Question

Consider an employee who does not receive employer-based health insurance and must divide her $\mathbf{\backslash (}\mathbf{1}\mathbf{,}\mathbf{000}$per week in after-tax income between health insurance and “other goods.” Draw this worker’s opportunity set if the price of health insurance is$\mathbf{\backslash )}\mathbf{200}$per week and the price of “other goods” is$\mathbf{\backslash (}\mathbf{100}$per week. On the same graph, illustrate how the opportunity set would change if the employer agreed to give this employee$\mathbf{\backslash )}\mathbf{200}$worth of health insurance per week (under current tax laws, this form of compensation is non taxable). Would this employee be better or worse off if, instead of the health insurance, the employer gave her a$\mathbf{\$}\mathbf{200}$per week raise that was taxable at a rate of$\mathbf{25}$percent? Explain.

Short answer

Illustration is represented via two graphs.

Step-by-step solution

Find the horizontal and vertical intercept

Use the following equation to find the budget line of goods,

${\mathrm{P}}_{\mathrm{x}}\mathrm{X}+{\mathrm{P}}_{\mathrm{y}}\mathrm{Y}=\mathrm{M}$

Here,

${\mathrm{P}}_{\mathrm{x}}$is the price of the insurance

$P_y$is the price of the other good

$M$represents the consumer’s income

Given,

$P_x=\mathrm{\$}200$

${\mathrm{P}}_{\mathrm{y}}=\mathrm{\$}100$

$M=\$1000$

Then the budget line will be:

$200\mathrm{X}+100\mathrm{Y}=1000$

To identify the horizontal intercept, use the following equation:

$X=\frac{M}{P_x}$

By substituting the budget line in equation we will get,

$\begin{array}{c}X=\frac{M}{P_x}\\ =\frac{1000}{200}\\ X=5\text{units}\end{array}$

Therefore, horizontal intercept$=5\text{units}$

Use the equation, for getting the vertical concept;

$Y=\frac{M}{P_y}$

By substituting the budget line in equation, we will get,

$\begin{array}{c}Y=\frac{M}{P_y}\\ =\frac{1000}{100}\\ Y=10\text{units}\end{array}$

Therefore, vertical intercept$=10\text{units}$

Plot the graph

Here, horizontal intercept$=5$

Vertical intercept $=10$

Finding the new value of X and  Y axis intercept

If the employer gave a $\mathrm{\$}200$per week raise that was taxable at a rate of $\mathrm{\$}25$instead of the health insurance, the total income of the employee will be $\mathrm{\$}1150$because of the $25\%$ tax.

To get the new horizontal intercept, calculate:

$\begin{array}{c}X=\frac{M}{P_x}\\ =\frac{1150}{200}\\ X=5.75\text{units}\end{array}$

Therefore, the new horizontal intercept$=5.75\text{units}$

Use the equation, for getting the new vertical intercept;

$\begin{array}{c}Y=\frac{M}{P_y}\\ =\frac{1150}{100}\\ Y=11.5\text{units}\end{array}$

Therefore, the new vertical intercept$=11.5\text{units}$

Plot the graph

With the new values the graph will be:

Therefore, it can be seen that the employee will be better off if the employer gave her a $ $\mathbf{200}$raise per week.