Economic growth-Ramsey model

Question 1

Environment in the Ramsey model

Answer 1

• Single homogeneous good that can be invested or consumed
• Closed economy
• Households choose consumption and savings

Question 2

Assumptions Households

Answer 2

• Infinitely lived
• u is increasing and concave
• each household has N individuals, N=e^(nt), n a constant
• They owned labor and capital, which they rent to firms

Budget constraint is given by:

Question 3

Household problem

Answer 3

Question 4

Euler equation

Answer 4

• The more risk averse the individual is, the lower the effect of the interest rate over the consumption path

Question 5

Coefficient of relative risk aversion in the context of intertemporal decisions

Answer 5

o=u’‘(c)/u’(c)*c meausures the concavity of the funcition, the higher the o, the less willingness to deviate from a regular pattern of intertemporal consumption

o also influences the initial decision over consumption

Question 6

Firm assumptions

Answer 6

• Use labor, income and technology
• Technology grows at a constant rate x
• Production function satisfies the neoclassical production function properties
• Technological progress is labor augmenting
  
  • ​Needed to have balanced growth path

Question 7

Rental price of capital def

Answer 7

R=r+delta

• Assets and capital must be perfect subsitutes for the household

Question 8

Definition of equilibrium

Answer 8

Question 9

Steady state propositions

Answer 9

Question 10

Modified golden rule

Answer 10

• Transversality condition implies that capital will always be to the left of the golden rule capital.

Question 11

Implications of TVC

Answer 11

• Inefficient oversaving observed in Solow model when s>sg does not occur, k is always smaller than the capital implied by the golden rule
• The TVC implies:

Question 12

Differences with the Solow growth model

Answer 12

• In the solow growth model, increment of n=> reduction in k*
• In the Ramsey model, k* is independent from n, what happens is that with an increase in n, households change their consumption but not their investment
• What determines k* is the interest rate, net of the discount factor delta+rho+σx

Question 13

Savings rate dynamics along the transition path

Answer 13

Unclear. Two opposing forces:

• If I’m converging from below
  
  • Income effect: today I’m poor. If anything I want to dissave. As I grow richer I will increase my savings.
  • Substitution effect: as k increasis, the MPK decreases then r goes down => savings decrease.
• If income effect dominates => savings go up. Otherwise they go down.
• Quantitatively, Ramsey predicts declining saving rate along the transition path.

Question 14

Dynamic system

Answer 14