Consider a Bertrand model with two firms, 1 and 2. They produce identical goods in the same market with demand function P = 65 - 2QP=65−2Q, where Q=q_1+q_2Q=q1​+q2​. Furthermore, both of them have MC = 5MC=5, i.e. TC_i=5q_iTCi​=5qi​ for i=1,2i=1,2

Ugly Dolls Inc. (UD) is a firm in Mytown that sells its products on a market under monopolistic competition. The cost function of UD is represented by TC = 100+10Q. Lately, because of the UD is making a big amount of profit, some firms enter the market to compete.  Assume that Mytown engages in free trade in the dolls markets with Yourtown, who also faces a market with monopolistic competition. Because of this we can expect that, (a)  The numbers of firms operating in this market will not change. (b)  At equilibrium the profit of firms will increase. (c)  The quantity of types of dolls available to consumers will increase. (d)  All the above answers are correct.

The marginal cost of a product is fixed at MC = 20. The demand for the product is Q = 100 - 2P.   (a) Now consider a Cournot model with two firms that are choosing quantities simultaneously. What is the best reply (best response) function for each firm? What is theNash equilibrium? What is the total surplus? (b)What do you expect the total surplus would be with three firms? Why? (You do not need to calculate an exact value. You can say ”total surplus is at least 100”, or ”total surplus is at most 80”)

Consider a homogeneous good industry (such as an agricultural product) with just two firms and a total market demand Q = 400−P, so the inverse demand is P = 400 − Q. Suppose both firms have a constant marginal cost equal to $100 per unit of output and a fixed cost equal to $10,000. Suppose that the firms compete by simultaneously setting price, not simultaneously setting output. That is, suppose we consider the Bertrand model instead of the Cournot. Show that the two firms must earn lower profits. Hint: Create a two-by-two game using two different prices for each firm. One price should be the Cournot price (the Cournot is price of the good when firms produce the Cournot output you found above, which is 100 and 100, so the price is P = 400 − 100 − 100 = 200). The second price should be under 200 and over 150. Then show that the Nash equilibrium of this game is the lower of the two prices. When calculating profits, assume that each firm has equal sales (one half of demand) if they charge…