Part A: Consumption

Suppose that a household lives for two periods and has a utility function and intertemporal budget constraint as follows:

(c!(#) . 5  + c2(#) . 5 )!&'

1 − y

ITBC: c!  +  = y!  +

a) Derive step by step the Euler equation faced by this consumer (define the Lagrangian and  then obtain first order conditions as we did it in the lecture). Explain the intuition of the Euler equation.

b) Find a solution for optimal consumption in both period 1 and 2 as a function of the parameter  as well as the variables r, y!  and y2 .

c) What is the ceteris paribus effect on consumption today (c! ) and tomorrow (c2 ) of the following shocks:

(i)   An increase in  .

(ii)  A decrease in lifetime income.

(iii) An increase in y .

d) Is there a condition where c! = c2 ? If so, what value must β assume?

Part B: Fiscal Policy

Consider an economy existing for four periods following the government budget constraint as follows:

Bt)!  = (1 + i)Bt  + Gt  − Tt

a) Define each of the variables above and explain, in words, why the equality holds. Re-write this budget constraint during each of the four periods that the economy exists.

b) The Australian government is trying to decrease the country’s stock of debt. Using the       equation above, discuss two possible ways this could be achieved using fiscal policy, only.    What challenges do you anticipate? (Hint: think of how tax collections change given changes to government spending).