Week 1: 04/02/21
ECN302 – Advanced Macroeconomics
Deterministic Economy – Video 1
Deterministic economy means an economy where there is no uncertainty.
We are focussing on a Dynamic General Equilibrium (DGE) model.
• It is ‘general’ because we look at individual agents and then aggregate.
• It is ‘dynamic’ because the choices that each individual make are intertemporal.
-Endowment economy, no govt & no foreign sector
This is the simplest form of a DGE.
There are only consumers.
It is a closed economy or small open economy.
Looking at the environment, specification and equilibrium of the model. Then we will apply these.
We need 2 tools: FODEs and dynamic optimisation.
Environment:
The model environment is the description of all assumptions that define the model of the economy.
Time starts a t = 0
There is only one good (e.g. apples)
The economy is populated by a large number, N, of individuals (consumers/households/individuals
will be used interchangeably).
Each individual is born in t = 0 and lives forever (infinitely lived agents’ model)
Individuals are all equal along three dimensions (representative-agent model):
• Endowment
• Preferences
• Initial assets holding
This is a model of the aggregate economy.
Individual variables are denoted in lower case. For t ≥ 0: (yt income, ct consumption, etc).
Aggregate variables are denoted in upper case. For t ≥ 0: (Yt income, Ct consumption, etc).
From individual to aggregate:
Yt = Nyt , Ct = Nct , etc.
This is because all individuals are the same, so you can multiply individual consumption by N to get
aggregate consumption.
Endowment:
In t = 0 each the representative agent finds out her lifetime allocation of the good:
{y0, y1, y2, . . . , yt , . . .} = {yt} ∞t=0
{yt} ∞t=0 represents the entire lifetime of the agent.
Assumptions of endowments:
• Endowment income is known with certainty in t = 0 (no real income uncertainty)
• The sequence of income is bounded: ∑∞ t=0 yt < ∞
, Week 1: 04/02/21
Preferences:
Preferences are described by an intertemporal utility function (additively separable).
We sum the utility of consumption from each period. To do this we must discount utility by using
beta as a discount factor, like so:
This is the discounted lifetime utility from consumption.
Beta is between 0 and 1 & is the individual discount factor.
,where ρ is the individual discount rate and is non-negative. This is a crucial
assumption of our model.
The discount factor is the reciprocal of the gross interest rate.
u(ct) is an instantaneous utility function.
u(0) = 0
The marginal utility from consumption is positive:
Marginal utility increases at a decreasing rate:
Two Inada conditions:
First condition: The limit has consumption very close to zero for when the marginal utility of
consumption is infinity, meaning that if someone is consuming very little and then increase
consumption by a little bit, it will reduce happiness significantly.
Second condition: Marginal utility of consumption increases almost by nothing if consumption is
already very high.
Initial assets holding:
We denote initial assets holding as a-1. This represent the units of good available to the individual at
the beginning of period t = 0.
t = -1, represents the assets available to an individual when they are born.
Objective:
In t = 0 the individual decides her lifetime consumption allocation or consumption plan, i.e. how
many units of the good she wants to consume in that period and for t ≥ 1. This consumption plan is
made in t = 0. After t = 0, no consumption plans are made – the plan is just executed.
The individual also makes a savings plan at t = 0 since:
ECN302 – Advanced Macroeconomics
Deterministic Economy – Video 1
Deterministic economy means an economy where there is no uncertainty.
We are focussing on a Dynamic General Equilibrium (DGE) model.
• It is ‘general’ because we look at individual agents and then aggregate.
• It is ‘dynamic’ because the choices that each individual make are intertemporal.
-Endowment economy, no govt & no foreign sector
This is the simplest form of a DGE.
There are only consumers.
It is a closed economy or small open economy.
Looking at the environment, specification and equilibrium of the model. Then we will apply these.
We need 2 tools: FODEs and dynamic optimisation.
Environment:
The model environment is the description of all assumptions that define the model of the economy.
Time starts a t = 0
There is only one good (e.g. apples)
The economy is populated by a large number, N, of individuals (consumers/households/individuals
will be used interchangeably).
Each individual is born in t = 0 and lives forever (infinitely lived agents’ model)
Individuals are all equal along three dimensions (representative-agent model):
• Endowment
• Preferences
• Initial assets holding
This is a model of the aggregate economy.
Individual variables are denoted in lower case. For t ≥ 0: (yt income, ct consumption, etc).
Aggregate variables are denoted in upper case. For t ≥ 0: (Yt income, Ct consumption, etc).
From individual to aggregate:
Yt = Nyt , Ct = Nct , etc.
This is because all individuals are the same, so you can multiply individual consumption by N to get
aggregate consumption.
Endowment:
In t = 0 each the representative agent finds out her lifetime allocation of the good:
{y0, y1, y2, . . . , yt , . . .} = {yt} ∞t=0
{yt} ∞t=0 represents the entire lifetime of the agent.
Assumptions of endowments:
• Endowment income is known with certainty in t = 0 (no real income uncertainty)
• The sequence of income is bounded: ∑∞ t=0 yt < ∞
, Week 1: 04/02/21
Preferences:
Preferences are described by an intertemporal utility function (additively separable).
We sum the utility of consumption from each period. To do this we must discount utility by using
beta as a discount factor, like so:
This is the discounted lifetime utility from consumption.
Beta is between 0 and 1 & is the individual discount factor.
,where ρ is the individual discount rate and is non-negative. This is a crucial
assumption of our model.
The discount factor is the reciprocal of the gross interest rate.
u(ct) is an instantaneous utility function.
u(0) = 0
The marginal utility from consumption is positive:
Marginal utility increases at a decreasing rate:
Two Inada conditions:
First condition: The limit has consumption very close to zero for when the marginal utility of
consumption is infinity, meaning that if someone is consuming very little and then increase
consumption by a little bit, it will reduce happiness significantly.
Second condition: Marginal utility of consumption increases almost by nothing if consumption is
already very high.
Initial assets holding:
We denote initial assets holding as a-1. This represent the units of good available to the individual at
the beginning of period t = 0.
t = -1, represents the assets available to an individual when they are born.
Objective:
In t = 0 the individual decides her lifetime consumption allocation or consumption plan, i.e. how
many units of the good she wants to consume in that period and for t ≥ 1. This consumption plan is
made in t = 0. After t = 0, no consumption plans are made – the plan is just executed.
The individual also makes a savings plan at t = 0 since:
