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- Consider a simple Bertrand market in which N=3 firms compete by setting prices. As long as they can purchase for less than 20, 10 million consumers select to buy the good from the cheapest firm, and break indifferences at random with equal probabilities if more than one firm set the lowest price. a- The three firms have equal marginal costs c1 =c2 =c3 =5. Derive the demand and payoff function of each firm i as a function of the prices in the market. b- What is the set of non-dominated strategies (or prices) for each firm? c- Derive the Nash Equilibrium of this game. d- How do total consumer surplus, welfare, and profits in the market change relatively to a- above if firm 1 becomes more efficient, and specifically if c1 =2<c2=c3=5 How does total consumer surplus, welfare, and profits in the market change if relatively to d- above, while firm 1 becomes more efficient, firms 2 and 3 experience a cost-increase (e.g. inputs become harder to procure) so that c1 =2<c2 =c3 =7? f- In…An industry contains two firms producing homogenous goods, one whose costfunction is C(Q1) = 30Q1 and another whose cost function is C(Q2) = 30Q2. The demandfunction for the market is given by:P = 65 - QT where QT = Q1 + Q2. a. Assuming firms are choosing quantities according to the Cournot model, what iseach firm’s reaction function?b. Graph each firm’s reaction curve (on same graph).c. How much does each firm produce in the Nash equilibrium of Cournot's model?The total cost for a product-testing firm is C(q)=70 + 20q2 q= number of products tested Price of a product = average cost Each corporation purchases one product test per year from a product-testing firm in the same city. All other inputs are ubiquitous. Suppose five corporations are initially distributed uniformly, with one corporation in each city (A,B,C,D,E). Is the initial distribution a Nash Equilibrium? Demonstrate it is not by finding how much one corporation would pay if they deviate and move to another city? What is the average price of having two tests conducted? (Which is the price that the corporation would pay if they "live" in a city where two tests are conducted) The average price of moving and thus, having two tests is: $_____
- Assume the inverse demand function in a market is given by P ( Q ) = 500 − Q where Q is the total industry output, that is the sum of the output of all firms in the market. There are two firms (indexed by i = 1,2) who both have a cost of producing the good given by c ( q i ) = 10 ∗ q i The two firms are competing in the Cournot manner, that is they choose their quantities simultaneously in order to maximize profits. What is the best response of firm 1 if firm 2 chooses an output level of 200? (input a whole number:) The best response function of firm 1 with respect to firm 2's quantity choice takes the form: q 1 ( q 2 ) = w ∗ ( x − y ∗ q 2 − z ) where (w,x,y,z) are parameters of the problem. Solve for this best response function and provide the product (w*x*y*z) in the next blank: What is the Nash Equilibrium quantity produced by firm 1? (round to the nearest whole number)In the Bertrand model, suppose that each firm has a marginal cost of £5 and that firm 1 sets a price of £5, which of the following a best-response for firm 2? Click all the correct answers. £5.00 £4.98 £4.99 £5.20 £5.01In the two-firm linear demand case (with constant marginal costs) with homogeneous goods, let the superscript “c” denote Cournot, “s” denote Stackelberg, and “b” denote Bertrand. How does Consumer Surplus (CS) compare across the models? Choose the correct answer: (a) CSb > CSs > CSc (b) CSc > CSs > CSb (c) CSc > CSb > CSs (d) CSb > CSc > CSs (e) CSs > CSc > CSb (f) CSs > CSb > CSc
- Please sloved it carefully and with explaniation Carl and Simon are the only sellers of pumpkins at the market, where the total demand function for pumpkins is q =3 ,200−1,600p. The total number of pumpkins sold at the market is q = qC + qS, where qC is the number that Carl sells, qS is the number that Simon sells. The cost of producing pumpkins for each farmer is $.50 per pumpkin; the fixed costs are zero. .a. Find the Cournot equilibrium price and quantities. .b. Find the Bertrand equilibrium price and quantities. . .c. Suppose now that every spring the snow thaws off of Carl’s pumpkin field a week before it thaws off of Simon’s. Therefore, Carl can plant his pumpkins one week earlier than Simon while predicting Simon’s choice based on the previous year information. Simon observes Carl’s choice and chooses how much pumpkin to plant. Find the new equilibrium price and quantities. .d. Compare the quantities and prices in parts a, b, and c. Rank these outcomes according to Pareto…The steps for solving a maximization problem can include A. Using the constraints to eliminate some variables B. Finding the partial derivatives with respect to controls or choices C. Solving the FOC for the optimal choice D. All of the Above The definition of competitive equilibrium is A. A fight among firms that has drawn to a tie B. Allocations and prices such that all agents behave optimally and markets clear C. An economy in which each firm monopolistically sets prices D. Where the governmental exogenously sets prices to maximize welfareThe citizens of Ruritania are prodigious consumers of marmite. They can buy it from one of two sellers: Omni Corp (OCP) or the Umbrella Corporation. The marmite sold by each is identical to the other but for color of the packaging. OCP sells its marmite in a red package while Umbrella sells its marmite in a green package. Competition between the two rms follows the Cournot model. The inverse demand curve for marmite is p = 50 - q; where q is the total amount of marmite produced by OCP and Umbrella.The production costs consists of two components. The rst is processing, while the second comes from the price of the main ingredient. OCP has a constant marginal cost of processing of $2 a unit while Umbrella has a constant marginal processing cost of $4 a unit. The main ingredient of marmite is Soylent green which is sold by a monopolist, Soylent Corp. Soylent Corp enjoys a constant marginal cost of production for Soylent Green of $0 a unit. It requires 1 unit of Soylent…
- Consider a market with two firms. Each firm is located at one end of a line with lenght one. There is a mass one of consumers. The location of each consumer is given by 0 < x < 1 which is uniformly distributed (with density 1). Firms have no cost of production and set price simultaneously. a) Derive the demand for each firm by identifying the location of the indifferent consumer for each price pair. Assume that all consumers know about both products. b) Write down the profit functions and calculate the Nash equilibrium prices for both firms. c) Assume that consumers only know the product if they have received and ad. Suppose that ads are not targeted and each firm reaches any consumer with probability 0.5 with her ad. Calculate the size of the different consumer segments. Determine the resulting demand and the new Nash equilibirum prices of the firms. d) Suppose that the ads are costless. When do the firms make larger profits? With fully informed consuemers b) or with imperfect…Suppose that there are two firms competing in the market for taxi services. Big Ben Taxis has the marginal cost MCB = $9 per trip, and the fixed cost FCB = $3,000,000. While Whitehall Taxis has the marginal cost MCW = $15 per trip, and the fixed cost FCW =$1,000,000. Inverse demand for taxi trips in the market is given by the function, P=75− Q . 10,000 In this equation, P is the price of a taxi trip, and Q is the total quantity of taxi trips supplied by the two taxi companies. Question 1: Find the equilibrium price and quantities for the case in which the two taxi companies engage in Cournot (quantity) competition. What profits will Big Ben Taxis and Whitehall Taxis earn. Question 2: Using your answers to question 1, determine which firm has the greater market power. Question 3: Now suppose that a firm can only supply taxi services if it purchases a licence from the government. What is the highest fee that the government can charge for a license, if the government wants both Big Ben…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”)