Take a look at your student ID number (450549496). Define z as the sum of the first three digits of your SID

For example, if your SID is 123456789, then 2=1+2+3=6.

2. Two firms compete in a linear city of length 1 unit. Consumers are uniformly located along the city. Consumer i's utility derived from buying firmj's product is given by y=a-1(x-y)2-p

where j= 1, 2 indicate the two firms, t is the per unit cost of travelling along the city, xi is th

location of consumer i, yi is the location of firm j, and p is the price of product j Firm1 is locate at y1=a and Firm 2 is located at y2= 1, where a=z/100 and z is the number you calculated based on your SID. Each consumer buys a single unit of the good. Each firm has constant marginal cost of c and no fixed costs. Firms compete by simultaneously choosing price in a single period

(a) Find the demand for each firm in terms of market prices and transport costs

(b) Find the reaction function for each firm.

(c)Find the Nash equilibrium market price for each firm. Briefly explain your results.

(d) which firm has a better location? Explain carefully