Consider a Duopoly model, in which two firms decide a quantity simultaneously. The market demand is given by P=50 - Q, where Q is the total output (Q=Q1+Q2). Each firm has an identical cost function, TCi=6Qi, i=1, 2. If Firm 1 believes Q2=10, Firm 1 should sell Q1= ____ units in order to maximize its profit.
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Consider a Duopoly model, in which two firms decide a quantity simultaneously. The market demand is given by P=50 - Q, where Q is the total output (Q=Q1+Q2). Each firm has an identical cost function, TCi=6Qi, i=1, 2. If Firm 1 believes Q2=10, Firm 1 should sell Q1= ____ units in order to maximize its profit.
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- Consider a Duopoly model, in which two firms decide a quantity simultaneously. The market demand is given by P=120 - 3Q, where Q is the total output (i.e., Q=Q1+Q2). Each firm has an identical cost function, TCi=12Qi, i=1, 2. If Firm 1 believes Q2=12, Firm 1 should sell Q1= _____ units in order to maximize its profit.Suppose a market is served by two firms (a duopoly). The market demand function given by P = 1200 - Q_{1} - Q_{2} where Q_{1} is the output produced by firm and Q_{2} is the output produced by firm 2 . Firm cost of production is given by the function C(Q_{t}) = 120Q_{t} and firm 2's cost of production is given by the function C(Q_{2}) = 120Q_{2} The average cost of firm 1 is given by A*C_{1} = 120 and the average cost of firm 2 is given by A*C_{2} = 120 Marginal profit function for firm 1: Delta pi 1 Delta Q 1 equiv1080-2Q 1 -Q 2; (d*pi_{2})/(Delta*Q_{2}) = 1080 - Q_{1} - 2Q_{2} Marginal profit function for firm 2: What will be the equilibrium profit levels earned by the Stackelberg leader firm and the Stackelberg follower firm?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.
- Consider two price-setting oligopolies supplying consumers in a certain region of a country. Firm 1 employs many of the people living there and the local government subsidizes its operations. In all other respects, the firms are identical-they have the same constant marginal cost, MC = 4, and produce the same good. The demand function for Firm 1 is q1 = 600 - 50p1 - 20p2 and for Firm 2 is q2 = 600 - 50p2 - 20p1, where p1 is Firm 1's price and p2 is Firm 2's price. a. What are the Nash-Bertrand equilibrium prices and quantities without the subsidy? b. What are they if Firm 1 receives a per-unit subsidy of S = 1? Compare the two equilibria.Two firms compete on price every year. The inverse demand function each firm faces depends on which firm has chosen the lowest price that year. The one that did captures the entire market. If, on the other hand, both prices are the same then they split the market evenly. Consumers round up prices to the nearest integer. For the firm with the lowest price p, demand is given by: q = 24-2p: Marginal costs are constant and equal to $4 for both firms. a. Define the Normal form of the stage game and determine the Nash Equilibria, the Cooperative Equilibrium and the Optimal Deviation from cooperation. b. For the once repeated (2 stages) game, determine if a Nash Equilibrium exists that improves on simply playing the (better) Nash Equilibrium of the stage game twice c. For the infinitely repeated game, determine what the interest rate would have to be to prevent the firms from cooperating. d*. Determine the relation between the interest rate and the number of punishment periods in a…Firm 1 and firm 2 are Bertrand duopoloists. Firm 1 has a marginal cost of $6.00 per unit, and firm 2 has a marginal cost of $8.01 per unit. The demand for their product is p=23.00−Q, where Q is the total quantity demanded. How much does each firm sell in equilibrium? Assume that prices can only be set to the nearest cent, firms split the market if they set the same price, and there are no fixed costs. Firm 1 production:______ Firm 2 production:______ What are the profits for each firm in equilibrium? Firm 1 profit: $______ Firm 2 profit: $______
- There are two firms with the same cost function c(q)=c*q. The aggregate inverse demand is D(Q)=100-Q, where Q=q1+q2 Use the Stackelberg model , where firm 1 chooses first the quantity Use Cournot model What is the estimated deadweight loss of these two duopoly market?Consider the following market demand function: Q= 20-2P, where P is the market price. Suppose there are two firms- A,B in the market and they have the same cost function: the per unit cost of producing output is 4. The firms compete by choosing quantities. Find the reaction functions for both the firms if they are maximizing profits. What is the profit maximizing output for each firm and corresponding market price? If there was only one firm in the market how would your answer change?Consider a Cournot Duopoly model. The inverse demand for their products is given byP = 200 − 6Q, where Q is the total quantity supplied in the market (that is, Q = Q1 + Q2). Each firm has an identical cost function, given by TCi = 2Qi, for i = 1, 2.(a) In the Cournot model, what does each firm choose?(b) What is the timing of each firm’s decision?
- Two firms A and B produce an identical product (Note: Industry Output = Q). The firms have to decide how much output qA and qB (Note: qA = Firm A Output; qB = Firm B Output) they must produce since they are the only two firms in the industry that manufacture this product. Their marginal cost (MC) is equal to their average cost (AC) and it is constant at MC = AC = X, for both firms. Market demand is given as Q = Y – 2P (where P = price and Q = quantity). Select any value for X between [21 – 69] and any value for Y between [501 – 999]. Using this information, calculate the Industry Price, Industry Output, Industry Profit, Consumer Surplus and Deadweight Loss under each of the following models; 1)Cournot Model 2) Bertrand Model 3) Tacit Collusion Model.Consider the following Cournot duopoly. Both firms produce a homogenous good. The demand function is Q = 100 -2P, where Q is the total quantity produced. Firm 1's cost function is TC(q,)=59, + 1. Firm 2's marginal cost of production is c =6 with probability 0.5 and c5 =3 with probability 0.5. Firm 2 knows its own cost function and firm 1's cost function. Firm 1 knows its own cost function and the probability distribution of firm 2's marginal cost. How much does firm 2 produce in a Bayesian Nash Equilibrium? O 175/6 if the marginal cost is high and 193/6 if the marginal cost is low O 86/3 if the marginal cost is high and 98/6 if the marginal cost is low O 92/3 98/6Suppose that Raleigh and Dawes are the only sellers of bicycles in the UK. The inverse market demand function for bicycles is ?(?)=200−2?. Both firms have the same total cost function: ??(?)=12? and the same marginal cost: ??(?)=12.Suppose this market is a Stackelberg oligopoly and Raleigh is the first mover.a) Write down a formula for the reaction function of Dawes.b) Calculate the equilibrium quantity that each firm produces and the equilibrium price in the market.c) At the Stackelberg equilibrium, how much profit does each firm make?Suppose now that the two firms decide to act like a single monopolist.a) What will the total quantity of bicycles sold in the market be and what will the equilibrium price be? Represent the profit maximisation problem on a graph and indicate the price and quantity at the equilibrium.b) Calculate the total profit made by the two firms when they act like a monopoly. Compare it with the total profit they were making in the Stackelberg oligopoly.c) For the…