ECON 481: Economics Questions Homework Help
Spring 2018, Homework Assignment #7 Due Date: April 18, 2018, 1:30 p.m.
1. Career Choice and Wage Differentials?
Consider an 18-year old high school graduate who is making life decisions that will
affect her/him for fifty years, that is, for ages 18 through 67 inclusive. This person is thinking
about a possible investment in a college education. Throughout this problem, assume an interest
rate (discount rate) of 4.125%.
If a person does not go to college, then (s)he goes to work in the present period at age 18,
earning a yearly salary of $20,000 per year; working in such a “high school” job the person’s
salary will increase at a rate of 1½% per year. This person would work on the “high school”
track through age 67.
Suppose there are two types of college education, an “undergraduate” track or a
“professional/doctoral” track. Note, to pursue the professional/doctoral track one must first
complete the undergraduate track.
Suppose an undergraduate education begins now and continues for three more years into
the future. Suppose this year’s tuition is $35,000 and tuition increases 10% per year while
enrolled. For simplicity, let there be 0% probability of failing/dropping out of school.
With an undergraduate diploma in hand, suppose a person begins work at age 22 at a
salary of $30,000 per year; working in an undergraduate career suppose the person’s salary
increases at a rate of 2½% per year.
To pursue professional/doctoral education a person must first complete an undergraduate
education. Suppose a professional/doctoral education begins four years from now and lasts for
four years. Suppose professional/doctoral tuition begins at $75,000 and tuition increases 15%
per year while enrolled. For simplicity – and this really is simplicity – once enrolled suppose
there is 0% probability of failing/dropping out of school.
With a professional/doctoral diploma in hand, suppose a person begins work at age 26 at
a salary of $50,000 per year; working in a professional/doctoral career the person’s salary
increases at a rate of 4½% per year.
Now suppose there are two different types of person. A “Type 1” person has a
meaningful likelihood of career interruption(s). A “Type 2” person with a college degree has a
meaningful likelihood of an early career ending (that is, stopping work before age 67).
For a Type 1 person, at age 28 there is a 60% probability of a 7-year career interruption;
for a Type 1 person, at age 35 there is a 30% probability of a 7-year career interruption. Suppose
career interruptions are independent events, meaning the occurrence (or absence) of an “early”
interruption is independent of the occurrence (or absence) of a “late” interruption.
For a Type 1 person working on the “high school” track, during an interruption the
person earns only 75% of the pre-interruption salary, and there are no pay raises; following an
interruption the person returns to the pre-interruption salary and in following years there are
1½% pay raises.
For a Type 1 person in an “undergraduate” career, at the start of an interruption the
person earns only 90% of the pre-interruption salary but there are still 2½% annual pay raises.
For someone experiencing only an early interruption or only a late interruption, the
person starts the interruption at 90% of the pre-interruption salary and in following interruption
years there are still 2½% pay raises; after the interruption the person moves to 90% of what the
salary would have been with no interruption and in following years there are still 2½% pay
raises.
For someone experiencing both an early interruption and a late interruption, the person
starts the long interruption stretch at 90% of the pre-interruption salary and in following
interruption years there are still 2½% pay raises; after the long interruption stretch the person
moves to only 80% of what the salary would have been without interruptions but in following
years there are still 2½% pay raises.
For a Type 1 person working on the “professional/doctoral” track an interruption means a
permanent change in earnings trajectory. Specifically, for someone experiencing an early
interruption the person moves to 75% of the pre-interruption salary and experiences 4% annual
pay raises thereafter; for someone experiencing only a late interruption the person moves to 90%
of the pre-interruption salary and experiences 4% annual pay raises thereafter.
For a Type 2 person there is no possibility of a mid-career interruption. But there is a
40% probability that a Type 2 person, regardless of education, will not work past age 59.
A. Given all of this information, what education track would a Type 1 person choose and
what education track would a Type 2 person choose? Demonstrate and explain. Be sure to show
the formulae you used to reach your answers. (I have to be able to figure out how you calculated
your answer.) Can we expect a pay gap between Type 1 and Type 2 persons at age 45? At age
55? Demonstrate and explain. (I have to be able to figure out how you arrived at your answer.)
B. Now suppose people can see the future clearly. Specifically, suppose a Type 1 person
knows with certainty that (s)he will experience a late interruption (and a late interruption only);
suppose a Type 2 person knows with certainty that (s)he will not work past age 59. Now what
education track would a Type 1 person choose and what education track would a Type 2 person
choose? Demonstrate and explain. Be sure to show the formulae you used to reach your
answers. (I have to be able to figure out how you calculated your answer.) Will there be a pay
gap between Type 1 and Type 2 persons at age 45? At age 55? Demonstrate and explain. (I
have to be able to figure out how you arrived at your answer.)
2. Wage Discrimination?
A. Suppose there are two types of person, Type M and Type F. Suppose a researcher
named Smith is interested in analyzing possible pay discrimination between the two types of
person. With a representative sample of observations from a reliable survey, suppose Smith
estimates that monthly earnings (W) are related to schooling (S) as follows:
WM = 895 + 210SM,
WF = 905 + 180SF,
where the subscripts “M” and “F” stand, respectively, for “Type M” and “Type F”. Suppose SM
exhibits a mean value of 15.2 years. Suppose SF exhibits a mean value of 15.9 years. Is there a
pay gap, and if so, how big is it? Demonstrate and explain. If there is a pay gap, how much of it
cannot be “explained,” meaning how much appears to be due to discrimination? First,
demonstrate exactly the method one could use to go about making such calculations. Second,
make the calculations and explain your findings. Will Smith conclude that pay discrimination is
a serious problem? Explain why or why not.
B. Suppose a researcher named Smythe is also interested in analyzing possible pay
discrimination between the two types of persons. With the same sample of observations used in
Part A above, suppose Smythe estimates that monthly earnings (W) are related to schooling (S)
and actual work experience (Exp) as follows:
WM = 151 + 60SM + 120ExpM,
WF = 405 + 55SF + 125ExpF.
Of course, SM still exhibits a mean value of 15.2 years and SF still exhibits a mean value
of 15.9 years. Suppose ExpM exhibits a mean value of 25.2 years. Suppose ExpF exhibits a mean
value of 19.9 years. Is there a pay gap, and if so, how big is it? Demonstrate and explain. If
there is a pay gap, how much of it cannot be “explained,” meaning how much appears to be due
to discrimination? First, demonstrate exactly the method one could use to go about making such
calculations. Second, make the calculations and explain your findings.
C. Will Smith and Smythe reach similar or different conclusions about pay
discrimination? Based on your analysis above, are researchers likely to reach consensus about
pay discrimination? Explain why or why not.
