Consider a firm in an oligopoly in which a few sellers offer differentiated brands of widgets. Suppose that if Firm 1 were to cut its price in order to sell more widgets, its competitors would quickly lower their own prices to protect their market shares. If, however, Firm 1 were to raise its price, its competitors would not follow, and Firm 1 would lose market share. Under these (non-ceteris-paribus) assumptions, the demand curve faced by Firm 1 is, in effect, highly elastic at prices above the current price, and less elastic at prices below the current price. Suppose that Firm 1's current price is P* = $10 and it sells Q* = 4 widgets per day. If Firm 1 were to raise its price, it would face the demand: P = 12 – 2Q (P > 10) If Firm 1 were to reduce its price, it would face the demand: P = 14 - Q (P< 10) a) Write the firm's marginal revenue function for prices above and below $10. MR = (P > 10, so: Q* < 4) MR = (P < 10, so: Q* > 4) b) GRAPH Firm 1's demand (D) and marginal revenue (MR) curves. Label point E (4, $10). c) Firm 1 has no incentive to change its price as long as: $. < MC < $ d) Calculate the elasticity of demand for each demand function at E(4, $10). If Firm 1 raises price: ED = If Firm 1 lowers price: ED =

Consider a firm in an oligopoly in which a few sellers offer differentiated brands of widgets. Suppose that if Firm 1 were to cut its price in order to sell more widgets, its competitors would quickly lower their own prices to protect their market shares. If, however, Firm 1 were to raise its price, its competitors would not follow, and Firm 1 would lose market share. Under these (non-ceteris-paribus) assumptions, the demand curve faced by Firm 1 is, in effect, highly elastic at prices above the current price, and less elastic at prices below the current price. Suppose that Firm 1's current price is P* = $10 and it sells Q* = 4 widgets per day. If Firm 1 were to raise its price, it would face the demand: P = 12 – 2Q (P > 10) If Firm 1 were to reduce its price, it would face the demand: P = 14 - Q (P< 10) a) Write the firm's marginal revenue function for prices above and below $10. MR = (P > 10, so: Q* < 4) MR = (P < 10, so: Q* > 4) b) GRAPH Firm 1's demand (D) and marginal revenue (MR) curves. Label point E (4, $10). c) Firm 1 has no incentive to change its price as long as: $. < MC < $ d) Calculate the elasticity of demand for each demand function at E(4, $10). If Firm 1 raises price: ED = If Firm 1 lowers price: ED =

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.5P

See similar textbooks

Similar questions

Consider Firm A and Firm B, each with cost functions C(qA) = 5qA, and C(qB) = 5qB, The inverse market demand is given by p = 30 − Q, where Q = qA + qB represents the total quantity demanded in the market. a) Suppose the firms compete in a Cournot oligopoly model. What are the quantities supplied by each firm and their profits? b) Now let Firm A be the first-mover. If the firms compete in a Stackelberg oligopoly model, what are the quantities supplied by each firm and their profits? c) How can you interpret the difference in profits between parts (a) and (b)? In other words, if you were Firm A, which scenario would you prefer, and what might this say in general?
How would the Cournot equilibrium change in the airline example if American's marginal cost were $90 and United's were $180? The demand the duopoly quantity-setting firms face is Q=339−p with an inverse demand function of p=339−1qA −1qU where qA is the quantity produced by American and qU is the quantity produced by United. The Cournot-Nash equilibrium occurs where qA equals ? enter your response here and qU equals? enter your response here. (enter numeric responses using integers) Furthermore, the equilibrium occurs at a price of ? (round your answer to the nearest penny)
Suppose that there are only two firms in a market in which demand is given by p = 64 - Q, where Q is the total production of the two firms. Each firm can choose either a low level of output, qL = 15, or a high level of output, qH = 20. The unit cost of production for both firms is $4. Write down the normal-form representation of the game in which the strategic variable for each firm is the quantity of output and the firms make their choices simultaneously. Find the pure strategy Nash equilibrium of this game (quantities produced and market price).
Refer to the normal-form game of price competition in the payoff matrix below. Suppose the game is infinitely repeated, and the interest rate is 10 percent. Both firms agree to charge a high price, provided no player has charged a low price in the past. (a) If both firms stick to this agreement, then what is the present value of firm A's payoffs? Please show your calculations. (b) If firm A cheats, what is the present value of the returns for Firm A for cheating? Please show your calculations.
Sometimes oligopolies in the same industry are very different in size. Suppose we have a duopoly where one firm(Firm A) is large and the other firm (Firm B) is small, as the prisoner’s dilemma box in Table 10.4 shows. Assuming that both firms know the payoffs, what is the likely outcome in this case?
Consider duopoly model with firm 1 and firm 2. Firms have constant marginal costs, c_1 = c_2 = 10. Demand functions are given by equations: Q_1= (7*100) - 2*P_1 + P_2 Q_2 = (7*100) + P_1 - 2*P_ 2 Note that * signifies the multiplication sign. Assume that firm 1 chooses its price first. Then, after observing firm 1’s price, firm 2 chooses its price. Find the prices each firm chooses in the roll-back equilibrium of this game. Is it good to be a leader or a follower in this game? Why?
Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each earn as profit? How does the price compare to the marginal cost? Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd = 10,000 – 100P, where P is the price of a cubic yard of concrete and Qd is the number of cubic yards demanded per year. Marginal cost is $25 per cubic yard. Suppose that Joe and Rebecca compete in quantities and competition in this market is described by Cournot model. What are Joe and Rebecca’s Nash equilibrium outputs? What is the resulting price? What do they each…
Suppose Telkomsel and Indosat are the only two firms in the internet market. They face the following payoff when the want to invest in the research budget: When both companies invest in small budget, Telkomsel will gain Rp 40 billion and Indosat will gain Rp 50 billion. When both of them invest in large budget, Telkomsel will gain Rp 20 billion and Indosat will gain Rp 30 billion. When Telkomsel invest in large budget and Indosat in small budget, Telkomsel will gain Rp 30 billion and Indosat will gain zero. When Telkomsel invest in small budget and Indosat in large budget, Telkomsel will gain zero and Indosat will gain Rp 70 billion. a). Draw the payoff matrix b). Is there a Nash Equilibrium for that case? Explain.
Consider a “punishment” variation of the two-firm oligopoly situation shown in Figure 14.1. Suppose that if one firm sets a low price while the other sets a high price, then the firm setting the high price can fine the firm setting the low price. Suppose that whenever a fine is imposed, X dollars is taken from the low-price firm and given to the high-price firm. What is the smallest amount that the fine X can be such that both firms will want to always set the high price?