14.471/Fall 2012: PS 1: Solutions
September 24, 2012
Question 1
Assume that a consumers utility function is given by u (x1 , x2 , x3 ) = 1 log (x1
1 ) + 2 log (x2
2) +
3 log (x3 ) and that the consumer faces consumer prices q1 and q2 , with the price of g
14.471 / Fall 2012
Problem Set 1 / Due 9/19/12
Question 1
Assume that a consumer's utility function is given by:
u(x1, x2, x3) = 1 log (x1 - 1) + 2 log (x2 - 2) + 3 log x3
and that the consumer faces consumer prices q1 and q2, with the price of good three
14.472 Problem Set 2 Suggested Solutions
Question 1: Because each individuals discount rate is equal to the interest rate (0), there
are no savings and borrowing constraints, and the utility of consumption function is the
same in every period, the individ
14.472
Annuities
PROBLEM SET #1 SOLUTIONS
General Notes:
1) A lot of Peters problem sets and exam questions are set up this way basic
problem in 1, then add tweaks to the model in subsequent problems. When
possible, you dont have to re-derive the answers
14.471: Fall 2012: PS4
Due on Friday December 7
November 25, 2012
1. Optimal Income Taxation - Numerical Exploration
This question asks you to solve the Mirrlees (1971) model numerically. Assume that an individuals utility
is given by
l2
U (c, l) = c
2
w
14.472 Problem set 3
Spring 2004
Question 1
Set up an olg model with the following characteristics (use similar notation to that in
the handouts) and describe steady state equilibrium:
Technology is linear.
There is no population growth.
The fraction of t
We will consider an economy with two classes of workers: 1' = H , L. Assume that workers work
until some retirement age and do no work thereafter (that is, we ignore indifference to the timing
of work). Assume that there are equal numbers of the two types
14.471/Fall 2012: PS 2: Solutions
October 30, 2012
Question 1
You are invited to a small tropical island nation to become a tax policy consultant, with particular responsibility for analyzing tax-induced distortions in labor supply. Sensing the opportunit
Problem Set #3 Suggested Solutions
QUESTION 1:
Because technology is linear, the wage and the interest rate will be constant.
T = Lump-sum tax
t = payroll tax
w = wage (like an endowment in 2 periods since labor supply is inelastic)
b = benefits per elder
14.471: Fall 2012:PS3 Solutions
December 4, 2012
1. Commodity Taxation
Consider an economy consisting of identical individuals with preferences given by
U (x1 , x2 , l) = 1 log (x1 ) + 2 log (x2 ) + (1 1 2 ) log (1 l) .
Individuals supply labor, l, at a m
14.471: Fall 2012: PS4: Solutions
December 11, 2012
1. Optimal Income Taxation - Numerical Exploration
This question asks you to solve the Mirrlees (1971) model numerically. Assume that an individuals utility
is given by
l2
U (c, l) = c
2
where y = l and
14.471/Fall 2012
Problem Set 2
_
Due Date: Friday, October 12, 2012
1. You are invited to a small tropical island nation to become a tax policy consultant, with
particular responsibility for analyzing tax-induced distortions in labor supply. Since it is w