isi 2008

[Seecha]

. (a) On a tropical island there are 100 boat builders, numbered 1 through 100. Each
builder can build up to 12 boats a year and each builder maximizes profit given the
market price. Let y denote the number of boats built per year by a particular builder, and
for each i , from 1 to 100, boat builder has a cost function Ci( y) = 11+ iy
 Assume that
in the cost function the fixed cost, 11, is a quasi-fixed cost, that is, it is only paid if the
firm produces a positive level of output. If the price of a boat is 25, how many builders
will choose to produce a positive amount of output and how many boats will be built per
year in total?
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plz help me out with this

[Diya]

Firms will enter as long as positive profit is made. The first up to the 24th boat builder will make positive
profit. The 25th builder can cover variable cost but not the quasifixed cost so the builder will not build.
Therefore, 24 builders will enter the market. Each will produce a maximum of 12 boats. Note that given
linear cost, each firm only has an option to produce 0 or a maximum of 12. Therefore there will be 288
boats created (12x24)

[Seecha]

thanks alot :)

[Seecha]

plz help me out with this one also
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10 (i) A college is trying to fill one remaining seat in its Masters programme. It
judges the merit of any applicant by giving him an entrance test. It is known
that there are two interested applicants who will apply sequentially. If the
college admits the first applicant, it cannot admit the second. If it rejects the
first applicant, it must admit the second. It is not possible to delay a decision on
the first applicant till the second applicant is tested. At the time of admitting or
rejecting the first applicant, the college thinks the second applicant’s mark will
be a continuous random variable drawn from the uniform distribution between 0
and 100. (Recall that a random variable x is uniformly distibuted on [a, b] if the
density function of x is given by f(x) = 1/b−a
for x ∈ [a, b]). If the college wants
to maximize the expected mark of its admitted student, what is the lowest mark
for which it should admit the first applicant?
(ii) Now suppose there are three applicants who apply sequentially. Before an
applicant is tested, it is known that his likely mark is an independent continuous
random variable drawn from the uniform distribution between 0 and 100. What
is the lowest mark for which the college should admit the first student? What is
the lowest mark for which the college should admit the second student in case
the first is rejected?