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经济代写|国际经济学代写International Economics代考|Non-traded Goods
Some goods cannot be traded due to their very nature. For example, many services are actually location-specific and cannot be dissociated from service providers. Thus, trade in those services essentially depends on the movement of the service provider from one country to the other. But in such cases, these are not service trade but factor movements. Of course, with improvements in telecommunications, many services can be provided without the service provider moving from one location to the other. A typical example is core banking systems whereby customers can operate their accounts and get related banking services even without having to be physically present in the branch that they have their accounts in. At the other extreme is a hair cut, the service for which the provider and the customer must have physical contact.
For goods, tradability depends on both transport costs and their perishable nature. The higher the cost of transportation and the shorter the self life, the less tradable a good is. Freshly prepared food (not the packaged, frozen, or ready-to-eat variety), for example, is not generally a tradable good. It will be sold in the location that it is prepared in.
The most important implication of a non-traded good is that arbitrage is not possible and hence cross-country (or cross-location) price differences will persist. Thus, cost of a hair cut will differ in the United States and in India (when denominated in the same currency). Similarly, freshly prepared food in one city or country does not directly compete with the same elsewhere. The law of one price thus does not hold for non-traded goods. Their prices are locally determined, and their output levels are constrained by local demand conditions. Unlike traded goods, the economy cannot produce these goods in excess of what their demand is locally. As a consequence, the independence of factor prices from domestic demand conditions does not hold even for a small country as discussed earlier. Second, one-to-one correspondence may also break down as the local factor market conditions become important too, thus creating scope for factor prices to differ across trading nations. A simple check for both these is whether the number of traded goods is at least equal to the number of internationally immobile domestic factors of production.
经济代写|国际经济学代写International Economics代考|Advanced Topic: FPE in Higher Dimensions
The above cases of a specific factor production structure and a non-traded good suggests a simple rule for the validity of the FPE theorem in higher dimensions with respect to the number of goods produced in an economy and the number of factors of production it is endowed with. Suppose there are $m$ number of goods that are produced even after trade by $n$ number of domestic factors of production, and among these goods $t$ number of goods are being traded. Of course, $t \leq m$. With all other assumptions of the HOS model being satisfied, commodity trade will equalize factor prices across the trading nations if $m>t \geq n$. That is, the number of traded goods being produced is at least equal to the number of factors of production. The reason is simple. As demonstrated by Samuelson (1953), for $m>t=n$, given the prices of the traded goods, the $t$ number of zero profit conditions for the traded goods and $t$ number of least-cost input choice condition specified below provides us a perfectly determinate system of $t+t n$ number of independent equations to solve for $n$ number of factor prices and $t$ number of least-cost input choices:
$$
\begin{aligned}
&P_j=a_{1 j} W_1+a_{2 j} W_2+\ldots \ldots . .+a_{n j} W_n, j=1,2, \ldots t \
&a_{i j}=a_{i j}(W), \quad i=1,2, \ldots, n ; j=1,2, \ldots t
\end{aligned}
$$
where, $W$ is the wage or return to the factor $i$, and $W$ is the wage vector. Thus, factor prices get determined solely by the prices of the traded commodities in this instance, which is the basis for the FPE theorem. The factor prices being so determined, the zero profit conditions for the non-traded good along with conditions for the input choices in these sectors, on the other hand, determine the price of the non-traded good:
$$
\begin{aligned}
&P_j=a_{1 j} W_1+a_{2 j} W_2+\ldots \ldots \ldots+a_{n j} W_n, j=t+1, t+2, \ldots m \
&a_{i j}=a_{i j}(W), \quad i=1,2, \ldots, n ; j=t+1, t+2, \ldots m
\end{aligned}
$$
Thus, prices of non-traded goods are cost-determined here as discussed earlier. Note that for $m=t$, the equation system (7.35) and (7.36) drops out and we have an extension of the HOS model in $t \times n$ (or $m \times n$ ) dimension.
When $t>n$, the system of equations in (7.29) and (7.30) may seem to be over determinate as we have more equations to solve for the factor prices and the least-cost input combinations. But that is not the case because only $n$ number of traded goods will be domestically produced with the rest $(t-n)$ traded goods being entirely imported. The reason is simple. Once the $n$ number of factor prices get determined (along with the least-cost input choices) from any $n$ number of zero profit conditions, given the price of these traded goods, the cost of production for the rest $(t-n)$ of the traded goods are tied down accordingly. The production costs for these $(t-n)$ traded goods thus determined by the prices of the other traded goods will most likely not match with their prices that are, in turn, determined in the respective world markets. If all these production costs exceed the prices, these goods will not be produced at all. If some of these production costs, on the other hand, are lower than the given prices, producers will shift resources from other sectors to reap the profit opportunities in these sectors. Factor prices will, therefore, change raising production costs in some of the $n$ traded goods sectors causing them to shut down. Thus, at equilibrium, the economy will produce at most the $n$ number of traded goods. The system is once again determinate meaning that the one-to-one correspondence and consequently the FPE theorem still hold good.
