O Two companies, player 1 and player 2, must decide how much time to devote to a jointproject. If player 1 contributes x > 0 hours and player 2 contributes y > 0 hours then thevalue of the project to the companies is x + y + xy/2.The contribution of the two companies come at different costs: (1) Contributing x costsplayer 1 a? /2; (b) contributing y costs player 2 cy² where c = 1/2 or c = 1.Player 2 knows the value of c bụt player 1 does not. Player 1 believes that c =1/2 withprobability p and c = 1 with probability 1 – p.(i) Write down the maximisation problem that player 2 needs to solve to optimise theirown effort, and hence show that2+ xYopt4c(ii) Write the maximisation problem facing player 1 in optimising their effort.(iii) Find the Bayes-Nash equilibrium as a function of p for x and y at the two costvalues.

As per the question, we consider a game between two players who must independently choose their…

Answered: (i) Write down the maximisation problem…

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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Minimize subject to C = 18x₁ + 2x2 4x₁ + x₂ ≥17 3x₁ + x₂ ≥4 X1, X₂ ≥0 a. Form the dual problem. Maximize subject to P = y₁ +4Y2 Y₁ + | 2 y₂ ≤ 18 Y₁ + V1, V₂20 y₂ ≤
A dealer wishes to purchase a number of fans and sewing machines. He has only 5760 ETB to invest and has space for almost 20 items. A fan costs him 360 ETB and sewing machine 240 ETB. His expectation is that he can sell a fan at profit of 22 ETB and a sewing machine at a profit of 18 ETB. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit? (Note: ETB = Ethiopian Birr) Formulate it as a linear programming problem (LPP) Use the graphical method to solve it.
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P= 18x1 + X2 2x1 + X2 5 4 X1 + 8x2 5 4 X1, X2 20 Maximize subject to e.
A company produces two products in the amount x andy and the respective prices Px and Px. The two prices are given to be Px = 48-x-y Py = 60 - x - 2y If the unit cost of producing the first product is 8 and that of producing the second is 4, what are the production levels x and y that maximize profit? Prove that profit is indeed maximized.
3 Consider two assets: rı = (:) If the asset prices are qi 2, 1 r2 92 2 respectively, find the cost of the portfolio with returns ) in the two states -2 respectively.
Suppose the demand functions faced by the monopolist firm are as follows: Q1 = 40 -2P1 + P2 Q2 = 15 + P1 – P2 Whereas, the cost function is given as : C = Q21 +Q1Q2 +Q22 Find the Maximum level of profit and also identify the optimal level of P1 and P2.
The question is attached in the image. I mostly encounter problems while calculating competitive equilibrium prices. I sincerely request the expert to resolve all of the following doubts. Please answer the questions individually. The questions asks us to find competitive price equilibrium. Please answer the following questions: 1. Find the competitive equilibrium prices. 2. Notice that the endowment is a parito efficient point. If endowment is pareto efficient, then why will they even trade? Agent 1 lexicographically prefers y and has all of y; so Agent 1 has not incentive to trade. Could a price equilibrium still exist? 3. The correct answer is C, px/py belongs to (0,1] according to university's records. If px=0 and py>0 (lets say py=1) then agent 2 demands only x and agent 1 demands y irrespective of prices. So, supply will be equal to demand, market clears and px/py=0. Why can px/py not be equal to 0 and correct option be B? (I understand that we could not have py=0 since…
Consider a two-period small open economy without production and a representative household, which lives for two periods. It receives endowments in the first period (Qi) and second period (Q2), respectively. The household inherits no wealth and optimally decides how much to consume in the first period (C1) and second period (C2) as well as international bond holdings (B1) in the first period, which pays the interest rate R. Household preferences are given by U(C1; C2) = log(C1)+log(C2). Explain in THREE sentences the effects of anticipated permanent improvement in terms of trade

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