(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)
(Speaker)
Now the government changes the tax scheme and only the first 100 dollars of income is tax exempt. For Tamara, this means she pays no tax on the first five hours of work. But the government reduces the tax rate to 50 percent on the rest of her income. We are also told that after these changes Tamara finds herself as equally well of as before.
(Description)
The following text is briefly written:
The government changes the tax scheme. Now only the first 100 dollars of income is tax-exempt. That is, for the first 5 hours she works, Tamara’s net wage rate is 20 dollars per hour. But the government reduces the tax rate on all other income to 50 percent. That is, for all hours above the first 5 hours, Tamara’s net wage rate is now 10 percent. After these changes, Tamara finds herself exactly equally as well off as before. That is, her new optimal choice is on the same indifference curve as her initial optimal choice.
B. Draw Tamara’s new time allocation budget line on the same diagram. Also illustrate her optimal choice. Bear in mind that she is equally as well off (on the same indifference curve) as before the tax changes occured.
(Speaker)
We are going to start with the graph from the last part.
(Description)
The graph from the previous part is shown.
(Speaker)
We are going to draw in the budget constraint.
(Description)
(Speaker)
Again, you will notice the kink in the budget costraint.
(Description)
A new line is drawn on the graph. It starts at point, 80 and 0, and moves upwards to the left. At some point it changes its slope and continues to move upwards to the left but at a slower rate. At some point it intersects first the previous budget constraint line, and then, vertical axis. The x-value of this line's kink is greater than the one of the previous budget line.
(Speaker)
Again, you will notice the kink in the budget constraint. The kink in the budget constraint will now occur after Tamara works fiver hours. Since her wage is 20 dollars per hour and pays no tax on the first 100 dollars, she will earn 20 dollars for every hour of work.
(Description)
There are 2 dotted lines drawn from points, 75, on the horizontal axis, and from point, 100 dollars, on the vertical axis. The first dotted line is parallel to the vertical axis, the second dotted line is parallel to the horizontal axis. These lines intersect at a right angle at the kink of the new budget constraint line.
(Speaker)
The slope of the budget constraint for the first five hours of work is negative 20, which implies for every hour of leisure Tamara give up, she will earn 20 dollars. We can also find the slope by taking 100 dollars and dividing by 5.
(Description)
The part of the new budget constraint line between 75 and 80 hours per week on the x-axis is labeled as Slope equals negative 100 divided by 5 equals negative 20.
(Speaker)
Next, we want to label the intercept on the y-axis. Again, we want to add the income Tamara earns in the first five hours, 100 dollars, where she pays no tax, with the income she earns in the last 75 hours, when her tax rate is 50 percent. If she chooses to work the next 75 hours, she will earn 1 thousand 500 dollars, but 50 percent, or 750 dollars, is paid in taxes, leaving her an income of 750 dollars. Together, she will earn 850 dollars.
(Description)
The value of intercept on the y-axis is, 850 dollars. It is also labeled as Intercept equals 100 plus (75 times 20 times 0.50) equals 100 plus 750 equals 850.
(Speaker)
When Tamara chooses to work more than five hours per week, her net wage will be 10 dollars. Remember, for every hour she works, she earns 20 dollars, but 50 percent, or 10 dollars, is paid in taxes, leaving her a take-home pay of 10 dollars.
The slope of the budget constraint when Tamara works more than five hours is negative 10.
(Description)
The part of the new budget constraint line between 0 and 75 hours per week on the x-axis is labeled as Slope equals negative 750 divided by 75 equals negative 10.
(Speaker)
Finally, we are told Tamara is exactly equally as well off as before. This means that she will chose the level of labor that corresponds with the point where her new budget constraint is tangent to the original indifference curve.
(Description)
There are 2 dotted lines drawn from points with approximate coordinates, 25 hours per week, on the horizontal axis, and, 450 dollars, on the vertical axis. The first dotted line is parallel to the vertical axis, the second dotted line is parallel to the horizontal axis. These lines intersect at a right angle at a point on the new budget constraint line. It is labeled as Tamara's new level of labor.
The new indifference curve line is drawn on the graph. The new budget constraint line is a tangent line which touches the new indifference curve at the point where the dotted lines mentioned above intersect.