Dynamic Model #2

Question 1

What are Government’s decisions to be made? Provide the Government’s budget constraints

Answer 1

• Government has its own objectives; GDP growth, unemployment, inflation, BoP
• Assumption that Government has its only objective is to make ‘ends meet’
• CURRENT: G = T + B, where T = tN [average rate of tax * population]
• FUTURE: G’ + (1+r)B = T’ where T’ = t’N
• Government’s lifetime budget contraint => G + G’ / (1+r) = T + T’ / (1+r)

Question 2

How can you find the competitive equilibrium? What markets are relevant?

Answer 2

• Combining consumer’s and producer’s problems can give us the competitive equilibrium
• All consumers optimise (intertemporal conditions and BC)
• Governments lifetime BC holds
• All markets clear (1/3 will be irrelevant)
• Credit Market: Σsi = Sp = B [Borrowing = saving]
• Output Market: ΣYi = Y = C + G; Y’ = C’ + G’

Question 3

Name the 5 equations and the 7 unknowns in a dynamic model (i=lending/borrowing)

Answer 3

• UNKNOWNS: r, C(1), C(2), C’(1), C’(2), t, t’
• EQ1: (1+r) = MRS(ci, c’i)
• EQ2: ci + c’i /(1+r) = yi + y’i /(1+r) - ti - t’i /(1+r)
• EQ3: G + G’ / (1+r) = tN + t’N / (1+r)
• EQ4: Σyi = ΣCi + G
• EQ5: Σy’i = ΣC’i + G’

Question 4

What is the Ricardian Equivolence?

Answer 4

• The Ricardian Equivolence states that a tax cut isn’t always good if G doesn’t change
• The change in timing of taxes does not affect permenant income
• There is no effect on welfare

Question 5

How can dynamic models be used to prove the Ricardian Equivolence

Answer 5

• You have to focus on lifetime budget constraint
• ci + c’i /(1+r) = yi + y’i /(1+r) - ti - t’i /(1+r)
• G + G’ / (1+r) = tN + t’N / (1+r)
• Combining the two:
  ci + c’i /(1+r) = yi + y’i /(1+r) - [1/N (G+G’ / {1+r})]
• This proves that consumer’s optimisation is independant of taxation

Question 6

What does the Ricardian Equivolence look like on a graph?

Answer 6

• Lower tax will increase endowment from E1 -> E2
• Welfare is not affected, so consumers stay at A
• Increases in savings by tax cuts will later increase, as if t is reduced, t’ will increase

Question 7

How does the credit market link to the Ricardian Equivolence?

Answer 7

• Credit Supply= consumer intertemporal conditions
• Credit Demand= governments deficit (G-T)
• Fall in tax rasises B1->B2 [shift outward of a vertical line]
• This shifts Sp to the right to clear the market

Question 8

What are some assumptions that must stay if the Ricardian Equivolence is to hold?

Answer 8

• Lump sum tax that affects everyone equally and not distorting consumer’s behaviour [reality, taxes are progressive/distorting]
• Tax changes occur within all consumers life time [reality, OLG structure]
• Credit Market is perfect [reality, CM has asymmetric info, causing IR spread]

Question 9

What is interest rate spread? How can this function be constructed?

Answer 9

• Interest Rate Spread: Asymmetric informations of lenders to borrowers, this can be good (a) or bad (1-a)
• Financial Intermediaries are established to improve risk tolerance (Law of Large numbers)
• Spread of risk between depositors IR(r1) and borrowers IR(r2)
• All borrowers will choose to loan L, but bad borrowers default

Question 10

What is the bank profit?

Answer 10

• π = aL(1+r2) + 0(1-a) - L(1+r1)
• Competition drives the profit 0; meaning that r2 = ([1+r1] / a) -1:
  so; r2 - r1 = (1-a)/a * (1+r)
• If a =1, r1=r2 so it is a competitive market
• If 0<a<1, r2>r1, default risk premium increased as a drops
• Overall, there is a kinked demand curve crossing over at point E (lenders is steeper)

Question 11

Graphically, how does interest rate spreads look? Why does the Ricardian Equivolence fail?

Answer 11

• Curves cuts the budget constraint at endowment points, then the budget constraint kinks
• Before tax is reduced, borrowers get I1
• With symmetric information, should be G where Utility is I3 (highest)
• Asymmetric information, utility is only I2
• E1 to E2, not E1 to G
• Ricardian Equivolence fails

Question 12

What is limited commitment (concerning lifetime wealth)?

Answer 12

• Lifetime Wealth; we = y - t + (y’ - t’ +pH) / 1+r, where pH is the asset price*assets
• If consumers can only borrow with collateralisable wealth as security against the loan then;
• -s < pH / (1+r) and c = y - t - s
• Combining the two:
  C < y - t + pH / (1+r)
• If t continues to rise, the Indifference curve shifts to the left
• Ricardian Equivolence fails

Question 13

Graphically, how does limited commitment look? Why does the Ricardian Equivolence fail?

Answer 13

• Indifference Curve I1 cuts the budget constraint at B
• After this point, you are not allowed to borrow so the borrowing section of your budget constraint is truncated
• If t continues to rise, the Indifference curve shifts to the left
• Ricardian Equivolence fails