Week 6: 15/03/21
ECN302 – Advanced Macroeconomics – Inequality & Redistribution
Video 1
In the OLG model, there is income inequality because there are different generations of individuals –
some are earning an income whilst some aren’t. There is also consumption inequality in an OLG model.
In this topic, we will revert back to individuals living infinitely. We assume that agents are
heterogeneous, where they differ for their ability & therefore their potential earnings. This will
generate income inequality in the economy.
In this model, consumers have the same preferences, so income inequality automatically results
in consumption inequality.
In this economy, there is no financial market, hence income inequality also implies wealth
inequality in this economy. Because individuals begin with different initial asset holding
positions, there is wealth inequality in this economy.
Agents live infinitely in this model. There are 2 types of agents, H and L.
Agent H has higher productivity (& therefore income). They work and pay taxes on labour
income.
Agent L also works but instead of paying taxes, they receive a subsidy from the govt.
This is the govts way of redistributing income.
-Production
There are 2 sectors in the economy, i=H,L.
i i i i
Profits generated by individual i: Π t = y t −wt ht
i i i
y t is the revenue produced in time t by individual i, w t is the wage per hour given to individual i and ht is
the hours of labour supplied by individual i.
i i i
Technology constraint: y t =ω t ht , where i=H, L and ω H>ω L.
ω (omega) is the productivity of individual i.
The solution to the firm maximization problem implies that the demand for labour is given by:
w it=ωit
This means that the firm demands labour until the marginal revenue of an additional unit of labour is
equal to the marginal cost.
How to get these two to equal is explained in the video.
-Households
H
φ, share of H household, receive high earnings of w t .
L H L
1 - φ, share L earn low earnings of w t , where w t >w t .
H L
Total consumption: ct = φc t + (1- φ)c t
, Week 6: 15/03/21
Preferences:
Utility function:
γ defines the extent of the desire of consumption of an individual.
When γ=0and consumption = 0, then the individual gets 0 utility.
c ty i γ
,
γ <0 and consumption = 0, then will be infinitely high.
γ
Budget constraints for t ≥ 0:
τ is the tax rate on labour income. 0<τ <1. If it is 0, there is no taxation. If it is 1, then all income is taxed.
xt is transfer from the government received by low-productivity type.
The govt therefore taxes income of the high income earners and redistributes it to low income earners.
Without government intervention, τ =0 and x = 0 and there will be wage, income, wealth and
consumption inequality in this model due to differences in ability between individuals.
-Government
The government runs a balanced budget.
H
For t ≥ 0 the budget constraint is: (1 - φ) xt + gt = φτ tw t ht
LHS = Govt expenditure and RHS = Govt revenue
xt measures intra-generations redistribution carried out by the government and gt government
consumption (per worker).
Video 2
-Feasibility
The feasibility condition says that aggregate output in the economic (which is the weighted average of
the output produced by the high and low productivity workers) must be equal to aggregate demand:
H L
yt = φ y t + (1 – φ) y t = ct +gt
-Solving the model for the high productivity type:
The Lagrangian and first-order conditions for consumption and labour of high-income are:
ECN302 – Advanced Macroeconomics – Inequality & Redistribution
Video 1
In the OLG model, there is income inequality because there are different generations of individuals –
some are earning an income whilst some aren’t. There is also consumption inequality in an OLG model.
In this topic, we will revert back to individuals living infinitely. We assume that agents are
heterogeneous, where they differ for their ability & therefore their potential earnings. This will
generate income inequality in the economy.
In this model, consumers have the same preferences, so income inequality automatically results
in consumption inequality.
In this economy, there is no financial market, hence income inequality also implies wealth
inequality in this economy. Because individuals begin with different initial asset holding
positions, there is wealth inequality in this economy.
Agents live infinitely in this model. There are 2 types of agents, H and L.
Agent H has higher productivity (& therefore income). They work and pay taxes on labour
income.
Agent L also works but instead of paying taxes, they receive a subsidy from the govt.
This is the govts way of redistributing income.
-Production
There are 2 sectors in the economy, i=H,L.
i i i i
Profits generated by individual i: Π t = y t −wt ht
i i i
y t is the revenue produced in time t by individual i, w t is the wage per hour given to individual i and ht is
the hours of labour supplied by individual i.
i i i
Technology constraint: y t =ω t ht , where i=H, L and ω H>ω L.
ω (omega) is the productivity of individual i.
The solution to the firm maximization problem implies that the demand for labour is given by:
w it=ωit
This means that the firm demands labour until the marginal revenue of an additional unit of labour is
equal to the marginal cost.
How to get these two to equal is explained in the video.
-Households
H
φ, share of H household, receive high earnings of w t .
L H L
1 - φ, share L earn low earnings of w t , where w t >w t .
H L
Total consumption: ct = φc t + (1- φ)c t
, Week 6: 15/03/21
Preferences:
Utility function:
γ defines the extent of the desire of consumption of an individual.
When γ=0and consumption = 0, then the individual gets 0 utility.
c ty i γ
,
γ <0 and consumption = 0, then will be infinitely high.
γ
Budget constraints for t ≥ 0:
τ is the tax rate on labour income. 0<τ <1. If it is 0, there is no taxation. If it is 1, then all income is taxed.
xt is transfer from the government received by low-productivity type.
The govt therefore taxes income of the high income earners and redistributes it to low income earners.
Without government intervention, τ =0 and x = 0 and there will be wage, income, wealth and
consumption inequality in this model due to differences in ability between individuals.
-Government
The government runs a balanced budget.
H
For t ≥ 0 the budget constraint is: (1 - φ) xt + gt = φτ tw t ht
LHS = Govt expenditure and RHS = Govt revenue
xt measures intra-generations redistribution carried out by the government and gt government
consumption (per worker).
Video 2
-Feasibility
The feasibility condition says that aggregate output in the economic (which is the weighted average of
the output produced by the high and low productivity workers) must be equal to aggregate demand:
H L
yt = φ y t + (1 – φ) y t = ct +gt
-Solving the model for the high productivity type:
The Lagrangian and first-order conditions for consumption and labour of high-income are:
