There are two firms in a homogenous product market described by the demand function P(q1,q2)%3D131-(1/5)(q1+q2), and both firms have marginal costs of 50. Firms choose once and simultaneously quantities. How much does firm 1 produce in equilibrium?
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- Two firms compete in selling homogeneous goods. They choose their output levels q1 and q2 simultaneously and face demand curve P=80-6Q, where Q=q1+q2. The total cost function of firm 1 is C1=8q1 and the total cost function of firm 2 is C2=32q2+2/3. a) Find and draw the reaction curves of the two firms. b) Compute equilibrium quantities, price and profits. Suppose now that firm 2, thanks to a technological innovation, becomes more efficient. The new total cost function of firm 2 is C2= 8q2 c) Compute the new equilibrium quantities, price and profits.Consider a market for crude oil production. There are two firms in the market. The marginal cost of firm 1 is 20, while that of firm 2 is 20. The marginal cost is assumed to be constant. The inverse demand for crude oil is P(Q)=200-Q, where Q is the total production in the market. These two firms are engaging in Cournot competition. Find the production quantity of firm 1 in Nash equilibrium. If necessary, round off two decimal places and answer up to one decimal place.Exercise 6.8. Two companies with cost functions C1 (q1 )=5q1 and C2 (q2)= 0.5 q2 ² supply the to the same market. If the inverse market demand function is given by P = 100 - 0,5Q , where Q = q₁ + q₂ , find a) The production level of each firm, the price and the profits if the companies compete according to the Cournot model. (b) The level of production of each undertaking, the price and the profits if the undertakings agree to jointly maximise their profits. Show the results with the help of graphs.
- Suppose that two identical firms produce widgets and that they are the only firms in the market. The average and marginal cost is €60 for each firm. Price is determined by the following demand curve: P = 300 – Q where Q = Q1 + Q2. Suppose firm 1 is the leader and firm 2 is the follower. The output produced by each firm in a Stackelberg equilibrium is A. Firm 1 will produce 60 and Firm 2 will produce 120 B. Firm 1 will produce 80 and Firm 2 will produce 40 C. Firm 1 will produce 120 and Firm 2 will produce 40 D. Firm 1 will produce 120 and Firm 2 will produce 60Assume 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)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?
- Consider two firms competing to sell a homogeneous product by setting price. The inverse demand curve is given by P = 40 − Q . Firm 1 has MC1(Q1) = 4 and firm 2 has MC2(Q2) = 4.5. Based on this information, we can conclude that the market price will be a. $4.25 and each firm will produce 18 units. b.$4 and each firm will produce 18 units. c. $4 and firm 1 will produce 36 units and firm 2 will produce 0 units. d. $4.50 and firm 1 will produce 36 units and firm 2 will produce 0 units.Consider two firms that produce the same product and sell it in a market with the following demand function: d(p) = max{0, 12 − p}, where p ≥ 0 is the unit price of the good. Suppose that, for technological reasons, firm 1 can produce either 4 units of output at the total cost of 10, or 6 units at the total cost of 15. Similarly, firm 2 can produce either 3 units of output at the total cost of 8, or 4 units at the total cost of 10. Assume that the firms make their production decisions simultaneously. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game. Now assume that firm 1 makes its decision first. Firm 2 decides how much to produce after it observes firm 1’s output. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game.Consider a market with two firms. Call them firm 1 and firm 2. The demand function describing the market is P = 216 – 0.4Q. Firms are initially identical, with the cost function C(q) = 140 + 40q. Calculate the total profits in the market. Under what conditions, the two firms may succeed to collude? How much would each firm earn if they could collude?
- Consider an identical n-firm Cournot market with market size S = 1, total demand p = 10 − Q (where Q is the total market quantity), and the total cost for each firm is C(q) = 1 + q. Assuming that firms continue to enter so long as profit is not negative, how many firms will enter the market in equilibrium?please solve the question completely. Suppose an industry consists of two firms that compete in prices. Each firm produces one product. The demand for each product is as follows: q1 = 25 - 5p1 + 2p2 q2 = 25 - 5p2 + 2p1 The cost functions are C(qi) = 2 + qi for i = 1; 2. (a) Are the products produced by these firms homogenous or differentiated? (b) Find the best response function for each rm. (c) How does the price firm 1 sets change with its belief about the price of its competitor\'s product? (d) What are the Nash equilibrium prices? (e) What is the percentage markup of price over marginal cost here (this is called the Lerner index)? Do the firms have market power? Why does the Bertrand paradox of zero variable duopoly profits apply here? (f) Suppose the firms merged. What is the new price of products 1 and 2? (g) Explain intuitively why the price is higher under monopoly than under Bertrand duopoly? (h) Are total monopoly profits higher or lower than the sum of Bertrand duopoly…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 efficiency.
