The image contains text regarding the Tax Cuts and Jobs (TCJ) Act of December 2017, which was a significant reform to the U.S. tax code, especially affecting wage income taxes with standard deductions for low-income workers. It describes a consumer's optimization problem with a tax rate adjustment. The optimization problem is given by:Maximize $ U(C, l) $ subject to:\[ C = \begin{cases} w(h - l) + \pi & \text{if } w(h - l) \leq x \$1-t)w(h-l) + tx + \pi & \text{otherwise}\end{cases} \]Where:- \( C \geq 0 $- $ l \geq 0 $1. Determine the effects of the introduction of the deduction on tax payments. In particular: (a) **Graph the consumer’s budget constraint.** The budget constraint changes based on the value of $ w(h-l) $ relative to $ x $. (b) **Determine the optimization point for the case of a person who does not pay any taxes.** Graphically explore the scenario where income does not exceed $ x $. (c) **Determine the optimization point for the case of a person who pays taxes.** Graphically analyze when the income exceeds $ x $.The text includes a mathematical formulation to address changes in tax policy, with specific focus on budget constraints before and after reaching a specified income level $ x $.

Answered: 1. Determine the effects of the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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The image contains text regarding the Tax Cuts and Jobs (TCJ) Act of December 2017, which was a significant reform to the U.S. tax code, especially affecting wage income taxes with standard deductions for low-income workers. It describes a consumer's optimization problem with a tax rate adjustment. The optimization problem is given by:

Maximize $ U(C, l) $ subject to:

\[
C =
\begin{cases}
w(h - l) + \pi & \text{if } w(h - l) \leq x \\
(1-t)w(h-l) + tx + \pi & \text{otherwise}
\end{cases}
\]

Where:
- $ C \geq 0 $
- $ l \geq 0 $

1. Determine the effects of the introduction of the deduction on tax payments. In particular:

(a) **Graph the consumer’s budget constraint.**
The budget constraint changes based on the value of $ w(h-l) $ relative to $ x $.

(b) **Determine the optimization point for the case of a person who does not pay any taxes.** Graphically explore the scenario where income does not exceed $ x $.

(c) **Determine the optimization point for the case of a person who pays taxes.** Graphically analyze when the income exceeds $ x $.

The text includes a mathematical formulation to address changes in tax policy, with specific focus on budget constraints before and after reaching a specified income level $ x $.

Expert Solution

Step 1

Consumption- leisure model shows the optimal bundle of the consumer subject to its budget constraints. Leisure is the time not spent working by the consumer. The decision-making process of a utility-maximizing consumer is to decide the number of hours to work to consume its goods and services.

The decision is made along the consumption-leisure budget constraint. The utility function given in the above question is subject to the budget constraint according to the wage rate. That is if the real wage income is less than equal to x, then the tax rate is zero. Below is the budget constraints for various incomes.

income is equal to w (h-l), "h" is the number of total hours and "l" is the leisure hours chosen by the consumer and "t" is the tax rate.

$C = w (h - l) + π if w (h - l) \leq x C = w (h - l) (1 - t) + tx + π if w (h - l) > x$

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