Economics

6. (5) Suppose that there is an industry with Bertrand competition, and two firms each with cost function c(q) = 20q + 30. Industry demand is given by q = 100 - p. What is the Bertrand equilibrium price? How much profit does each firm earn? Is this a long-run equilibrium? Explain briefly. 7. (10) Atsuko has utility function u = x y and income of M. Prices are px and py. a. Use the Lagrangian method to find her demand for x. b. Show that you can find the demand function by using two equations: (1) set the MRS equal to the price ratio, and (2) the budget constraint. 8. (10) Samsung seeks to maximize its profits. The quantity it sells depends on price and advertising: q(p, a) = pa - 100. Its cost function is c(q, a) = 10q + 3a. Find its profit-maximizing price, advertising and profits. 9. (10) a. Find all NE of the following game assuming simultaneous play. b. Find all Subgame perfect equilibria assuming that 1 plays first. Player 2 L C R U 10,10 10,10 4,10 Player 1 M 5,20 4,10 4,10 D 5,20 10,10 3,20