Economics 620 Assignment 2 Due: Monday, November 15, in class Fall 2021 Instructions: Assignments must be written using a word processor (i.e. hand-written assignments will not be accepted) and...

All the questions are in the file I uploaded


Economics 620 Assignment 2 Due: Monday, November 15, in class Fall 2021 Instructions: Assignments must be written using a word processor (i.e. hand-written assignments will not be accepted) and submitted in class as a hard copy. Students can complete assignments individually or in a group of 2 or 3 students. Question 1: Oligopoly, welfare and entry (20 marks) A market consists of nL low cost firms and nH high cost firms. Total cost functions are given by ?? = ???? + ??? 2 + ? for low cost firms and by ?? = ???? + ??? 2 + ? for high cost firms where cH = c > cL. Firms face inverted market demand given by ? = ? − ? and have conjectural variation denoted ? = ??−? ??? ?ℎ??? − 1 ≤ ? ≤ ? − 1.  Solve for the conjectural variation equilibrium output, profits and welfare  Determine the comparative static effects of nL on output, profits and welfare.  Determine the comparative static effects of nH on output, profits and welfare.  Determine if profitable entry raises welfare (i.e. Does i > 0 implies ?? ??? > 0? ). Hint: Solve for output as a function of v, d, nL, nH, a, c and ? = ??−?? 1+?+2? Point of question: Welfare effects of entry depend on firm behavior. Question 2 : Innovation and endogenous market structure (30 marks) Consider a model with n firms of which m are innovators and n − m are non-innovators. Marginal costs and fixed costs are MC = c – x and F = 9000 for innovators and MC = c and F = 1800 for non- innovators. Market demand is given by ? = ? − ? ? , where S = market size. The firms play a 3 stage game involving entry, innovation and Cournot competition. a) (10 marks). Solve for Cournot equilibrium outputs and profits for both innovators (denoted I) and non-innovators (denoted N). Substitute a – c = 300 and x = 50 into your solutions. b) (10 marks). Let S = 1 and n = 6. Determine the equilibrium number of innovators m*. Show that there is no incentive for a firm to enter or exit. c) (10 marks). Let S = 2 and n = 6. Determine the equilibrium number of innovators m*. Show that there is an incentive for one or more firms to exit. Determine the new equilibrium n and m. Point of question: Increases in market size can increase market concentration by inducing innovation and exit. Fall 2021 EC620 Assignment 2 Page | 2 Question 3: Entry deterrence and Product Proliferation (20 marks) Market structure 2 single product firms Competition Differentiated Cournot Demand for product i pi = 200 – qi – 0.5Q-i Total cost function for product i Ci = 20qi + F Suppose that entry into this industry by a single product firm is (i) profitable if the 2 incumbent firms remained as single product firms but is (ii) unprofitable if one of the incumbent firms introduces a second product and becomes a two product firm with the other firm remaining as single product firms. Given that entry of a single product firm is profitable then determine whether a firm in this industry would have an incentive to introduce a second product in order to deter entry. Point of question: Does the market pre-emption argument apply to oligopoly? Question 4: Repeated games with cost asymmetries (30 marks) A market consists of firm 1 and firm 2 where MC1 = 20, MC2 = 40 and P = 240- 2Q. Firms adopt the Cournot Grim strategy and equally share the output when the collusive price is set charged. a) (5 marks). Solve for the range of discount factors for which collusion is sustainable for both firms when the collusive price is equal to the monopoly price of firm 2 (i.e. P = 140). b) (5 marks). Solve for the range of discount factors for which collusion is sustainable for both firms when the collusive price is equal to the monopoly price of firm 1 (i.e. P = 130). c) (5 marks). Now repeat part b) except assume that firm 1 produces 60% of the output when the firms are both charging the collusive price. d) (5 marks). Using your results from parts a), b) and c) what can you conclude about how firms can improve the sustainability of collusion when they have different marginal cost? e) (10 marks). Now suppose that each firm can compete in market 1 and market 2. Firm i’s marginal cost is 20 in market i and 40 in market j ≠ i. Inverted demand is the same in each market and is given by P = 240 – 2Q. Solve for the range of discount factors for which collusion is sustainable when the collusive price in market i is the monopoly price of firm i and if the collusive output for firm i is the monopoly output in market i and zero in market j ≠ i. Point of question: Can firms collude by agreeing to stay out of each other’s markets?