4 – Measurement of Gains from Trade

Introduction:

Gains from trade can be obtained in the classical model of exchange if there is a viable allocation that each agent prefers to her endowment. But how can we quantify the benefits of trade in an economy? Because interpersonal comparisons of welfare are often ineffective, we recommend assessing trade advantages in terms of goods volumes rather than welfare comparisons. To do this, we seek a “reference allocation” made up of “reference bundles,” one for each agent, such that.

(i) Each agent is indifferent between her endowment and her reference bundle and

(ii) The reference allocation is possible. Because there are no welfare gains, the difference between the aggregate endowment and the resources at the reference allocation offers a measure of the profits from trading from the endowment profile to the reference allocation.

In this way, we may calculate trade gains regarding product quantities. However, in most economies, there is a continuum of reference allocations, and the vectors of resources saved by trading vary. The set of all such vectors specifies the economy’s possible trade profits. We introduce the concept of a (vector-valued) “metric,” which is used to select one representative vector from a collection of feasible trade gains for each economy.

Two economies may have different tastes and endowment profiles but have equal potential trade advantages. We hypothesise that if two economies have equal sets of potential trade benefits, a measure should not distinguish between them and use the same representative vector of trade gains in both economies. As a result, the concept of a metric is analogous to the idea of a solution to a negotiating dilemma. A “bargaining problem” comprises a set of utility profiles and points of contention; a “solution” converts each problem into a utility profile. In our example, the set of utility profiles corresponds to the set of possible trade wins, and the disagreement point relates to each agent spending her endowment and no resources being saved. A metric converts each set of feasible trade profits into a vector of trade gains.

We employ a negotiation theory technique to find metrics that satisfy certain desirable qualities. Metrics should choose a vector representing the size of the set of prospective trading gains. As a result, we seek measures that meet the three qualities listed below and have great intuitive appeal in our context. The first characteristic is “maximality”: for each economy, no reference allocation results in a higher vector of trade benefits than the vector the metric selects. The second property is “monotonicity” about set inclusion: a metric chooses a more significant vector of trade gains in an economy with a more extensive set of possible trade gains. The third property is “homogeneity,” which states that a homogeneous expansion of the set of possible trade gains corresponds to a homogeneous expansion of the vector the metric has chosen.

4.1 Trade Profits

The sum of consumer and producer surpluses obtained by buyers and sellers during a market exchange. Gains from trade occur because buyers are often willing and able to pay a higher price to purchase a good than what they ultimately pay, and sellers are typically ready and able to accept a lower cost to sell a good than what they eventually receive. Both sides of the market exchange are thus better off, with a net gain in welfare as a result of the transaction. Even though all kinds of market transactions result in benefits from trade, this subject is probably the most important for understanding global trade.

Generally, both parties are better off after the transaction than before. Buyers benefit from a net increase in consumer surplus, and sellers benefit from the producer surplus because they gain a net profit.

Voluntary market exchanges are carried out because they benefit both parties involved in the transaction. Buyers and sellers would not freely engage in a trade if they did not stand to gain.

Gains from market exchanges provide insight into all forms of trading and the existence of a market-based economy used to allocate resources. They also provide a great deal of insight into trading among nations, i.e., international trade. When two countries engage in trade, they do so because they benefit from it. Both countries are better off now than they were before the trade.

Market Transactions

The reason for international trade is essentially the same as for any other market exchange. People buy and sell goods because they believe they will be better off due to the transaction. Consider the motivations of two hypothetical people, Horst Duncanstein and Francine von Sutter, who are ready to do some trading.

• From the Buyer’s Point of View: Consider Horst Duncanstein, who is particularly fond of turnip lasagna. Horst is a happy man after eating turnip lasagna. It boosts his overall well-being. It meets his wants and needs. To that end, Horst is willing to pay a premium for the turnips used in his turnip lasagna. Horst has a maximum price he is willing to pay for the required turnips, known as a demand price. If the price is too high, he will not buy turnips and will consume another food, such as carrots, for a carrot dish. However, he will profit if he pays his turnips less than his demand price. He spends less than the value he obtains, a situation known as consumer surplus. He benefits from this transaction.
• From the seller’s point of view: Consider Francine von Sutter, a turnip farmer. Francine does not particularly like turnips, but she does enjoy the farming business. She possesses the necessary land, labour, and capital to produce turnips. To that end, Francine is willing to sell turnips to willing consumers as long as she can recoup her production costs. Francine has a supply price that she is willing to pay to produce turnips. If the price is too low, she will not produce turnips and will grow another item, like carrots. However, if the price she obtains for her turnips is higher than her supply price, she will profit. She receives more than the production cost, known as producer surplus. She benefits from this transaction.

