(4) Three firms, F₁, F2, F3 share the market for a certain commodity. F₁ has 20%, F2 has 60%and F3 has 20%. In the following year the changes accour:F₁ keeps 85% of its consumers, loses 5% to F2 and 10% to F3F2 keeps 55% of its consumers, loses 10% to F₁ and 35% to F3F3 keeps 85% of its consumers, loses 10% to F₁ and 5% to F2.Write the matrix S = the initial share and the matrix T = tij, the transformation matrix,where tij = what F; gets from Fj. Compute T - S,T· (TS), T · (T · (T· S)). What do theyrepresent?(5) Calculate the following determinants:3 -1 20 −1 -16 1 22-0 3 -10 4 000 1-123 25-330 11 0 -120 5

The initial market share of the three firm is . keeps of its consumer losses to and to keeps of…

Answered: (4) Three firms, F₁, F2, F3 share the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A financial manager has to invest $ 200000 in two options, one risky with a return of 20% and second less risky with a return of 10% per year. If the goal is to make $ 32000 at the end of the year what should be distribution of the money in both options.
A factory that produces hygiene materials produces hygiene packages with three different contents, namely individual, family, xl-family, from masks, disinfectants and soap products. Stocks of hygiene products vary from week to week. For this reason, the factory applies a different production schedule for each week. For example, for the next week, how many boxes of individual, family and xl-family hygiene packages can they produce and put up for sale by using 270 thousand masks, 130 thousand disinfectants and 85 thousand soaps? Use the Gaussian Seidal method to reach the solution with an error of 0.1. Let the initial values for mask, disinfectant and soap are given as 49, 19 and 4, respectively. The amount of products in the packages is given in the table.(Note: do not use the values in thousands when trading.You can take 270, 230 and 85)
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There are three players in a public good game. Each player (i=1,2,3) has 100 dollars to contribute the amount of money cı, i=1,2,3, for a public good. Each player's payoff depend on the following: (i) The amount of her remaining wealth 100-c, i=1,2,3, for spending in private good. 3. (ii) The amount of public good is equal to the sum of contributions from all players. (iii) Each person cares about the amount of public good and her consumption of private goods. Based on the above assumption, each players ui-(100+c)+(c1+c2+c3)(100-c), i=1,2,3 (a) What is the amount of each player contribute to the public good for Nash equilibrium for the non-cooperative simultaneous game? .What is total payoffs for all players in the non-cooperative simultaneous game? What is the amount of each player contributes to the public for social optimum if (b) (c) there are no discrimination of all players? Hint: The social optimum is the maximum total payoff if all players cooperate together. You might think…
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