Ramsey Model Flashcards
The basics of the Ramsey models. What are we looking at.
What does the parameters mean?
k_t
c_t
β
δ
n
a
b_p
R_t = 1+r_t-δ
k_t , capital per worker
c_t , consumption per worker
β , discount rate (the bank rent on its loan), the patience.
δ , capital depreciation
n, population growth
a is wealth
b_p is lending to other households
R_t
r_t
In equilibrium / steady state in the Ramsey model, what will b_pt and a_t be equal to.
What condition need to hold in SS.
In equilibrium / steady state there will be zero net borrowing: b_pt = 0 and wealth must thus be equal to capital a_t = k
This condition
c_t = c_t+1 = c
k_t = k-t+1 = k
λ_t = λ_t+1 = λ
When we wanna make the graphical analysis of the Ramsey Model, what do we need?
Explain the derivation.
Explain the dynamics.
c-locus, where we use the Euler equation to derive it.
k-locus where we use the FOC from the Lagrangian wrt. λ to derive it.
At steady state both of these equations must hold.
The dynamic of c-locus:
We use the c-locus to investigate the dynamics of consumption. We know c_t+1 > c_t.
see the derivation in exercise 2
We get that k_t+1 < k* and the function is concave. Therefore we know that consumption is increasing, when k_t+1 < k* and decreasing when k_t+1 > k. If k_t+1 = k, then consumption is not changing.
Low capital implies larger marginal product, which results in higher returns to savings, thus making consumption today less attractive. “(Due to law of diminishing productivity.)” NOT SURE. Don’t get the right side of it?
The dynamic of k-locus:
To investigate the dynamics of capital, we use the capital law of motion.We also suppose k_t+1 > k_.
See equation exercise 2
The k-locus can be viewed graphically as a concave curve that will cross the x-axis eventually. The k-locus is growing due to the larger amount of investment, f(k_t), and falling due to the negative effects of capital depreciation and population growth.
Hence k_t+1 > k_t , when c_t is below the k-locus such that:
Low consumption implies larger amount of investments, which leads to capital accumulation.
Conversely, high consumption implies few investments. Capital per worker will therefore decrease due to depreciation of capital, δ, and population growth, n.
Describe the graphical analysis of the Ramsey Model.
The strange arrows.
The saddle path and convergence.
The strange arrows
- If we are over the k-locus the capital will decrease and if we are under the capital will increase
- If we are on the left of the c-locus the consumption will increase and on the right the consumption will decrease.
Combine them and you will have the strange arrows.
In the Ramsey model we can find a saddle path, that would be the line with arrows.
The economy will converge towards steady state (k,c) along the saddle path. If the economy is not on the saddle path, then the economy will diverge.
If the economy is not on the saddle path, there are two possible scenarios:
If consumption is above the saddle path, capital will decrease. This will lead to consumption growth due to increase in interest rates. This will further decrease capital accumulation. then the agents will consume
everything.
If consumption is below the saddle path, capital will increase, which will lower interest rates, which further decreases consumption and thus increases capital accumulation. Then the agents will invest everything.
This can be derived from the Euler equation:
What happen to consumption if k_t+1=k*?
Then consumption doesn’t change.
What happen when shock in δ?
???? Slides fra Carl
What happen if n increases?
If we differentiate wrt. n, it is clear that population growth only affects
consumption: ∂c/∂n = −k .
k is determined with the c-locus, thus preventing n from affecting k . Therefore n is only affecting the level of consumption. If n ↑ the
economy moves from point A to point B
Low capital implies larger marginal product, which results in higher returns to savings, thus making consumption today less attractive
