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computer science Question 2 [ 3 6 marks ] A mass of consumers is uniformly distributed along the interval 0 , 1 . Two firms,

computer science
Question 2[36 marks]
A mass of consumers is uniformly distributed along the interval 0,1. Two firms, A and B, are located at points 0 and 1 respectively. We denote by pi the price of firm iinA,B. A consumer located at point xin[0,1] obtains utility UA(x)=u-pA-tx2 if he consumes from firm A, and UB(x)=u-pB-t(1-x)2 if he consumes from firm B. In the following, we assume that the gross utility u is sufficiently high, so that the market will be covered and all consumers will get positive utility in equilibrium. Both firms have a cost function equal to Ti(qi)=(1+x)qi, where you should substitute x for the last number of your student ID number.
(a) Find the demand function for both firms.
[5 marks]
(b) Assume firms set their prices simultaneously. Solve for the Nash equilibrium prices, and compute the equilibrium profits.
marks]
(c) Now, assume a Stackelberg timing, where firm A is the leader. Explain briefly why we should not use the Nash equilibrium concept to solve this game, and solve for the equilibrium prices and profits.
marks code to Check if two strings are Anagram or not
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