Question 3 Suppose the total income of individuals is made up of three random components: income from work X (wages), income from assets Y, and government transfers T (such as pensions, welfare payments, etc). The government taxes non-asset income (that is, wage income and transfer income) at the same rate t, while it taxes asset income at the rate s. Note: these tax rates are constants and are in decimals. For example, a 10 percent tax rate on asset income means that s-0.1; tis to be interpreted in the same way. a. Write down the expression for total income after tax. Denote this as Z., b. Find an expression for E(2). Then find an expression for var(Z), assuming that cov(X, Y)= cov(T, Y)= 0 but cov (X, T)=10. Simplify the variance expression as much as you can. C. How would your answers to a. and b. change if t=s=0 and there was a flat (that is, constant) tax of Sh on non- asset income and Sk on asset income? Note: both h and k are constants. Show your work fully.
Question 3 Suppose the total income of individuals is made up of three random components: income from work X (wages), income from assets Y, and government transfers T (such as pensions, welfare payments, etc). The government taxes non-asset income (that is, wage income and transfer income) at the same rate t, while it taxes asset income at the rate s. Note: these tax rates are constants and are in decimals. For example, a 10 percent tax rate on asset income means that s-0.1; tis to be interpreted in the same way. a. Write down the expression for total income after tax. Denote this as Z., b. Find an expression for E(2). Then find an expression for var(Z), assuming that cov(X, Y)= cov(T, Y)= 0 but cov (X, T)=10. Simplify the variance expression as much as you can. C. How would your answers to a. and b. change if t=s=0 and there was a flat (that is, constant) tax of Sh on non- asset income and Sk on asset income? Note: both h and k are constants. Show your work fully.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please all solve
Transcribed Image Text:Question 3
Suppose the total income of individuals is made up of three random components: income from work X (wages), income
from assets Y, and government transfers T (such as pensions, welfare payments, etc). The government taxes non-asset
income (that is, wage income and transfer income) at the same rate t, while it taxes asset income at the rate s. Note:
these tax rates are constants and are in decimals. For example, a 10 percent tax rate on asset income means that s=0.13;
tis to be interpreted in the same way.
a. Write down the expression for total income after tax. Denote this as Z.,
b. Find an expression for E(Z). Then find an expression for var(Z), assuming that cov(X, Y)= cov(T, Y)= 0 but cov (X, T)-10.
Simplify the variance expression as much as you can.
c. How would your answers to a. and b. change if t-s=0 and there was a flat (that is, constant) tax of Sh on non-
asset income and Sk on asset income? Note: both h and k are constants. Show your work fully.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps with 4 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman