(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)
(Speaker)
In this question you are asked to draw Tamara's budget constraint, an indifference curve, under a couple of different scenarios.
As we can see in the problem, Tamara earns 20 dollars per hour, which is untaxed for the first 400 dollars, or 20 hours she works. On income above 400 dollars, she is taxed at a rate of 75 percent. In this problem, we want to draw her budget constraint and indifference curve corresponding to Tamara working 30 hours.
(Description)
The following text is briefly written:
Tamara has 80 hours per week that she can allocate to work or leisure. Her job pays a wage rate of 20 dollars per hour, but Tamara is being taxed on her income in the following way. On the first 400 dollars that Tamara makes, she pays no tax. That is, for the first 20 hours she works, her net wage — what she takes home after taxes — is 20 dollars per hour. On all income above 400 dollars, Tamara pays a 75 percent tax. That is, for all hours above the first 20 hours, her net wage rate is only 5 dollars per hour. Tamara decides to work 30 hours. Her indifference curves have the usual shape.
A. Draw Tamara's time allocation budget line for a typical week. Also illustrate the indifference curve at her optimal choice.
(Speaker)
We are going to start by drawing our axes with income on the y-axis and quantity of leisure on the x-axis.
(Description)
The coordinate plane with the horizontal x-axis and the vertical y-axis is drawn. The horizontal axis is labeled as Quantity of leisure measured in hours per week. The vertical axis is labeled as Income measured in dollars.
(Speaker)
Next, we are going to draw in our budget constraint. You'll notice this has a unique shape, which we will discuss in a moment.
(Description)
A line is drawn on the coordinate plane. 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 the vertical axis.
(Speaker)
For now, the problem states Tamara can work, or consume leisure, up to 80 hours per week. If she chooses to only consume leisure, she will have 80 hours of leisure and no income. This is the intercept on the x-axis.
The kink in the budget constraint will occur after Tamara works 20 hours.
(Description)
There are 2 dotted lines drawn from points, 60 hours per week, on the horizontal axis, and from point, 400 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 budget constraint line.
(Speaker)
Since her wage is 20 dollars per hour and pays no tax on the first 400 dollars, she will earn 20 dollars for every hour of work.
The slope of the budget constraint for the first 20 hours of work is negative 20, which implies for every hour of leisure Tamara gives up, she will earn 20 dollars.
We can also find the slope by taking 400 dollars and dividing by 20.
(Description)
The part of the budget constraint line between 60 and 80 hours per week on the x-axis is labeled as Slope equals negative 400 divided by 20 equals negative 20.
(Speaker)
Next, we want to label the intercept on the y-axis. This is the point that corresponds with Tamara working 80 hours and consuming no leisure. To find the intercept, we want to add the income she earns in the first 20 hours, where she pays no tax, with the income she earns in the last 60 hours, when her tax rate is 75 percent. Of she chooses to work the next 60 hours, she will earn 1 thousand 200 dollars. But 75 percent, or 900, is paid ion taxes, leaving her an income of 300 dollars. Together, she will earn 700 dollars.
(Description)
The value of intercept on the y-axis is, 700 dollars. It is also labeled as Intercept equals 400 plus (60 times 20 times 0.25) equals 400 plus 300 equals 700.
(Speaker)
When Tamara chooses to work more than 20 hours per week, her net wage will be 5 dollars. Remember, for every hour she works, she earns 20 dollars. But 75 percent, or 15 dollars, is paid in taxes, leaving her a take-home pay of 5 dollars.
The slope of the budget constraint when Tamara works more than 20 hours is negative five.
(Description)
The part of the budget constraint line between 0 and 60 hours per week on the x-axis is labeled as Slope equals negative 300 divided by 60 equals negative 5.
(Speaker)
We are told Tamara works 30 hours per week. This means she will consume 50 hours of leisure and earn 450 dollars, which is point A in our diagram.
(Description)
Point, A, is labeled on the graph. It lies on the budget constraint line. Point, A, has coordinates, 50 and 450.
There are 2 dotted lines drawn from points, 50 hours per week, on the horizontal axis, and from point, 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 point, A.
(Speaker)
Finally, we can draw in the indifference curve that corresponds with Tamara working 30 hours per week.
(Description)
The indifference curve line is drawn on the graph. The budget constraint line is a tangent line which touches the indifference curve at point, A.