Consider two identical firms with a unit cost of production of $10 and a market demand of p= 60-y. (a) What is firm 1’s optimal output level as a function of firm 2’s output? (b) What is firm 2’s optimal output level as a function of firm 1’s output? (c) What is the Cournot equilibrium output level for these firms? (d) What is the Cournot equilibrium price level? Show your work step by step.
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- The inverse market demand for fax paper is given by P=100-Q. There are two firms who produce fax paper. Firm 1 has a cost of production of C1= 15*Q1 and firm 2 has a cost of production of C2=20*Q2 a) Suppose firm 1 and firm 2 compute simultaneously in quantities. What are the Cournot quantities and prices?What are the profits of firm 1 and 2?b) Suppose firm 1 and firm 2 compete simultaneously in prices. What are the Bertrand quantities and prices?What are the profits of firm 1 and 2?1. Suppose you are the economic adviser of a company producing three brands of mobile phones; Nokia 10, Samsung X and iPhone Z. Suppose further that, your company currently sells 120 Units of iPhone Z at ¢800 per unit, 150 units of Samsung X at ¢800 per unit and 200 units of Nokia 10 at ¢100 per unit, but in a bid to maximize profit, the company’s managing director proposes an increase in price of Samsung X from ¢800 to ¢1000 per unit for which quantity demanded is anticipated to fall from 150 to 100 units; iPhone Z from ¢800 to ¢1200 per unit for which quantity demanded is anticipated to fall from 120 to 100 units; and Nokia 10 from ¢100 to ¢200 per unit for which quantity demanded is expected to fall from 200 to 100 units. I. Using the mid-point formula, compute the price elasticity of demand for each brand. II. From your answer in i, what is the type and economic interpretation of each brand’s value of elasticityConsider an industry with two firms, each of which has a constant marginal cost of 20. The inverse demand facing this industry is P(Y) = 220 −Y, where Y = y1 + y2 is the total output. 1. What is the competitive level of output? (Recall: price equals marginal cost at the competitive equilibrium.) 2. What is the output of each firm in the Cournot equilibrium? 3. What is the output of each firm in the Stackelberg equilibrium when firm 1 is the follower and firm 2 is the leader?
- a)Consider a homogeneous goods industry where two firms operate and the linear demand is given by p(y1 + y2 ) = a - b(y1 + y2 ), where p is the market price, and y1 (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 2. Explain the term best response (reaction curve). Illustrate the best responses in a diagram. b) For the case in (a) determine the Cournot equilibrium (Nash equilibrium in quantities) when firm 1 and firm 2 compete simultaneously in quantities. How large are firm 1’s and firm 2’s profits? What is the industry output? c) Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its price to maximise its profit. Firm 1 correctly forecasts that the follower takes the price leader’s…a)Consider a homogeneous goods industry where two firms operate and the linear demand is given by p(y1 + y2 ) = a - b(y1 + y2 ), where p is the market price, and y1 (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 2. Explain the term best response (reaction curve). Illustrate the best responses in a diagram. b) For the case in (a) determine the Cournot equilibrium (Nash equilibrium in quantities) when firm 1 and firm 2 compete simultaneously in quantities. How large are firm 1’s and firm 2’s profits? What is the industry output? c) Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its price to maximise its profit. Firm 1 correctly forecasts that the follower takes the price…(a) Consider a homogeneous goods industry where two firms operate and the linear demand is given by p(y1 + y2 ) = a - b(y1 + y2 ), where p is the market price, and y1 (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 2. Explain the term best response (reaction curve). Illustrate the best responses in a diagram. b) For the case in (a) determine the Cournot equilibrium (Nash equilibrium in quantities) when firm 1 and firm 2 compete simultaneously in How large are firm 1’s and firm 2’s profits? What is the industry output?
- Suppose that Market demand for golf balls is described by Q= 90-3p,Where Q is measured in kilos of balls. There are two firms that supply the market. Firm 1 can produce a kilo of balls at a constant unit cost of $15 whereas firm 2 has a constant unit cost equal to $10.a. suppose firms compete in quantities. How much does each firm sell in a Cournot equilibrium? What is the market price and what are firms' profit?b. suppose firms compete in price. How much does each firm sell in a Bertrand equilibrium. What is market price and what are firms' profits?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?You are the manager of BlackSpot Computers, which competes directly with Condensed Computers to sell high-powered computers to businesses. From the two businesses’ perspectives, the two products are indistinguishable. The large investment required to build production facilities prohibits other firms from entering this market, and existing firms operate under the assumption that the rival will hold output constant. The inverse market demand for computers is P = 5,900 − Q, and both firms produce at a marginal cost of $800 per computer. Currently, BlackSpot earns revenues of $4.25 million and profits (net of investment, R&D, and other fixed costs) of $890,000. The engineering department at BlackSpot has been steadily working on developing an assembly method that would dramatically reduce the marginal cost of producing these high-powered computers and has found a process that allows it to manufacture each computer at a marginal cost of $500. How will this technological advance impact…
- You are the manager of BlackSpot Computers, which competes directly with Condensed Computers to sell highpowered computers to businesses. From the two businesses’ perspectives, the two products are indistinguishable. The large investment required to build production facilities prohibits other firms from entering this market, and existing firms operate under the assumption that the rival will hold output constant. The inverse market demand for computers is P=5900-Q , and both firms produce at a marginal cost of $800 per computer. Currently, BlackSpot earns revenues of $4.25 million and profits (net of investment, R&D, and other fixed costs) of $890,000. The engineering department at BlackSpot has been steadily working on developing an assembly method that would dramatically reduce the marginal cost of producing these high-powered computers and has found a process that allows it to manufacture each computer at a marginal cost of $500. How will this technological advance impact your…1. Suppose that market demand is given by ? = 120 − ?/3. The two identical firms in the market both have marginal costs of 20. Draw the reaction curves on a graph and find the Cournot equilibrium quantities and price.A homogeneous products duopoly faces a market demand function given by Q = 20-2P, where Q = Q1 + Q2. Both firms have a constant marginal cost MC = 4. 1. Suppose the two firms set their quantities simultaneously by guessing the other firm's quantity choice. Derive the equation of each firm's reaction curve and then graph these curves. 2. What is the Cournot equilibrium quantity and price in this market for each firm? 3. What would the equilibrium price in this market be if it were perfectly competitive? 4. What is the Bertrand equilibrium price in this market?