Use of the Nash Equilibrium on Firms Questions Homework Help

Use of the Nash Equilibrium on Firms Questions Homework Help

 
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Name: Chik Min Cheung AnsonI.D: 30092515Question 1:1)An indifference bend, with regard to two commodities, could be a chart appearing those combinations of the two commodities that take off the buyer similarly well off or similarly satisfied—hence indifferent—in having any combination on the bend.Standard indifference bend investigation works on a basic two-dimensional chart. Each hub speaks to one sort of financial great. Along the impassion bend, the shopper is detached between any of the combinations of products spoken to by focuses on the bend since the combination of products on an lack of interest bend give the same level of utility to the buyer.Y1Y2X1X2Quantity of yQuantity of x2) The indifference curves cannot meet each other. It is since at the point of tangency, the higher bend will grant as much as of the two commodities as is given by the lower lack of concern bend. This can be inconceivable.Indifference curves cannot meet each other because it would break down the indifference bend investigation. Usually since the buyer would have more than one point on the impassion bend giving him a diverse level of fulfillment.Quantity of xQuantity of yi3)We refer to X as a choice set consisting of n alternatives, and each alternative x ∈X is a consumption bundle of k different items. For example, the first element of the bundle could be food, the second element could be shelter and so on. We will denote preferences byշ, where x շy means that “x is strictly preferred to y.” All this means is that when a decision maker is asked to choose between x and y they will choose x. Similarly, x % y, means that “x is weakly preferred to y” and x շ∼y indicates that the decision maker is “indifferent between x and y.”The preference relationship % defines an ordering on X × X. We make the following three assumptions about preferences.Completeness. For all x, y ∈X either x շy, y շx, ory ∼x.given two alternatives the decisionmaker can compare the alternatives, and will strictly prefer one of thealternatives, or will be indifferent.Transitivity. For all triples x, y, z ∈X if x շy and y շzthen x շz.This result can be extended to environmentswith uncertainty, aswas shown by Leonard Savage. Consequently, we can say that individuals behave as if they are maximizing utility functions, which allows formarginal and calculus arguments. There is, however, one qualification.The utility function that represents the preferences is not unique. The utility function (preferences) are monotone increasing if x ≥ y implies that u1≥ u2and x > y implies that u2> u1. So the ranking will be b, c and a.If a third utility function is implemented the ranking will become a, c and b to maximize utility of bundles.4) MRS= y/2x, this calculation shows that when the slope of x1 increases the slope of x2 will decrease showing a clear view of the budget constraint.Question 3:1)Firm 1's best response function gives, for each possible output of firm 2, the profit-maximizing output of firm 1. Firm 1's profit-maximizing output when firm 2's output is y2 is the output y1 that maximizes firm 1's profit; that is, the value of y1 that maximizesP(y1 + y2)y1 TC1(y1).Differentiating with respect to y1 (treating y2 as a constant), we conclude that the profit-maximizing output y1 satisfiesP'(y1 + y2)y1 + P(y1 + y2) MC1(y1) = 0.firm 2 best responsefirm 1 best response2)To find a Nash equilibrium, we need to put together the two best response functions. Any pair (y1, y2) of outputs at which they intersect has the property thaty1 = b1(y2) and y2 = b2(y1)The best response functions are superimposed in the following figure.Firm 2’sNash equilibrium is higher than that of firm 1 because firm 2 is able to better allocate its resources and create more efficient production. 3)In a Nash equilibrium, each firm's output maximizes its profit given the output of the other firm. As we saw above, this implies that for a Nash equilibrium (y1*, y2*), firm 1's output y1* satisfiesP'(y1* + y2*)y1* + P(y1* + y2*) = MC1(y1*),and firm 2's output y2* satisfiesP'(y1* + y2*)y2* + P(y1* + y2*) = MC2(y2*).In particular, unless P'(y1* + y2*) = 0 (the demand curve is horizontal) the price P(y1* + y2*) is not equal to either firm's marginal cost at the output the firm produces.We conclude that the firms' outputs and the price are different in a Nash equilibrium than they are in a competitive equilibrium. If P'(y1* + y2*) < 0, as we should expect (the demand curve slopes down), price exceeds marginal cost, so that, as for a monopoly, the total output produced by the firms is less than the competitive output.An implication is that, as for a monopoly, the Nash equilibrium outcome in a Cournot duopoly is not Pareto efficient.Question 4:1)A) if only good H is produced at equilibrium and the consumer does not identify the type of umbrella that they want to purchase before purchasing it, the customer will likely not care as much about the quality and will initiate the game based on their previous belief that the umbrella will shield them from the rain. With this being said, should they decide to purchase umbrella L.it is worth noting that the costs to produce are higher than the selling price which shows that the game will be in favor of the customer.b) if only good L is produced at equilibrium, prices will rise on the short term and quantity will increase in the long-term depending on the players that want to enter the game. When competitors enter the game quantities will go up and prices will decrease which will work in favorably for the customer who seeks umbrellas forcing the equilibrium price and quantity to decrease.c) when the quantities produced are split half in half, equilibrium price and quantity will decrease because the customer will seek for the best option including mainly the price. In this duopoly when the competitors are in agreement with the pricing that they seek to create it will work best for the producers while if they are at conflict, they will have to compete with their prices which will naturally be in favor of the customer. With that being said, the customer goes into the game having the lower hand since the game starts depending on the decisions of both producers to be in compliance or at odds.2) A costly signalcan solidly uncover data. Since such signals are costly as a result less settled sorts care less almost an issue, as it were settled sorts are willing to pay them. This permits for sound data transmission. Since sanctions result in proficiency misfortunes, they can act as exorbitant signals.Costly signaling that can help seller H to distinguish themselves from seller L is the introduction of new technology in the umbrella market or the diversification of products.



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