Suppose that we have an economy with many identical households. There is government that exogenously consumes...

 

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Suppose that we have an economy with many identical households. There is government that exogenously consumes some output and pays for it with lump sum taxes. Lifetime utility for a household is: U In C + 3 ln C++1 The household faces two within period budget constraints given by: C+ St=Y-T Ct+1=Ytel-T+1+(1+r) St (a) Combine the two budget constraints into one intertemporal budget constraint. (b) Use this to find the Euler equation. Is the Euler equation at all affected by the presence of taxes, T, and T.1? (c) Use the Euler equation and intertemporal budget constraint to derive an expression for the consumption function. The government faces two within period budget constraints: G + S = T Gt+1=T+1+(1+r)5 (d) In equilibrium, what must be true about S, and S? (e) Combine the two period budget constraints for the government into one intertemporal budget constraint. (f) Suppose that the representative household knows that the government's intertemporal budget constraint must hold. Combine this information with the household's consumption function you derived above. What happens to T, and T+1? What is your intuition for this? (g) Equilibrium requires that Y = C + G. Plug in your expression for the consumption function (assuming that the household knows the government's intertemporal budget constraint must hold) to derive an expression for Y. (h) Derive an expression for the "fixed interest rate multiplier," i.e. dre- (i) Assuming that Y, is exogenous, what must happen to r, after an increase in G? Suppose that we have an economy with many identical households. There is government that exogenously consumes some output and pays for it with lump sum taxes. Lifetime utility for a household is: U In C + 3 ln C++1 The household faces two within period budget constraints given by: C+ St=Y-T Ct+1=Ytel-T+1+(1+r) St (a) Combine the two budget constraints into one intertemporal budget constraint. (b) Use this to find the Euler equation. Is the Euler equation at all affected by the presence of taxes, T, and T.1? (c) Use the Euler equation and intertemporal budget constraint to derive an expression for the consumption function. The government faces two within period budget constraints: G + S = T Gt+1=T+1+(1+r)5 (d) In equilibrium, what must be true about S, and S? (e) Combine the two period budget constraints for the government into one intertemporal budget constraint. (f) Suppose that the representative household knows that the government's intertemporal budget constraint must hold. Combine this information with the household's consumption function you derived above. What happens to T, and T+1? What is your intuition for this? (g) Equilibrium requires that Y = C + G. Plug in your expression for the consumption function (assuming that the household knows the government's intertemporal budget constraint must hold) to derive an expression for Y. (h) Derive an expression for the "fixed interest rate multiplier," i.e. dre- (i) Assuming that Y, is exogenous, what must happen to r, after an increase in G?