HAND-IN ASSIGNMENT 1
General instructions
In this assignment you should perform some experiments on the linear income tax model
that we have discussed in the lectures. The assignment should be uploaded to the Assign-
ments page on Studium latest on November 19th and should consist of your modified
MATLAB files as well as the answers to the questions in this document. Make sure the
code is well-documented by using ”%” at the beginning of a line to generate comments.
Background
The starting point of this lab is the linear income tax model. The government designs a
tax system consisting of a linear tax rate on income z equal to and uses the resulting
tax revenue to finance a transfer given to everyone in the population equal to R. In
addition, each individual has some additional (non-labor) income, such as spousal income
or inheritance income, equal to yi.
Individuals are characterized by their potential income which is distributed according
to some probability distribution with density function f(zp) over the support zp > 0.
The discrete analogue of this distribution is a set of potential earnings levels {zip}Ni=1 with
associated probability mass { i}Ni=1. To avoid having to compute integrals in MATLAB,
we will focus on this discrete formulation which implies that we can use sums (i.e.
P
)
instead of integrals. We interpret i as the fraction of individuals in the population that
have potential income equal to zip (
PN
i=1
i = 1). Henceforth, we will refer to an individual
with potential income zip, simply as ”type i”. Thus, letting !
i denote the ”welfare weight”
attached by the government to agent i, the government wishes to choose and R in order
to maximize the social welfare function:
(V 1, V 2, . . . , V N) =
NX
i=1
!i iV i
subject to the government budget constraint
