GitHub

RamseyGrowthModel.jl

Simple example

using RamseyGrowthModel

my_model = GrowthModel(
    0.95,  # discount factor
    0.02,  # depreciation rate on capital
    2.0,   # coefficient of relative risk aversion
    0.3,   # return to capital per capita
    1,     # technology
)

allocation = solve(
    my_model,
    5,     # time horizon
    1.0    # initial capital
)

print(allocation)
[ Info: The best allocation has been found after 25 iterations.
6×3 DataFrame
 Row │ t      K         C
     │ Int64  Float64   Float64
─────┼───────────────────────────
   1 │     0  1.0       0.884107
   2 │     1  1.09589   0.967806
   3 │     2  1.13402   1.05663
   4 │     3  1.09316   1.15689
   5 │     4  0.941491  1.28216
   6 │     5  0.622579  1.4776

Defining and Solving a Growth Model

RamseyGrowthModel.GrowthModel — Type

Defines a Ramsey Growth Model.

Fields

  • β - discount factor
  • δ - depreciation rate on capital
  • u - utility function
  • f - production function

Constructors

If you want to use a CRRA utility function and a Cobb-Douglas production function, use constructor

GrowthModel(β::Real, δ::Real, γ::Real, α::Real, A::Real)

where γ is a parameter for RamseyGrowthModel.sample_u, and α and A are parameters for RamseyGrowthModel.sample_f.

However, if you have some other utility and production functions you want to use, constructor

GrowthModel(β::Real, δ::Real, u::Function, f::Function)

is also avaible.

source
RamseyGrowthModel.steady_state_K — Function

Returns steady state capital $K$, to which capital $K_t$ converges for large values of $T$.

steady_state_K(model::GrowthModel)

Arguments

  • model - previously defined growth model

This value is mostly useful for plotting purposes and as a starting point of a simulation.

source
RamseyGrowthModel.solve — Function

Returns the best possible capital and consumption allocation (as a DataFrame).

solve(model::GrowthModel, T::Union{Integer,typeof(Inf)}, K₀::Real; kwargs...)

Arguments

  • model - previously defined growth model
  • T - considered time horizon
  • K₀ - initial capital

Argument T should be of type Integer or equal to Inf. Passing a floating point value will raise an error.

Keyword Arguments

The algorithm uses a binary search; if you want, you can override the default maximum number of iterations (max_iter=1000) or error tolerance (tol=K₀/1e6).

source

Sample Functions Used in the Model

Info

You probably should not be using these functions directly in your program. Instead, use a constructor of the GrowthModel.

RamseyGrowthModel.sample_u — Function

Returns CRRA (constant relative risk aversion) utility function $u(c)$ with a given $γ$.

\[u(c) = \frac{c^{1 - γ} - 1}{1 - γ} + 1\]

What does it look like? See for yourself here.

source