This is a Hotelling model question There are two firms, A and B. Firm A has a marginal cost=$4, and Firm B has a marginal cost=$6. For both: N=4,000 V=max willingness to pay=$40 travel cost=$8/1mile Please find the best response functions for both firms and graph them.
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This is a Hotelling model question
There are two firms, A and B. Firm A has a marginal cost=$4, and Firm B has a marginal cost=$6.
For both:
N=4,000
V=max
travel cost=$8/1mile
Please find the best response functions for both firms and graph them.
Step by step
Solved in 3 steps with 2 images
- k : ces As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 50 percent chance of low demand and a 50 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P= 300,000-400Q and P= 500,000 -225Q, respectively. Your cost function is CQ) = 165,000+ 243,750Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes Profits you can expect: $1In the hotelling model, suppose firm 2 locates at 25 meters. Which of the following location choices for firm 1 gives highest profits? The scale goes up to 100 meters. 24 metres 25 metres 85 meteresA large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 150 - 0.02 x Demand for an annual printing of this particular product. The fixed costs per year (ie., per printing) = $46,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 3,000 units per year. The maximum profit that can be achieved is $. (Round to the nearest dollar.) The unit price at the point of optimal demand is $ per unit. (Round to the nearest cent.) Enter your answer in each of the answer boxes.
- A jewelry store makes necklaces and bracelets from gold and platinum. The store has developed the following lin- ear programming model for determining the number of necklaces and bracelets (x, and x,) to make in order to maximize profit: Maximize Z = 300x, + 400x2 (profit, $) subject to 3x1 + 2x2 < 18 (gold, oz) 2x, + 4x2 s 20 (platinum, oz) x2 54 (demand, bracelets) X1, x2 2 () a. Solve this model graphically. b. The maximum demand for bracelets is 4. If the store produces the optimal number of bracelets and neck- laces, will the maximum demand for bracelets be met? If not, by how much will it be missed? c. What profit for a necklace would result in no bracelets being produced, and what would be the op- timal solution for this problem?As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 300,000 – 400Q and P = 500,000 – 275Q, respectively. Your cost function is C(Q) = 140,000 + 240,000Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes Profits you can expect: $As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 400,000-400Q and P=900,000-2500, respectively. Your cost function is C(Q)=125,000+ 430,0000. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes
- Two firms, Firm 1 and Firm 2, compete by simultaneously choosing prices. Both firms sell an identical product for which each of 100 consumers has a maximum willingness to pay of $40. Each consumer will buy at most 1 unit, and will buy it from whichever firm charges the lowest price. If both firms set the same price, they share the market equally. Costs are given by ci(qi) = 16q₁. Because of government regulation, firms can only choose prices which are integer numbers, and they cannot price above $40. Answer the following: a) If Firm 1 chooses p₁ = 25, Firm 2's best response is to set what price? 24 b) If Firm 2 chooses the price determined in the previous question, Firm 1's best response is to choose what price? 23 c) If Firm 1 chooses p₁ = 12, Firm 2's best response is a range of prices. What is the lowest price in this range? 16 d) Now suppose both firms are capacity-constrained: Firm 1 can produce at most 34 units, and Firm 2 can produce at most 42 units. If firms set different…A supplier is selling tomatoes in two cities, Antalya and Istanbul. It costs him 1 TRY per kg of tomatoes delivered in each city. Let p1 be the price of a kg of tomatoes in Antalya and p2 be the price of a kg tomatoes in Istanbul. The price-response curves in each city: Antalya: d1(p1) = 500 - 100p1 Istanbul: d2(p2) = 1,200 - 200p2 Assuming the supplier can charge any price he likes, what prices should be charged for a kg of tomatoes in Antalya and Istanbul to maximize total contribution? What are the corresponding demands, revenues, and total contributions in each city? What is the total demand, total revenue, and total contribution over the two cities?Exercise 6.6. Consider a duopoly in which companies compete according to Cournot's model. The inverse market demand curve is: P(Q)=100-Q , where Q=Q1+Q2 and the average and marginal costs of firms are constant and equal to 40 Calculate profits would each company make? How much would company 1 be willing to invest to reduce its CM from 40 to 25, assuming company 2 does not support it? Graphically show and comment on all results.
- if the best response of firm 1: p1 = R1(p2) = (a - p2 - k) / 4 and the best response of firm 2: p2 = R2(p1) = (a - p1 - k) / 4. When subsitituting in a=8 and k=1 how do you solve this step by step to produce a best response functions simultaneously which will = 3.5Firm B Q=5 Q=6 Q=5 (24, 24) (30, 10) Q=6 (10, 30) (19, 19) Firm A This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide how much output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A, Profit for Firm B). Refer to Table. The dominant strategy For Firm A is to produce 5 units and the dominant strategy for Firm B is to produce 6 units. 5 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 6 units.As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 30 percent chance of low demand and a 70 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 400,000-250Q and P = 900,000-125Q, respectively. Your cost function is C(Q) = 185,000 + 652, 500Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes Profits you can expect: $