Consider the price function y²-5Y+26, 0≤Y ≤ 10 Y≥ 10 P(Y) = where y₁ denotes the output of firm 1 and y2 denotes the output of firm 2 such that Y = y₁ + y2. Suppose that the total cost to each firm is given by TC;(yi) = 2y; for i = 1, 2. Use Cournot's Duopoly Model to find outputs y₁ and y2, profits ₁ and 72, and price P.
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- Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively isYou are the manager of Taurus Technologies, and your sole competitor is Spyder Technologies. The two firms' products are viewed as identical by most consumers. The relevant cost functions are (Q) = 4Qj, and the inverse market demand curve for this unique product is given by P= 940 -3 Q. Currently, you and your rival simultaneously (but independently) make production decisions, and the price you fetch for the product depends on the total amount produced by each firm. However, by making an unrecoverable fixed investment of $2,000, Taurus Technologies can bring its product to market before Spyder finalizes production plans. (Assume Taurus Technologies is the leader in this scenario.) What are your profits if you do not make the investment? What are your profits if you do make the investment? Instructions: Do not include the investment of $2,000 as part of your profit calculation. $ %24In the domestic airline market, where companies compete on the number of seats they make available in the market measured in millions (x), the inverse of the demand for seats is pd(x) = 40 - 4x.Assume that there are 2 airlines: LON and Pacific Airlines. The marginal cost per seat of both airlines is 10:(a) Determine the market equilibrium (quantity produced by each firm, market price and profits). Graph(b) Assume that LON and Aerolineas del Pacifico collude and act as a monopoly. Calculate the number of seats (x) and the selling price.(c) What is the efficient number of seats that should be made available to consumers, and at what price would each seat be sold?
- Consider the following oligopolistic market. In the first stage, Firm 1 chooses quantity q. Firms 2 and 3 observe Firm 1's choice, and then proceed to simultaneously choose q2 and q1, respectively. Market demand is given by p(O) = 100 – Q, and Q = q1 + 42 + 41. Firm 1's costs are c, (41) = 34, firm 2's costs are cz(4,) = 34; and firm 3's costs are cs(qs) = 3q,. Starting from the end of the game, you can express Firm 2's best response function in terms of q and q3, and you can similarly express Firm 3's best response function in terms of qi and q2. Using these, answer the following questions. a) If Firm 1 chooses q1 = 9, what quantity will Firm 2 choose? b) If Firm 1 chooses qi = 100, what quantity will Firm 2 choose? c) in the subgame perfect Nash equilibrium of this game, firm 1 produces what quantity? d) In the subgame perfect Nash equilibrium of this game, firm 2 and firm 3 each produce what quantity?The inverse market demand eurve for a Covid-19 mask is given by P(y) = 120 – 2y , and the total cost function for any firm in the industry is given by TC(y) = 4y • What will be the total output and price if there are two Cournot firms competing in the industry? • What would be the total output and price if two firms have decided to collude?You are the manager of Taurus Technologies, and your sole competitor is Spyder Technologies. The two firms’ products are viewed as identical by most consumers. The relevant cost functions are C(Qi) = 2Qi, and the inverse market demand curve for this unique product is given by P = 410 −2 Q. Currently, you and your rival simultaneously (but independently) make production decisions, and the price you fetch for the product depends on the total amount produced by each firm. However, by making an unrecoverable fixed investment of $1,000, Taurus Technologies can bring its product to market before Spyder finalizes production plans. (Assume Taurus Technologies is the leader in this scenario.)What are your profits if you do not make the investment? $What are your profits if you do make the investment?Instructions: Do not include the investment of $1,000 as part of your profit calculation. $.
- Consider the differentiated goods Bertrand price competition model where firms A and B produce similar goods and sell them at pA and pB. The demand for each firm’s product is given byqA =60−2pA +pB andqB =60–2pB +pA ,and there are NO costs of producing either good (all costs are 0). (a)Calculate the (Bertrand) equilibrium prices and the net profits of each firm (b) Now suppose that -instead of competing to maximize their own individual profits- the firms decide to “collude” and set prices pA and pB to maximize their joint profits (sum of their profits). What would be each firm’s optimal price and net profits? Compare these prices and profits with what you found in (a) (greater/smaller/the same?).Consider a duopoly with homogenous goods where Firm 1 has the following production function: Q1 = F1(L,K) = L1/2 K1/2, where Q and K are measured in units and L in hours. Firm 2 uses labour and capital as well but has a different production function, given by Q2 = F2(L,K) = L1/3 K2/3. You may assume that the market for labour and capital is perfectly competitive and the current wage rate is £40 and the rental rate on capital is £10. Both firms sell their products on the same market with inverse demand function P = 52 – (Q1 + Q2), where P is measured in pound sterling. Which production function(s) exhibit(s) decreasing returns to scale? Suppose Firm 1 wishes to produce 6 units. What is the cost minimising input mix for Firm 1? Suppose Firm 2 wishes to produce 4 units. What is the cost minimising input mix for Firm 2? Assume both firms now have the option to produce either 4 units or 6 units. We will consider the situation where both firms simultaneously, but independently,…Question 3:Suppose the inverse demand for a good is given by P = 50 – 4Q, where Q is the totalquantity supplied by all firms in the market. Suppose each firm in the market has a constantmarginal cost of 18.Q3 a) Assume the market consists of two firms that set their quantities simultaneously.Calculate the duopoly levels of production and the equilibrium price. Q3 b) Now assume firm 1 chooses its production level before firm 2 does. What will be theequilibrium quantities, price and profits in this case?Q3 c) Now instead suppose that the two firms compete over prices rather than quantities.What will be the equilibrium price and profits of firms 1 and 2 in this case? Finally, if firm 1manages to lower its marginal cost to 14, what will be the new equilibrium price, quantitiesand profits?
- 1. Consider a market where there are only two firms that produce a homogeneous product. The two firms face the direct market demand curve given Q = 15-p, where Q = 9₁ +92 and 9₁ and q2 are the quantities of firm 1 and firm 2, respectively. Suppose firm 1's total cost is C₁ = 9₁ and firm 2's total cost function is C₂ = 2q2. Suppose that the two firms act independently and choose their outputs simultaneously as in the Cournot model. Show the basis and briefly explain what is going on as you answer each of the following questions. Your mark will depend upon the correctness of your basis and explanation. 1. What is the equation of the demand curve faced by firm 1? What is the equation of the demand curve faced by firm 2? Find the output reaction function of each firm. 2. 3. Find the Nash-Cournot equilibrium quantity that each firm will produce. 4. At the Nash-Cournot equilibrium, at what price does each firm sell its output? 5. Find the consumer surplus, producer surplus at the…In the Cournot equilibirum, what is the market price and units produced by firm 1 and firm 2?Suppose Giocattolo of Italy and American Toy Company of the United States are the only two firms producing toys for sale in the U.S. market. Each firm realizes constant long-term costs so that the average total cost (ATC) equals the marginal cost (MC) at each level of output. Thus, MCo = ATCO is the long-term market supply schedule for toys. Suppose Giocattolo and American Toy Company operate as competitors, and the cost schedules of each company are MCo = ATCO = $10. On the following graph, use the grey point (star symbol) to identify the competitive market equilibrium. Then, use the green triangle (triangle symbols) to identify consumer surplus in this case. Note: Select and drag the point from the palette to the graph. Dashed drop lines will automatically extend to both axes. Then select and drag the shaded region from the palette to the graph. To resize the shaded region, select one of the points and move to the desired position. ? PRICE (Dollars per toy) 20 18 16 14 10 00 6 4 2 0…