Two Period Model Fundamentals

Question 1

What are the consumers budget constraints for the two periods in the two period model?

Answer 1

• 1. c + s = y - t

- 2. c’ = y’ - t’ + (1+r)S

Question 2

What is the consumers lifetime budget constraint in the two period model?

Answer 2

• c + c’/(1+r) = (y-t) + (y’ - t’)/(1+r) = we

- PV of consumption = PV of income

Question 3

How is the lifetime budget constant graphed in the two period model?

Answer 3

• c’ = -(1+r)c + (1+r)we
• E: Endowment point, consumption of disposable income in current and future periods
• Slope is -(1+r)
• Savings is the difference between current consumption and (y-t)

Question 4

What is the consumers optimal point in the consumption/savings decision in the two period model?

Answer 4

• MRSc,c’ = 1+r
  
  • MRS of current for future consumption is equal to the relative price of current for future consumption in terms of future consumption

Question 5

In the two period model what is the effect of a current period tax cut for a lender?

Answer 5

• C↑
• C’↑
• S ↑
  
  • Δs = Δy - Δt - Δc

Question 6

In the two period model what is the effect of a future tax cut for a lender

Answer 6

• C↑
• C’↑
• S ↓

Question 7

What is the permanent income hypothesis?

Answer 7

• Changes in income that are temporary yield small changes on permanent income (lifetime wealth), which have small effects on current consumption
• Changes in income that are permanent have large effects on permanent income (lifetime wealth) and current consumption

Question 8

In the two period model what is the effect of an interest increase for a lender?

Answer 8

• c’ ↑
• c ↓ if SE > IE (point B should be to the left)
• S ↑ if SE > IE
  
  • An increase in r makes saving more attractive because the relative price of c’ is lower (substitution effect), but it makes saving less attractive as there is a positive income effect on c, which tends to reduce savings

Question 9

In the two period model what is the effect of an interest increase for a borrower?

Answer 9

• c’ ↑if SE > (-)IE
• c ↓
• -S ↓ if SE > (-)IE

Question 10

What is the saving function derived from the consumption/saving decision in the two period model?

Answer 10

S and r are positively related

Question 11

What is the consumption function derived from the consumption/saving decision in the two period model?

Answer 11

r and c are negatively related

Question 12

In the two period model what is the effect of a tax on interest earnings?

Answer 12

• ↓c’
• ↑c: SE > IE
• S↓

Question 13

What are the governments 2 period and lifetime budget constraints in the two period model?

Answer 13

• 1. G = T + B
• 2. G’ + (1+r)B = T’
• G + G/(1+r) = T + T’/(1+r)

Question 14

What are the assumptions made in regard to the Ricardian Equivalence?

Answer 14

• When taxes change they change for everyone by the same amount
• Any debt issued by the government is paid off during the lifetimes of people who were alive when it was issued
• Taxes are lump sum
• Credit market constraints - people who can’t access credit normally would likely spend a tax cut

Question 15

What is the working of the Ricardian Equivalence?

Answer 15

• Because each of the N consumers shares an equal amount of the total tax burden in current a future periods, we substitute T = Nt and T’+Nt’ into the governments PV budget constraint:
  
  • G + G’/(1+r) = Nt + Nt’/(1+r)
  • Rearranging gives:
  • t + t’/(1+r) = (1/N)(G + G’/(1+r))
• Inserted into PV lifetime budget constant:
  
  • c + c’/(1+r) = y + y’/(1+r) - (1/N)(G + G’/(1+r))

Question 16

What is the tax burden in regard to the Ricardian Equivalence?

Answer 16

(1/N)(G + G’/(1+r))

Question 17

How would a change in t’ affect the consumer’s optimisation?

Answer 17

Shift the budget constraint UP

Question 18

How would a change in t affect the consumer’s optimisation?

Answer 18

Shift the budget constraint OUT