Posted by
Ayushya Kaul on
Jun 17, 2013; 10:27pm
URL: http://discussion-forum.276.s1.nabble.com/DSE-2012-Doubts-tp7582497.html
Hey, couldn't wrap my head around these questions:
QUESTION 14. Integral of x^n.sin(x) dx for limits 0 to 1.
(a) Does not exist
(b) Is necessarily greater than 1
(c) Is greater than 1/(n + 1)
(d) Is less than 1/(n + 1)
Can anyone show the steps for solving this?
QUESTION 23. Consider a homogenous goods market with the demand
function Q = 30 P, where Q and P denote quantity and price respectively.
There are two fi rms playing a price game in the following manner: rm 1
quotes a price and then rm 2 chooses a price. When they charge the same
price they share the market equally and otherwise the market demand goes
to the fi rm charging lower price. Firm 1 has a capacity constraint at the
output level 5 units such that upto fi ve units the marginal cost of production
is Rs 3 per unit of output, however beyond 5 units it cannot produce any
output. Firm 2 does not have any capacity constraint, it can produce any
amount with the marginal cost Rs 6. What would be the equilibrium price
in the market?
(a) 3
(b) 6
(c) 6 -e , where e is very small positive number
(d) 3 +e , where e is very small positive number
QUESTION 46. What is the total number of local maxima and local min-
ima of the following function
f(x) =(2 + x)^3 if -3 <x<= -1
x^2/3 if -1<x< 2
(a) 1
(b) 2
(c) 3
(d) 4
Also questions 36 and 39 part A of DSE 2012.
The questions have too many cumbersome signs for it to simply copy and paste so here's the link:
http://econdse.org/wp-content/uploads/2012/07/2012-Option-A.pdfOnce again, any help is greatly appreciated.