QUESTION 1B. Continuing with the inverse demand, P = 50 - Q, if each firm has a marginal cost of 0, what is the difference between the equilibrium price under Cournot competition and under Bertrand competition?
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- Inverse elasticity rule Use the first-order condition (Equation 15.2 ) for a Cournot firm to show that the usual inverse elasticity rule from Chapter 11 holds under Cournot competition (where the elasticity is associated with an individual firm's residual demand, the demand left after all rivals sell their output on the market). Manipulate Equation 15.2 in a different way to obtain an equivalent version of the inverse elasticity rule: pMCp=sieQ,p , where si=qi/Q is firm i's market share and eQp is the elasticity of market demand. Compare this version of the inverse elasticity rule with that for a monopolist from the previous chapter.Two firms engage in Cournot competition in the Everlasting Gobstopper industry. The price elasticity of demand is-2. Firm 1 has aconstant marginal cost of $110.00 per unit, and firm 2 has a constant marginal cost of $181.50 per unit. If the two firms are currently inequilibrium, what is firm 2's share of the market? Enter your answer as a decimal, rounded to two places if necessary.______ Please show all stepsSuppose that there are two firms producing a homogenous product and let the market demand besiven by Q(P) = 120 -P/2 . For simplicity assume that each fir operates with zero total cost. a) Assuming that firms compete over quantities, find the price best-response functions of firms 1 and2. Draw a diagram that shows the BRFs and the equilibrium, Are outputs strategic substitutes orcomplements? Find each firm's Cournot equilibrium output, price, profit, and total surplus. DefineNash equilibrium and argue that it is indeed a Nash equilibrium. b) Show that the duopolists have incentives to collude, Find their joint profit-maximizing price, output,and profit: find each firm's output and profit. Is collusion a Nash equilibrium? If not, what is theoptimal defection for each firm? Show this game in a 2X2 matrix form. What does this imply aboutthe Nash equilibrium or the stability of their collusive agreement? Is it a Prisoner's Dilemma Type? c) Suppose now that fims play the above game in…
- Consider a duopoly market with 2 firms. Aggregate demand in this market is given by Q = 500 – P, where P is the price on the market. Q is total market output, i.e., Q = QA + QB, where QA is the output by Firm A and QB is the output by Firm B. For both firms, marginal cost is given by MCi = 20, i=A,B. Assume the firms compete a la Cournot. What are the equilibrium quantities? What is the total quantity supplied on this market? What is the equilibrium price in this market?Two firms engage in Cournot competition in the Everlasting Gobstopper industry. The price elasticity of demand is -2. Firm 1 has a constant marginal cost of $365.00 per unit, and firm 2 has a constant marginal cost of $602.25 per unit. If the two firms are currently in equilibrium, what is firm 2's share of the market? Enter your answer as a decimal, rounded to two places if necessary.Consider the Cournot duopoly with linear demand function ? = 2000 − 2Q, where P is the price and Q = q1 + q2 is the total supply. Firm 1 and firm 2 has constant marginal cost of 600. Just answer the E, F and G, thank you bartleby! a. If firm compete in price, draw in detail the best response of each firm.b. Determine and explain the Bertrand equilibrium.c. What is the equilibrium quantity and how much profit for each firm?d. Explain the Bertrand Paradox in (c)!e. If firm 1 has capacity of production 450 and firm 2 has capacity of 200. Determine the Bertrand equilibrium.f. What is the equilibrium quantity, and how much profit for each firm?g. Is there any paradox in (f)?
- Two firms, 1 and 2, compete in price Market demand in period t is given by D(t) = AtD(p) with A > 0 The common discount factor is ? ? (0, 1) Suppose the firms use trigger strategies to collude at the monopoly price pm = arg max(p ? c)(A)tD(p) ? (A)t?m (note that pm does not depend on A and t due to the function form) Suppose the punishment after deviation is returning to marginal cost pricing forever If the firms collude, they set the same prices and evenly split the profits What are firms’ collusive profits in period t? If a firm undercuts below pm in period t, what are the (optimal) deviating price and deviating profit Write down the no-deviating condition in period t? Simplify the no-deviating condition and derive the critical discount factor ? Compared to when the market is shrinking (A 1) make collusion easier? Explain in words your finding in [e]consider a market with inverse demand P(Q) = 10 − Q and two firms with cost curves C1(q1) = 2q1 and C2(q2) = 2q2 (that is, they have the same marginal costs and no fixed costs). They compete by choosing quantities. Suppose that Firm 1 chooses quantity first and is able to credibly commit to this choice. Then firm 2 choose its quantity after observing firm 1’s quantity. In the SPNE of this game, what is the price faced by consumers?- p = 3- p = 4- p = 5- p = 6- p = 7Suppose two firms engage in simultaneous quantity competition. Both firms have 0marginal cost. Firm A : P(Q)= 24-Q Firm B: P(Q)= 24-2Q a) Find the Nash Equilibrium quantities q^NE and profits.(b) Find the Monopoly Quantity QM and Profit.(c) Now suppose the game is repeated infinitely and each firm has a common discountfactor δ. Find the required discount factor to sustain the following grim triggerstrategy as a SPNE: Play Q^M /2 if this has been played in every previous period,otherwise play q^NE.
- Consider a duopoly, i.e., an industry with only two firms: firm A and firm B, making the same product. The industry’s inverse demand is P(Q)=320−(1/5)Q, where P is the market price and Q is the total industry output. Each firm has a marginal cost MC of $20. There are no fixed costs and no barriers to exit the market. a) Suppose that the two firms engage in Cournot competition. Find the equilibrium price PNE in the industry, the equilibrium outputs QANE and QBNE, as well as the profits πANE and πBNE, for each firm. b) Suppose the marginal cost for firm B increases from $20 to $140, while everything else remains unchanged. Find the new equilibrium price PNE in the industry, the new equilibrium outputs QANE and QBNE, as well as the new profits πANE and πBNE for each firm. c) Suppose that, in addition to the marginal cost increase from $20 to $140 from sub question b), firm B also has a fixed cost of $2500, out of which $2100 may be recouped if it shuts down; everything else remains…Consider a duopoly in which two identical firms compete by setting their quantities but Firm 1 has first mover advantage (i.e., Firm 1 is the Stackelberg Leader). We want to consider whether Firm 1 should use its advantage to drive Firm 2 out of the market.There are two firms in the market (duopoly). These two firms are competingsimultaneously. The first firm chooses its output level (x) by predicting the second firm’soutput (y). Let c denote the total cost function c(x) = x and c(y) = y. Also, let’s assumethat the inverse demand function is p(Y) = 7 - Y where Y = x + y. (1) Obtain the reactionfunction of the first firm. (2) Find the equilibrium (output and profit of each firm) whentwo firms simultaneously compete
