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1. (Cournot's game with many firms) Consider Cournot's game in the case of an arbitrary number n of firms; retain the assumptions that the inverse demand function p(Q) = a - Q if Q ≤ a and 0 if Q > a. The cost function of each firm i is ci(qi) = (c/2)*qi^2 with c < a. Find the best response function of each firm and set up the conditions for(q*1, . . . , q∗n) to be a Nash equilibrium, assuming that there is a Nash equilibrium in which all firms' outputs are positive. Solve these equations to find the Nash equilibrium. (First show that in an equilibrium all firms produce the same output, then solve for that output. If you cannot show that all firms produce the same output, simply assume that they do.) Find the price at which output is sold in a Nash equilibrium and show that this price decreases as n increases as the number of firms increases without bound. 2. (Common pool resource game) Consider a common pool resource game with two appropriators. (If you don't know what is a common pool resource, read the Wikipedia article about the "Tragedy of the Commons".) Each appropriator has an endowment e > 0 that can be invested in an outside activity with marginal payoff c > 0 or into the common pool resource. Let x ∈ X ⊆ [0, e] denote the player's investment into the common pool resource (likewise y denotes the opponent's investment). The return from investment into the common pool resource is (x/(x+y))*(a(x+y)-b(x+y)^2 ), with a, b > 0. So the symmetric payoff function is given by π(x, y) = c(e-x)+ (x/(x+y))*(a(x+y)-b(x+y)^2 ) if x, y > 0 and c • e otherwise. Find Nash equilibrium of the game. Proceed by deriving the best response correspondences first. How does Nash equilibrium depend on parameters a, b, and c (varying one at a time and keeping the others fixed)?
A negative mean change in the LHS variable in the absence of a change in the RHS variable since you subtract the earlier period from the later period b. that the panel estimation approach is flawed since differencing the data eliminates the consta..
Wildcat Oil has recently discovered a new 500 million barrel crude oil reservoir in Kasakstan. Reservoir engineers predict recovery of about 300 million barrels with current technology. The firm needs a preliminary cost estimate for a feasibility stu..
A local cell phone monopoly faces the following monthly inverse-demand for lines from a typical family: P = 100 – 20Q. The total cost to the monopoly is C(Q) = 20Q. This implies that the marginal monthly cost to the monopoly is $20 per line.
1.the following information is available for an economyconsumption functionnbspnbspnbsp nbspnbspnbspnbspnbspnbsp c 220
Two months later, Mrs. Dodge split the workforce into two specialty groups, appointing Betty as the supervisor of one section and taking the other for herself. Betty's group consisted of three people: the two newest, whom she had trained, and one ..
draw a supplydemand diagram of the market for loanable funds in the u.s. use the interest rate as the price of loanable
It has often been said that craft unions (electricians, carpenters, etc.) possess considerably greater power to raise wages than do industrial unions (automobile workers, steel workers, etc.) How would you explain this phenomenon in terms of deman..
A certain engine lathe can be purchased for $270,000 and depreciated over three years to a zero salvage value with the SL method. This machine will produce metal parts that will generate revenues of $180,000 (time zero dollars) per year. It is a poli..
Suppose that Apple must pay a royalty on each mobile device that it produces. How should Apple adjust its production and price in response to the royalty?
What was the most "eye opening" information you learned about droughts? Why did you find it so interesting?
Lenders and borrowers are all so nervous that the huge planned increase in the money supply ,refrred to as 'quantitative easing' , may have much smaller stimulating effect than it would have in normal circumstances.This strategy is not without ris..
BMW Goes to War Against Chinese Carmaker
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