# 经济代写|国际经济学代写International Economics代考|ECN422

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学代考|高级主题:更高维度的FPE

\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}

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