经济代写|国际经济学代写国际经济代考|非贸易商品
有些商品由于其本身的性质而不能交易。例如，许多服务实际上是特定于位置的，无法与服务提供者分离。因此，这些服务的贸易基本上取决于服务提供者从一个国家到另一个国家的流动。但在这种情况下，这些不是服务贸易，而是要素流动。当然，随着电信技术的改进，许多服务都可以在服务提供者不从一个位置移动到另一个位置的情况下提供。一个典型的例子是核心银行系统，在这个系统中，客户可以操作他们的账户并获得相关的银行服务，甚至不需要亲自到他们的账户所在的分行。在另一个极端是理发，这种服务的提供者和顾客必须有身体接触
对于货物来说，可贸易性既取决于运输成本，也取决于其易腐性。运输成本越高，自身寿命越短，商品的可交易性就越低。例如，新鲜准备的食物(不是包装的、冷冻的或即食的品种)通常不是可交易的商品。它将在准备它的地点出售。
非贸易商品最重要的含义是套利是不可能的，因此跨国家(或跨地区)的价格差异将持续存在。因此，在美国和印度(以同样的货币计价)，理发的费用是不同的。同样，一个城市或国家的新鲜食品也不会与其他地方的同类食品直接竞争。因此，单一价格定律不适用于非贸易商品。它们的价格由当地决定，它们的产量受到当地需求条件的限制。与贸易商品不同，经济生产的这些商品不能超过当地的需求。因此，即使是像前面讨论的那样，对一个小国来说，要素价格独立于国内需求条件也不成立。其次，由于当地要素市场条件也变得重要，一对一的对应关系也可能被打破，从而为不同贸易国家之间的要素价格差异创造了空间。对这两种情况的一个简单检验是，贸易货物的数量是否至少等于在国际上不流动的国内生产要素的数量
经济代写|国际经济学代写国际经济学代考|高级主题:更高维度的FPE
以上关于特定要素生产结构和非贸易商品的例子，提出了一个关于经济中生产的商品数量和它所拥有的生产要素数量的高维FPE定理有效性的简单规则。假设有$n$个国内生产要素在贸易后生产的商品是$m$个，在这些商品中有$t$个正在进行贸易。当然，$t \leq m$。在满足HOS模型的所有其他假设的情况下，如果$m>t \geq n$，商品贸易将使贸易国的要素价格均衡。也就是说，被生产的贸易商品的数量至少等于生产要素的数量。原因很简单。正如Samuelson(1953)所证明的，对于$m>t=n$，在给定贸易商品价格的情况下，贸易商品的零利润条件的$t$个数和下面指定的最小成本投入选择条件的$t$个数，为我们提供了一个完全确定的系统，它有$t+t n$个数的独立方程来求解$n$个数的要素价格和$t$个数的最小成本投入选择:
$$
\begin{aligned}
&P_j=a_{1 j} W_1+a_{2 j} W_2+\ldots \ldots . .+a_{n j} W_n, j=1,2, \ldots t \
&a_{i j}=a_{i j}(W), \quad i=1,2, \ldots, n ; j=1,2, \ldots t
\end{aligned}
$$
，其中，$W$是工资或对因子$i$的回报，$W$是工资向量。因此，在这种情况下，要素价格完全由交易商品的价格决定，这是FPE定理的基础。在这样确定的条件下，非贸易商品的零利润条件以及这些部门的投入选择条件，另一方面决定了非贸易商品的价格:
$$
\begin{aligned}
&P_j=a_{1 j} W_1+a_{2 j} W_2+\ldots \ldots \ldots+a_{n j} W_n, j=t+1, t+2, \ldots m \
&a_{i j}=a_{i j}(W), \quad i=1,2, \ldots, n ; j=t+1, t+2, \ldots m
\end{aligned}
$$
因此，如前所述，非贸易商品的价格在这里是由成本决定的。注意，对于$m=t$，方程系统(7.35)和(7.36)被删除了，我们在$t \times n$(或$m \times n$)维度有了HOS模型的扩展
当$t>n$时，(7.29)和(7.30)中的方程组可能看起来过于确定，因为我们有更多的方程需要求解要素价格和最低成本投入组合。但事实并非如此，因为只有$n$数量的贸易商品将在国内生产，其余$(t-n)$贸易商品将完全进口。原因很简单。一旦从任何$n$数量的零利润条件中确定了$n$数量的要素价格(以及成本最小的投入选择)，给定这些贸易商品的价格，其余$(t-n)$的贸易商品的生产成本也相应受到限制。这些$(t-n)$贸易商品的生产成本因此由其他贸易商品的价格决定，很可能与它们在各自的世界市场上决定的价格不匹配。如果所有这些生产成本都超过了价格，这些货物就根本不会被生产出来。另一方面，如果其中一些生产成本低于给定的价格，生产者就会从其他部门转移资源，以获得这些部门的利润机会。因此，要素价格将发生变化，一些$n$贸易商品部门的生产成本上升，导致它们倒闭。因此，在均衡状态下，经济最多将生产$n$数量的贸易商品。这个系统再次被确定，这意味着一一对应，因此FPE定理仍然成立。
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