Q3. The dominant firm (Part A is 10 points, Part B is 5 points, Part C is 5 points) PART A The dominant firm's total cost function is TC(g) = g. (The dominant firm has a constant marginal cost MClg) = 1 for all g = 0. It also has a constant average cost AC(g) = 1 for all g = 0.) The market demand is given by Q(P) = 22 - 4P. There are 10 small firms, each of these firms has the following total cost function: TClg) = g + 0.625q. These small firms behave competitively: they take the market price as given and choose the profit maximizing quantity g. Therefore the total guantity these 10 firms will supply is given by the following equation, which we refer to as the \"fringe supply 5'P) = =8 + 8P Please compute the dominant firm equilibriom (follow the steps from the \"dominant firm\" lecture). Clearly show your work. 1) What is the quantity the dominant firm produces in equilibrium? 2} What is the total quantity supplied by the fringe in equilibrium? 3} What is the market price? For this equilibrium please compute 4) the Lerner index for the dominant firm 5) the HHI of market concentration 6) the dominant firm's profit 7} the total profit of the 10 small firms g8} the consumer surplus PART B Suppose the dominant firm achieves a technological breakthrough and now its cost function is TC|g) = 0.5q. (The dominant firm now has a constant marginal cost MC[g) = 0.5 for all g = 0, and a constant average cost AC(g) = 0.5 for all g = 0.} Everything else s the same. [The market demand: Q(P) = 22 = 4P, the cost functions of the 10 firms that behave competitively is TC[g) = g + 0.625g% and the fringe supply is given by 5P} = -8 + 8F] The dominant firm equilibrium for this new situation (which we have computed in the lecture) is as follows: The dominant firm produces Q7 = 12, the other firms supply 0.4 units each, so the total quantity supplied by these 10 firms is 4 units, and the market price is P = 1.5. For this equilibrium please compute 1} the Lerner index for the dominant firm 2} the HHI of market concentration 3} the dominant firm's profit 4} the total profit of the 10 small firms 5) the consumer surplus PART C Please compare the equilibrium of part A to the equilibrium of part B where the dominant firm has a more efficient technology. 1} Which equilibrium has a higher Lerner index? 2} Which eguilibrium has a higher HHI of market concentration ? 3} Which equilibrium has a larger consumer surplus? 4} Which equilibrium has a larger total profits + consumer surplus? COMMENT: 15 a rising industry concentration and a higher Lerner index a sure sign that the market is creating a larger deadweight loss (getting less efficient) and consumer welfare is reduced? Please explain