Find the agreement compatible with PAR, SYM, and IIA for the bargaining problem (U, d) in which U is the triangle with corners at (0,0), (1,1), and (2,0), and d = = (0,0).
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- Consider a duopoly market, where two firms sell differentiated products, which are imperfect substitutes. The market can be modelled as a static price competition game, similar to a linear city model. The two firms choose prices p, and p2 simultaneously. The derived demand functions for the two firms are: D1 (P1, P2) = SG+P1)and D2 (P1, P2)= S(;+-P2), where S > 0 and the parameter t > 0 measures the 2t 2t degree of product differentiation. Both firms have constant marginal cost c> 0 for production. (a) Derive the Nash equilibrium of this game, including the prices, outputs and profit of the two firms. (b) From the demand functions, qi= D¡ (p; , p¡ )= SG+P), derive the residual inverse demand functions: p; = P; (qi , p¡) (work out: P; (qi , P;)). Show that for t > 0, P;(qi , P;) is downward 2t aPi (qi ,Pj) . sloping, i.e., c, i.e., firm į has market power. %3D (c) Calculate the limits of the equilibrium prices and profit as t → 0 ? What is P; (qi , p;) as t → 0? Is it downward sloping?…QUESTION 13 Consider a market where two firms (1 and 2) produce differentiated goods and compete in prices. The demand for firm 1 is given by D₁(P₁, P2) = 140 - 2p1 + P2 and demand for firm 2's product is D2 (P1, P2) 140 - 2p2 + P1 Both firms have a constant marginal cost of 20. What is the Nash equilibrium price of firm 1? (Only give a full number; if necessary, round to the lower integer; no dollar sign.)Solve part 2 and 3 Only
- Describe the four fundamental principles of integrative negotiation.Pre-mixed concrete is an important input for the construction industry. Concrete cannot be stored or transported over long distances as it begins to set after only a few hours. For this reason, only the three local firms—Aggregate Inc., Big Industries and ConCorp—are in a position to compete in the market. Moreover, the capital and regulatory requirements for constructing a new concrete plant are substantial, creating an effective barrier to entry. Pre-mixed concrete is regarded as a homogeneous good by the construction industry. Inverse demand in the market has been estimated to be,P = 670 − Q/40,where P represents the price of a cubic metre of concrete in dollars, and Q is the total number of cubic metres of concrete supplied into the market on a given day. At present the three firms appear have identical production costs, with each firm facing fixed costs of $400,000 per day and a marginal cost of $190 per cubic metre. Big Industries and ConCorp estimate that the proposed merger…Pre-mixed concrete is an important input for the construction industry. Concrete cannot be stored or transported over long distances as it begins to set after only a few hours. For this reason, only the three local firms—Aggregate Inc., Big Industries and ConCorp—are in a position to compete in the market. Moreover, the capital and regulatory requirements for constructing a new concrete plant are substantial, creating an effective barrier to entry. Pre-mixed concrete is regarded as a homogeneous good by the construction industry. Inverse demand in the market has been estimated to be,P = 670 − Q/40,where P represents the price of a cubic metre of concrete in dollars, and Q is the total number of cubic metres of concrete supplied into the market on a given day. At present the three firms appear have identical production costs, with each firm facing fixed costs of $400,000 per day and a marginal cost of $190 per cubic metre. Big Industries and ConCorp estimate that the proposed merger…
- Suppose that there are two firms in the market. The market demand is given by P=220 - 2Q, where Q is the total output (Q=Q1+Q2). Each firm has an identical cost function, TCi=8Qi, i=1, 2. Consider the collusion, in which they decide the output level together to maximize the joint profit. If they divide the production into half, then each firm should produce Qi= _______ units in order to maximize the joint profit.There are two adjacent coal fields A and B. Under the fields is a common pool of coal worth $12 million. Drilling to extract the coal costs $1 million. If each company drills, each will get half the coal and each will earn a $5 million profit. Either company could drill a second time. If one company has two of the three wells drilled, that company gets two-thirds of the coal, yielding a profit of $6 million, and the other company gets one-third of the coal, for a profit of $3 million. If both companies drill a second well, the companies again split the coal, and each earn a profit of $4 million. What is company A's dominant strategy? Should it drill one well, two wells, or is there no dominant strategy? What is company B's dominant strategy? Should it drill one well, two wells, or is there no dominant strategy? What is the Nash equilibrium?Sport O Rama Equipment Inc., makes two different types of baseball gloves: a regular model and a catcher’s model. The firm has 900 hours of production time available in its cutting and sewing department, 300 hours available in its finishing department, and 100 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: MODEL Production time (hrs): Cutting & Sewing Production time (hrs): Finishing Production time (hrs): Packaging & Shipping Profit/Glove ($) REGULAR 1 1/2 1/8 $ 5 CATCHER'S 3/2 1/3 1/4 $ 8 Assume that Sports O Rama Equipment Inc. is interested in maximizing the total profit contribution, answer the following: How many hours of production time will be scheduled in each department? What is the slack time in each department?
- Extend the Cournot model discussed in class to two firms with setup costs. Firm 2 chooses to produce q; at cost cq; where c> 0. The set up costs are denoted by K₁ < K2 respectively for firm 1 and 2. The selling price is P(Q) = (a - bQ) where Q = 91 + 92. What are the optimal production quantities for each firm? (Hint: A firm has the option of not producing at all with a cost of zero).Pre-mixed concrete is an important input for the construction industry. Concrete cannot be stored or transported over long distances as it begins to set after only a few hours. For this reason, only the three local firms—Aggregate Inc., Big Industries and ConCorp—are in a position to compete in the market. Moreover, the capital and regulatory requirements for constructing a new concrete plant are substantial, creating an effective barrier to entry. Pre-mixed concrete is regarded as a homogeneous good by the construction industry. Inverse demand in the market has been estimated to be,P = 670 − Q/40,where P represents the price of a cubic metre of concrete in dollars, and Q is the total number of cubic metres of concrete supplied into the market on a given day. At present the three firms appear have identical production costs, with each firm facing fixed costs of $400,000 per day and a marginal cost of $190 per cubic metre. Big Industries and ConCorp estimate that the proposed merger…Pre-mixed concrete is an important input for the construction industry. Concrete cannot be stored or transported over long distances as it begins to set after only a few hours. For this reason, only the three local firms—Aggregate Inc., Big Industries and ConCorp—are in a position to compete in the market. Moreover, the capital and regulatory requirements for constructing a new concrete plant are substantial, creating an effective barrier to entry. Pre-mixed concrete is regarded as a homogeneous good by the construction industry. Inverse demand in the market has been estimated to be,P = 670 − Q/40,where P represents the price of a cubic metre of concrete in dollars, and Q is the total number of cubic metres of concrete supplied into the market on a given day. At present the three firms appear have identical production costs, with each firm facing fixed costs of $400,000 per day and a marginal cost of $190 per cubic metre. Big Industries and ConCorp estimate that the proposed merger…