Question

1. Consider an economy that exists for 3 periods: period 1, period 2 and period 3. In each case the government must satisfy the budget constraint: Be+1 = (1 + i)B,+G -T; (a) Write this budget constraint for each period. (b) What must be true for B.? (c) Using the results from part (b), solve the period 3 budget constraint for B3 and substitute this back into the period 2 constraint. (d) Solve this new version of the period 2 budget constraint for B2 and substitute the result back into the period 1 budget constraint. (e) You should have the intertemporal budget constraint for the three-period economy. Interpret this equation. Suppose a government has an initial debt of $10 billion and the nominal interest rate is 5 percent. (a) If the government keeps its primary budget in balance, what is the growth rate of its debt? (b) If the government keeps its total budget in balance, what is the growth rate of its debt? (c) Suppose the country's GDP grows at 3 percent per year. What happens to the debt-GDP ratio over time in cases (a) and (b)? Are these situations sustainable? Explain. 3. Explain, using the household and government budget constraint, what is meant by Ricardian Equiva- lence.

Answer 1

1. (a) Period i Perioda: Period 3: B₂ = citid B, &G, TI B3 = (1+i) B 2 + Gez-Tz. BA = (1+i) B 3 + Gez-T3 (6) As the economy is for 3 periods; the government budget constraint must balance in period 3. :. Ba=0 (c) As B4 = 0; citi) Bg. +613-T3 = 0 or, citi) B3 = Tz - G3 . .::B3 = T3 - Giz T3-cu - G13 = (1+i) B₂ + G2 - Tz cas . : B2 = 72.692 + 73.643 .. The one = (1+i) 8,46,- To -6 Ts-C3 Tz ci

budget constraint for three e) Then intertemporal period : e Then this constraint implies that the initial debt of the government must equal to the present name of the bar primary sweplus in three period. That is the govt. must pay its initial debt in three consecutive periods. 2.a) Growth rate of debt: .. If a Get-Tz = o ; primary budget balance i. Bt+!.. = = 5 percent The debt grows at rake of nominal interest rate 5. Bt b) Keeping total budget in balance implies Betio 1. Then the bad debt remaint constant at Be. c) Debt-to-GDP ration (1+i) B+ + GE TE Yttl Now if GDP grows at a rate g; Yeti= (1+9) It Yttl WS is that ntent that come to this

Now, ;: 5% , 9=30%. Get- tt so 5 2 Then in this case debt to GDP well grow at 2 % forever. This situation in sustainable as long as primary budget is balanced. In case the government balance its budget in each period and Bt is constant; the debt to GDP ratio becomes smaller each period and tends to zero in very long run. 1. 3. The Ricardian equiralance states that the changes in taxes that keep government budget balanced has no effect on the consump" decision of the consumer. Let taxes in each period : Ti, Tz Geort. budget constraint: Get Casper = Title her Let the budget constraint of the consumer at = (.-71) + y2i72 het the gort change Teutz such a warg that be a Sze = 71 72 remains unchanged. Them from consumer inter temporal budget ; the present ratue of the budget remain unchanged. As consumer makes decision based on present raine of budget which remain unch- -anged after tax change, the changes in tax has no effect on consumption. This is the main notion of Ricardian Equiralence