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Labour Economcis assignment

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Économie du travail
姚启翔
Ms. Aura is a psychic. The demand for her services is given by
,
where Q is the number of one-hour sessions per year and P is the price of each
session. Her marginal revenue is
. Ms. Aura's operation has no
fixed costs, but she incurs a cost of $150 per session (going to the client's house).
a. What is Ms. Aura’s yearly profit?
In order to maximize her utility, she'll keep going to client's place until the cost equals
to her marginal revenue. That is
, solve
. Her profit is
b. Suppose Ms. Aura becomes famous after appearing on the Psychic Network.
The new demand for her services is
is
. Her new marginal revenue
. What is her profit now?
The process is similar.
, solve
. Profit is
c. Advances in telecommunications and information technology revolutionize the
way Ms. Aura does business. She begins to use the Internet to find all relevant
information about clients and meets many clients through teleconferencing. The
new technology introduces an annual fixed cost of $1,000, but the marginal cost
is only $20 per session. What is Ms. Aura’s profit? Assume the demand curve is
still given by Q = 2,500 - 5P.
The fixed cost is sunken cost and thus should be considered in the decision making
process. Ms. Aura will still provide her services till marginal revenue equals marginal cost.
, solve
. Her profit is
d. Summarize the lesson of this problem for the superstar phenomenon.
The advent of internet allows people to provide their services or products to a far
larger group of customers. Technology decreased the cost, increased the number of
customers and lowered the cost. Not only did the provider enjoys a better income, the
customers can benefit from cheaper price as well.
Suppose the bottom 50 percent of a population (in terms of earnings) all receive
an equal share of
percent of the nation's income, where
50 percent of the population all receive an equal share of
. The top
percent of the
nation's income.
a. For any such p, what is the Gini coefficient for the country?
b. For any such p, what is the 90-10 wage gap?
As we've listed the function, we can easily obtain the 10 percentile wage and the 90
percentiile.
The 90-10 wage gape is: