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经济代写|国际经济学代写International Economics代考|Returns to Scale and Convexity of the Production Set

Shape of PPF depends on how does the opportunity cost or MRT change when production of cotton textiles is increased and correspondingly the production of computers is decreased. If the opportunity cost or MRT increases, PPF is strictly concave. Opportunity cost is essentially the ratio of social marginal costs, and in absence of any production externality private and social marginal costs are the same. Thus a change in the ratio of private marginal costs, which is determined by both the returns to scale and the law of diminishing marginal productivities, governs the shape of PPF.

To explain, suppose at an initial relative price $p_o$, the economy was producing $T_o$ units of textiles and $C_o$ units of computers. Suppose also that at the initial wage-rental ratio, computers were produced by a relatively capital-intensive technique of production and textiles were produced by a relatively labour-intensive technique of production. Now consider an additional unit of production of textiles. With all resources initially fully employed, this requires a corresponding reduction in the production of computers. At the initial wage-rental ratio, producers of textiles will maintain the same technique of production while expanding their production. There will thus be a scale expansion in the textiles sector, that is, use of labour and additional capital will be increased proportionately. For similar reasons, a scale contraction will take place in the computer sector. Corresponding changes in marginal costs of production in the two sectors will therefore be governed by the returns to scale. If both the goods are produced under constant returns to scale (CRS) technology, the marginal cost of production, at initial factor prices, should remain constant in both the sectors. Hence, at initial factor prices, an expansion in the production of textiles and a corresponding contraction in the production of computers along PPF will not change the opportunity cost or MRT. If the goods are, however, produced under IRS, then the marginal cost of production should decline in the expanding textiles sector and should rise in the contracting computer sector. Note that IRS technology means that an additional unit of production of textiles requires less than one unit of additional labour and capital, and this is why average and marginal costs decline. Thus, under IRS, MRT declines at initial factor prices. Similarly, if the goods are produced by decreasing returns to scale technology, MRT at initial factor prices rises as textiles production expands.

经济代写|国际经济学代写International Economics代考|MEASURING THE WELFARE CHANGE

Gains from trade (GFT) is a theorem regarding pre- and post-trade welfare levels. But social welfare is not always measurable, particularly because of its ordinal utility dimension. The duality approach, however, provides us a more convenient way of measuring GFT in terms of the expenditure function. The expenditure function, which indicates the minimum expenditure to attain a particular level of welfare or utility, can be used to measure change in welfare or utility in monetary units. Two concepts are particularly relevant here. One is the compensating variation (CV) and the other is the equivalent variation (EV).

Compensating variation (CV) requires the amount of money that is to be given to a consumer to fully offset her for the loss from a price rise, that is, to allow her to remain on the same indifference curve as before the price rise. Equivalent variation (EV), on the other hand, considers what fall in money income would hurt a buyer as much as the price increase does. Figure $3.1$ illustrates these two measures for a typical consumer’s choice problem. The representative buyer allocates her given money income $M_o$ on two goods- $X$ and $Y$-and does not save. Her preference ordering satisfies all the standard axioms and assumptions, which can be represented by smooth, downward sloping, and a strictly convex set of indifference curves, with successively higher indifference curves indicating successively higher utility indices. Given a budget set $\left{M_o, P_X^o, P_Y^o\right}$, the consumer’s most preferred bundle is indicated by $C_o$ on the budget line $A B_{\mathrm{o}}$. An increase in price of good $X$, ceteris paribus, rotates her budget line to $A B_1$, and changes the most preferred bundle to $C_1$. Her utility falls to $U_1$.

Under compensating variation, the consumer must be given a money income that pushes her budget line to the one labeled $\mathrm{CV}$ to allow her to consume the bundle $C_O^*$ on the earlier higher indifference curve $U_0$. Let $e\left(p_1, U_0\right)$ and $e\left(p_1, U_1\right)$ denote respectively minimum expenditures required to attain utility level $U_n$ and $U_1$ at the new price $p_1=\left{P_X^1, P_Y^o\right}$. Hence, the CV measure of welfare change of this price increase is the difference $\left[e\left(p_1, U_0\right)-\right.$ $\left.e\left(p_1, U_1\right)\right]$

On the other hand, for measuring the welfare change by EV, we allow the consumer to buy goods at the initial prices but hypothetically tax the consumer so that her budget line shifts down to the one labeled $\mathrm{EV}$ to enable her to purchase the bundle $C_1^*$. This amount of money income that is taxed away, $\left[e\left(p_0, U_0\right)-e\left(p_0, U_1\right)\right]$, is the EV measure of the change in welfare following the price rise.

In the next two sections, we use these alternative monetary measures of welfare change to measure or estimate GFT.

