Answer all parts a b c show work please Question 1 Suppose t

Answer all parts a, b, c

show work please

Question 1: Suppose that two firms produce differentiated products and compete in prices. As in class, the two firms are located at two ends of a line one mile apart. Consumers are evenly distributed along the line. The firms have identical marginal cost, S60. Firm B produces a product with value S110 to consumers Firm A (located at 0 on the unit line) produces a higher quality product with value S120 to consumers. The cost of travel are directly related to the distance a consumer travels to purchase a good. If a consumer has to travel a mile to purchase a good, they incur a cost of S20. If they have to travel x fraction of a mile, they incur a cost of S20x. Write down the expressions for how much a consumer at location d would value the products sold by firms A and B, if they set prices Pa and Pb (a) (b) Based on your expressions in (a), how much will be demanded from each firm if prices Pa and P are set? (c) What are the Nash equilibrium prices?

Solution

1) Surplus from Firm A = $120 - $20d - Pa

Surplus from B = $110 - $20(1-d) - Pb

2) We will set surplus A = surplus B, to solve for d

Thus, $120 - $20d - Pa = $110 - $20(1-d) - Pb

It gives: d* = (30 + pb - pa) / 40

Because the consumers are evenly distributed along the unit interval

Qa = (30 + pb - pa) / 40;

Qb = (10 + pa - pb) / 40

3) Writing profits for firm A, we get _{A = Qa (Pa - 60)}

When we sSubstitute Qa into the above equation and takes the derivative to Pa, then:

p*a = (90+pb) / 2

Similarly, p*b = (70+pb) / 2

Solving it we get nash equibrium pa* = 83.33; pb* = 76.66