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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 经济代写|产业经济学代写Industrial Economics代考|Appendix

Assume that locations $(x)$ along the circle of unit length are measured in a trigonometric manner. Firm 1 is at $x=0$ and firm 2 at $x=s$ with $0<s \leq 1 / 2$.
$(U, U)$ : Consumers are indifferent between purchasing from either firm at points $x=\left(p_2-p_1+t s^2\right) 1 / 2 t s$ and $y=p_1-p_2+t\left(1-s^2\right) / 2 t(1-s)$. Consequently, profits of firm 1 are $\pi_1=p_1(1-\bar{y}+\bar{x})$ and profits of firm 2 are $\pi_2=p_2(\bar{y}-\bar{x})$. The unique price equilibrium is given by $(t s(1-s), t s(1-s))$, yielding equilibrium profits $(t s(1-s) / 2, t s(1-s) / 2)$.
$(D, D)$ : If both firms price discriminate, it is readily verified that the equilibrium price schedule is given by
$$p^(x)=\left{\begin{array}{l} \max \left{t x^2, t(x-s)^2\right} \text { for } 0 \leq x \leq 1 / 2 \ \max \left{t(1-x)^2, t(x-s)^2\right} \text { for } 1 / 2 \leq x \leq 1 / 2+s \ \max \left{t(1-x)^2, t(1-x+s)^2\right} \text { for } 1 / 2+s \leq x \leq 1 . \end{array}\right.$$ The market boundaries are given by $\bar{x}=s / 2$ and $\bar{y}=1 / 2+s+s / 2$, whereas the equilibrium profits are $$\pi_1=\int_0^{s / 2}\left[p^(x)-t x^2\right] d x+\int_{1 / 2+s}^1\left[p^*(x)-t(1-x)^2\right] d x=\frac{t s(1-s)}{4}$$
similarly
$$\pi_2=\frac{t s(1-s)}{4} .$$
$(U, D)$ : Firm 1 is the leader and prices uniformly at $p_1$. Given $p_1$, firm 2 sets a price at $x$ which is equal to the maximum of firm 1’s full price at $x$ and firm 2’s transportation cost to $x$.

## 经济代写|产业经济学代写Industrial Economics代考|Non-selective discounting

We begin by analysing the second stage of the two-stage game, so that the common list price, $\bar{p}$, and the distribution of list-price sales are given. We first consider the incentive to discount when $\bar{p}$ is strictly greater than marginal cost for each firm; subsequently we consider the determination of equilibrium list prices and contract quantities. The analysis in this section concerns discounts that must be made nonselectively to all current and potential buyers in a market where all contracts contain best-price provisions. We discuss the incentives to use such contracts subsequently.
Incentives to discount non-selectively
Consider a firm’s incentive to offer a discount price, $p_d$, if the list price $\tilde{p}$ is greater than the marginal cost for each seller. If all producers use the meet-or-release clauses in their contracts to match a discount, then the firm offering a small non-selective discount will not divert existing sales from its competitors. The potential new sales at a price $p_d($ below $\bar{p})$ are $\left[D\left(p_d\right)-D(\bar{p})\right]$. We analyse the profitability of non-selective discounting under the following assumption.
Assumption 3
If contracts contain meet-or-release and most-favoured-customer provisions, a discounter offering a price $p_d$ that exceeds other firms’ marginal costs will anticipate new sales of $\left[D\left(p_d\right)-D(\bar{p})\right]$ units.

If a firm did not exercise its meet-or-release option to match a discount that exceeds its marginal cost, it would lose all sales because the discount is non-selective, so that it is reasonable to assume that discounting can only be motivated by the prospect of new sales. The assumption that the discounter expects to obtain all new sales maximizes the incentive to give a unilateral non-selective discount. If we show that with this assumption there are some supracompetitive prices at which no firm has a unilateral incentive to discount, this result also holds under more conservative assumptions about the expected gains to discounting.

# 产业经济学代考

## 经济代写|产业经济学代写Industrial Economics代考|附录

$(U, U)$ 在某些情况下，消费者对从这两家公司购买商品漠不关心 $x=\left(p_2-p_1+t s^2\right) 1 / 2 t s$ 和 $y=p_1-p_2+t\left(1-s^2\right) / 2 t(1-s)$。因此，公司1的利润为 $\pi_1=p_1(1-\bar{y}+\bar{x})$ 公司2的利润是 $\pi_2=p_2(\bar{y}-\bar{x})$。唯一的价格均衡由 $(t s(1-s), t s(1-s))$，产生均衡利润 $(t s(1-s) / 2, t s(1-s) / 2)$.
$(D, D)$ :如果两家公司都有价格歧视，那么很容易证明均衡价格表由

$$\pi_2=\frac{t s(1-s)}{4} .$$
$(U, D)$ 1号公司是领导者，价格统一在 $p_1$。给定 $p_1$，公司2设定的价格 $x$ 哪一个等于公司1的全价最大值 $x$ 公司2的运输成本 $x$。

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