经济代写|国际经济学代写International Economics代考|EC3016

经济代写|国际经济学代写International Economics代考|Returns to Scale and Convexity of the Production Set

PPF的形状取决于当棉纺织品的产量增加而相应的计算机产量减少时机会成本或MRT如何变化。如果机会成本或 MRT 增加,则 PPF 是严格凹的。机会成本本质上是社会边际成本的比率,在没有任何生产外部性的情况下,私人和社会边际成本是相同的。因此,由规模报酬和边际生产率递减规律决定的私人边际成本比率的变化决定了 PPF 的形状。

为了解释,假设在初始相对价格p○, 经济正在生产吨○纺织单位和C○计算机单位。还假设在最初的工资-租金比率下,计算机是由一种相对资本密集型的​​生产技术生产的,而纺织品是由一种相对劳动密集型的生产技术生产的。现在考虑一个额外的纺织品生产单位。在所有资源最初得到充分利用的情况下,这需要相应减少计算机的生产。在最初的工资-租金比率下,纺织品生产商将在扩大生产的同时保持相同的生产技术。因此,纺织行业将出现规模扩张,即按比例增加劳动力和额外资本的使用。出于同样的原因,计算机领域也将出现规模收缩。因此,这两个部门的边际生产成本的相应变化将受规模回报的支配。如果这两种商品都是在规模报酬不变 (CRS) 技术下生产的,那么在这两个部门中,以初始要素价格计算的边际生产成本应该保持不变。因此,在初始要素价格下,纺织品生产的扩张和 PPF 计算机生产的相应收缩不会改变机会成本或 MRT。然而,如果货物是在 IRS 下生产的,那么边际生产成本在不断扩大的纺织部门中应该会下降,而在收缩的计算机部门中应该会上升。请注意,IRS 技术意味着增加一个单位的纺织品生产需要少于一个单位的额外劳动力和资本,这就是平均成本和边际成本下降的原因。因此,在 IRS 下,MRT 以初始要素价格下降。类似地,如果商品是通过规模收益递减技术生产的,则 MRT 的初始要素价格会随着纺织品生产的扩大而上升。

经济代写|国际经济学代写International Economics代考|MEASURING THE WELFARE CHANGE

贸易收益 (GFT) 是关于贸易前后福利水平的定理。但社会福利并不总是可衡量的,特别是因为它的序数效用维度。然而,对偶方法为我们提供了一种根据支出函数来衡量 GFT 的更方便的方法。支出函数表示达到特定福利或效用水平的最低支出,可用于衡量货币单位的福利或效用的变化。有两个概念在这里特别重要。一种是补偿变化(CV),另一种是等效变化(EV)。

补偿变化(CV)要求给予消费者的货币量以完全抵消价格上涨造成的损失,也就是说,允许她保持与价格上涨前相同的无差异曲线。另一方面,当量变化 (EV) 考虑到货币收入下降对购买者的伤害与价格上涨对购买者的伤害一样大。数字3.1说明了典型消费者选择问题的这两个度量。代表买方分配她给定的货币收入米○在两种商品上——X和是- 并且不保存。她的偏好排序满足所有标准公理和假设,可以用平滑的、向下倾斜的和严格凸的无差异曲线集来表示,无差异曲线越高表示效用指数越高。给定一个预算集\left{M_o, P_X^o, P_Y^o\right}\left{M_o, P_X^o, P_Y^o\right},消费者最喜欢的捆绑包由C○在预算线上一个乙○. 商品价格上涨X,在其他条件不变的情况下,将她的预算线旋转到一个乙1,并将最喜欢的捆绑包更改为C1. 她的效用下降到在1.

在补偿变差下,消费者必须获得将她的预算线推高到标有的那一项的货币收入C在让她吃掉包裹C○∗在较早的较高无差异曲线上在0. 让和(p1,在0)和和(p1,在1)分别表示达到效用水平所需的最低支出在n和在1以新价格p_1=\left{P_X^1, P_Y^o\right}p_1=\left{P_X^1, P_Y^o\right}. 因此,这种价格上涨的福利变化的 CV 度量是差[和(p1,在0)− 和(p1,在1)]

另一方面,为了通过 EV 衡量福利变化,我们允许消费者以初始价格购买商品,但假设对消费者征税,因此她的预算线下移到标有和在使她能够购买捆绑包C1∗. 被征税的这笔钱收入,[和(p0,在0)−和(p0,在1)], 是价格上涨后福利变化的 EV 度量。

在接下来的两节中,我们使用这些替代福利变化的货币措施来衡量或估计 GFT。

经济代写|国际经济学代写International Economics代考

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