来源: 学校期中考古题 科目: 区域经济学 问题: In the market of "alcohol", the consumer preference for the "degree of liquor" on the alcohol is during 8%-48%, and the consumers preference with liquor degree during 8% and 48% is uniform distribution, and assume that every consumer buys only one unit of this alcohol, and its utility of the consumer associated with the preference q with purchased the liquor from firm i is specified by U(x) = a - p(xi) - c(q-qi)^2, where a denotes the reservation price of consuming the alcohol for the consumer associated with the preference q, in which the reservation price is identical for all the consumers with the preference over q in [8%,48%], the marginal cost of producing the alcohol by each firm is identical and given by k, then(40%) (i), if the production on the degree of the alcohol for both firms is constrained with qi in [8%, 48%], and both firms compete the choice of the degree of alcohol (First stage), then price determination(Second stage), please find the equilibrium prices, the degree of the alcohol, and the profits with Nash game for both firms; (ii), if there is not any constrain for the degree of the alcohol to be produced by the both firms, that is, the firm can produce the alcohol with any degree, then follow the previous two-stage game, both firms can determine both the degree of the alcohol as well as prices to maximize their profits, then please find the Nash equilibrium degree of the alcohol, price, and profit for both firms. (iii), how to interpret the equilibrium result between assumption with constrain and non-constrain? 我的想法: 在练习题目的时候，对於题目中的变数一直搞不清楚 q指的是消费者偏好，那 U(x) = a - p(xi) - c(q-qi)^2中x指的是什麽呢？ 我是把它想做厂商所生产的degree 但是这样子的话，式子中的q-qi又代表什麽意义呢？ 我自己的想法是qi是某个消费者的偏好 而是式子中的q是厂商所生产的degree 所以我用xi来代换q，而变成U(x) = a - p(xi) - c(xi-qi)^2 亦即若厂商生产xi的与消费者偏好qi差越多则效用会减少 接着才开始求(i)两厂商竞争的解 求解过程如下： 先假设 x1 >= x2 >= 0 U(x2) = a - p(x2) - c(x2-q2)^2 q2 = x2 +- (a/c - p2/c)^(1/2) 再利用 U(x1) = a - p(x1) - c(x1-q1)^2 = a - p(x2) - c(x2-q1)^2 q1 = [p(x1) - p(x2)] / c(x1 - x2) + (x1 + x2) 目前是做到这 因为不确定想法对不对 想来请教一下版上的高手 因为我是自己跑去外系修课，所以没人能请教 希望大家可以帮忙一下，感谢！！！！ --

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