(11) Assume two firms with the same constant average and marginal cost, AC= MC= 5, facing the market demand curve Qı + Q2 = 53 – P. Use the Stackelberg model to analyze what will happen if one of the firms makes its output decision before the other. a. Suppose Firm 1 is the Stackelberg leader (i.e., makes its output decisions before Firm 2). Find the reaction curves that tell each firm how much to produce in terms of the output of its competitor. b. How much will each firm produce, and what will its profit be? Compare your results to the Cournot Equilibrium.
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- 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”)COURSE: MICROECONOMICS - Stackelberg ModelIn a given market good there are only 2 firms that satisfy the demand, and their respective total cost functions are: CTi = 400 and the demand that is estimated is P = 120 - 2QIf the exception variable of both firms is the quantity they will produce, such that the decisions to produce are made sequentially firm number 1 will be the leader who decides the quantity to produce and firm number 2 (follower) decides based on the production of firm number 1, we ask:(a) quantity produced by each firm and its equilibrium price in the market.(b) Profit of each company at equilibrium and (c) Graph your resultsQ2. Consider a two-firms Cournot model with constant returns to scale. Assume also that the inverse demand function is P = 100 – 2Q, with marginal cost equal to 20for both firms, where Q = q1 + q2 . b) How do equilibrium outputs and profits vary when firm1’s cost changes. Draw a picture of this outcome.
- Suppose market inverse demand function is p(y)=100-Yt where Yt is total production in the market. Assume that there are two firms with following marginal cost MC(firm 1)=Y1 MC(firm 2)=2*Y2+10 Assume that Yt=Y1+Y2 Set up profit function for both firms. What is the best response function of each firm by taking into account action of other firm? What output level is going to be produced by each firm in equilibrium? Assume that Firm 1 is leader in the market and going to act first. What will be the best response and output level of firm 2. What is difference between previous and new situation? Why? What is difference between Bertrand and previous competition? How would you like to find equilibrium price?Please no written by hand 1. Suppose the automobile manufacturing industry has two firms, General Motors and Ford. Assume that the market demand function is Q = 1,000 − p, and each firm’s marginal cost and average cost are $40. a. What is the marginal revenue for General Motors? Assume, ??? represent residual demand for General Motors and ?? represents residual demand for Ford. b. What is the best response function for General Motors and Ford? c. What is the Nash-Cournot equilibrium in this market? d. Graph the best response curves for both General Motors and Ford, placing the quantity produced by General Motors (???) in the x-axis. Label intercepts and Nash-Cournot equilibrium.This pertains to the Cournot model except that a. Both firms maximize profit b. Each firm anticipates the price movement of the other c. There are only 2 firms in the industry d. Each firm takes the output as given
- COURSE: MICROECONOMICS - Cournot Model:In the market for a given good there are only 2 firms satisfying the demand, and their respective total cost functions respond to the form: CTi = 10Qi + 5 and the demand is estimated to be: P = 31 - QIf the decision variable for both firms is that the quantity they will produce and realize will be decided simultaneously it is asked to:(a) calculate the profit and reaction function of each firmb) graph market equilibriumc) calculate the profits that both companies will obtain in equilibriumConsider a market with four firms. Firms A and B have a marginal cost of $7. Firm C has a marginal cost of $11. Firm D has a marginal cost of $5. What occurs if the firms compete in the Bertrand model? Group of answer choices None of the other answers are correct. Firm D will capture the entire market with a price of $6.99. All four firms will each have one quarter of the market with a price of $11. Firms A and B will each have half the market with a price of $7.00. Firm D will capture the entire market with a price of $5.00.We now consider a duopoly model where the firms offer products with different qualities and consumers differ from each other in how much they care for quality. Suppose the firms offer their products with quality si ∈ [0,1] and consumers’ ‘location’ in terms of how much they care about quality is given by a parameter θ ∈ [0,1] and consumers are uniformly distributed over this interval. Suppose the firms first choose their quality s1 and s2 and then set prices p1 and p2. A consumer of type θ derives utility vi = r − pi + θsi from consuming a unit from firm i and where reservation price r is high enough that everyone purchases from one of the two firms. Suppose the marginal cost of producing increases with quality. There are no fixed costs and the total variable cost is C(qi,si) = csiqi so that marginal cost is csi and increases with quality. Further, let c = 1 so marginal cost is si. Consider the second stage where given a choice of qualities s1 and s2 with s1 < s2, the firms…
- Exercise 1: Stackelberg model Suppose there are two firms, Firm 1 and Firm 2. Both firms have the same production cost and they face the industry demand given below. Demand: P = 500 - Q Costs: MC = ATC = 200 Suppose Firm 1 is the incumbent and the first-mover. Its profit is equal to ________________. a.$14,000 b.$12,000 c.$11,250 d.$22,500 Continue with Exercise 1... If Firm 2 enters, its profit is equal to _________. a.$5,625 b.$6,000 c.$7,000 d.$11,250 Hi there, our teacher gave exercises before the final exam in 5 days. I have a hard time solving the Stackelberg model. Please help me out:)There are two identical firms in an industry, 1 and 2, each with cost function , i = 1,2. The industry demand curve is P = 100 − 5X where industry output, X, is the sum of the two firms’ outputs (X1 + X2). (a) If each firm makes its output decisions on the assumption that the other will not react to its choices (the Cournot assumption), what is the equilibrium output for each firm? What is the equilibrium price? (b) Suppose that each firm takes it in turn to choose its level of output, on the assumption that the other’s output level is fixed. Would the process of adjustment be stable? (c) Suppose that firm 1 introduces a cost-saving innovation, so that its cost curve becomes C1 = 8X1. Firm 2’s cost curve and the industry demand curve are unchanged. What happens to the equilibrium quantity produced by each firm and to market price?Suppose we have a Hotelling model with N = 150 people who consider the good very valuable at V = $1000 so all consumers will buy from one store or the other, transport costs are t = $25 a mile. We have two competing firms at opposite ends of the road. Firm 2 is located at 0 and firm 2 at 1. Let marginal cost of production be $3. show that: D1= 150(p2 - p1 + $25)/50 Profit1= 3(p1 - 3)(p2 - p1 + 25)