the case. Consider the Two-Period Consumption model covered in class and assume that preferences are given by u(C₁, C₂, g) = 1-o - 0 + B 1-0 C2 1-0 + In (g) The endowment profile of the representative household is e₁ for the first period and is e₂ for the second one. Finally, to transfer resources from period 1 to period 2, the agent has access to savings. The return on savings is r. Assume that a government now imposes linear taxes (i.e, proportional taxes equal to t) on endowments. The resulting tax revenues are used to produce some form of public good, g, which contributes to the agents' utility as illustrated by the previous description of the utility function. a) Write down the two constraints that the agent faces during the two periods. b) Write down the government budget constraint? When answering the following questions make sure you provide all the relevant derivations and steps to obtain full marks. c) What are the optimal consumptions c₁ and c₂? d) What is the optimal savings? e) What is the impact of a change in tax rates on optimal first and second period consumption? f) What is the impact of a change in the interest rate on optimal savings? g) How would your answers in b), c) and d) change if the government now taxes only consumption (sales taxes)? h) Assuming that there are only sales taxes, how would your answers in c) and d) change if G=0.5? i) What type of tax scheme impacts the most the savings behaviour? Show and explain why that is the case.