# DSE 2012 Doubts

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## DSE 2012 Doubts

 This post was updated on . 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
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## Re: DSE 2012 Doubts

 This post was updated on . The 23rd question is on bertrand model price competition duopoly. As you must have read that in Bertrand model by the end due to cut throat competition amongst firms the nash equilibrium is to charge P=MCi, where i denotes the number of firm like i=1,2,3.....n. But this is a situation with capacity constraint. So the nash equilibrium amongst these firms will be to charge the higher MC as their price. As the firm with the lower MC gets the entire market share as the products are homogenous. So though this firm has lower MC it should not cut the price of the rival firm because as it is, it cannot by itself satisfy the entire market. So the answer is 6.
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## Re: DSE 2012 Doubts

 This post was updated on . In reply to this post by Ayushya Kaul QUESTION 46. i think 2 . for d first function we differentiate 3 times and find local minima at x = -2 and for d odr fn local minima at x = 0  btw if u know Q  27 then plese help with it . QUESTION 14.  Integral of x^n.sin(x) dx for limits 0 to 1. use ilate method , integ by parts u = sin x  dv= x^n dx  --> v =  x^n+1/n+1     du = =cosx dx int = sin x * x^n+1/n+1  - int x^n+1/n+1 (- cos x ) dx  if u look at d exp it does implies d http://discussion-forum.2150183.n2.nabble.com/DSE-2012-Ques-39-plzz-help-tp7581555.html;cid=1371550585574-761 36 ) no where ginni coeff is mentioned , cumulative dist fn sums up d exp fr every individual so we don't know about any one person's exp . i m nt sure .