Combining Horst and Francine is sure to be advantageous to both. Horst profits from the trade if he pays less than his desired price. Francine benefits from this trade if she receives more than her supply price. It is a win-win situation. In the most extreme instance, Horst’s price may be precisely his demand price, or Francine’s price may be her supply price. In this situation, neither side benefits from the deal nor suffers a loss. The trade will not take place if the price rises beyond Horst’s maximum demand price or falls below Francine’s minimum supply price. One of the parties will give up on the trade.

The eventual outcome of such voluntary trades between purchasers like Horst and sellers like Francine is that one or both parties benefit from the trade. They would not actively participate in the exchange if they did not gain anything (or at least break even).

Gains in Graphics

The exhibit depicts the gains from market transactions to the right. This illustration depicts a typical market graph. The negatively sloped demand curve, D, represents the demand price consumers (like Horst) are willing and able to pay to purchase various quantities of turnips. The positively sloped supply curve, S, represents the supply price that sellers (like Francine) are willing and able to accept to sell varying quantities of turnips.

If the market is competitive and devoid of other market failures and inconvenient problems, the intersection of the demand and supply curves yields the equilibrium price and quantity. The relationship between the market equilibrium price, the demand price on the demand curve, and the supply price on the supply curve represents trade gains.

This market’s consumer surplus is located below the demand curve and above the equilibrium price, while its producer surplus is above the supply curve and below the equilibrium price.

These two areas—above the supply and below the demand curves—combine to produce the gains from trade in this market. Additional satisfaction, welfare, profit, and so on would not exist if the market exchange did not occur.

Benefits of International Trade

The only difference between typical market trades, such as those between Horst and Francine, and international trades is where the buyers and sellers are. If Horst lives in one country, say the hypothetical Republic of Northwest Queoldiola, and Francine lives in another, say the similarly hypothetical United Provinces of Csonda, the previous market exchange example is likewise an example of international commerce. However, trade benefits continue to accrue.

Horst lives in the Republic of Northwest Queoldiola, and, like other Queoldiolans, he enjoys his turnip lasagna. Francine, on the other hand, is a turnip-growing citizen of the United Provinces of Csonda who is eager to sell her produce to purchasers from other nations.

Horst and Francine benefit from the turnip trade, but so do their respective countries. Northwest Queoldiola gains more consumer surplus due to Horst’s efforts, and the Csonda gains more producer surplus due to Francine’s efforts.

4.2 How to Calculate Trade Profits

Our idea for assessing trade benefits in goods quantities can be understood as a multi-agent expansion of some existing metrics of welfare changes in single-agent decision-making situations. The equivalent and compensating variations are welfare changes measured in terms of the difference in expenditure required to maintain an agent’s welfare constant after a price change. In our environment, trade between agents rather than pricing drives change, so assessing gains in product quantities seems reasonable without pre-set prices. The risk premium in choice under uncertainty evaluates how much an agent is prepared to forego to get a constant consumption stream; the certainty equivalent measures the level of consistent consumption across states that leaves the agent’s welfare unaltered. In our situation, we calculate how much a group of agents can profit by spreading risk among themselves.

This method of calculating an allocation’s inefficiency is comparable to ours. It also takes into account the economy’s potential profits from trade. However, instead of assessing trade gains as a vector of commodities, it measures trade gains as a scalar. Using a real-valued metric implies that we can order the set of all economies based on their trade gains. A vector-valued metric allows for partial order, which may be advantageous if commodity differences necessitate asymmetric treatment. Furthermore, because this measure is not monotonic, an increase in possible trade gains can lead to a drop in assessing these gains.

Another advantage of employing a vector-valued measure over a real-valued one is that it leads to a natural allocation in which trade gains are dispersed equally. The theory of fair allocation can be classified based on the nature of the problem under consideration: First, consider the circumstances in which a social endowment must be distributed among a group of agents. Second, there are instances in which agents have private endowments, and redistribution (trade) is conceivable. Two ideas of fairness are prominent in the problem of assigning a social endowment. The first principle is no envy (Foley 1967): no agent should favour another agent’s bundle over her own (Kolm (1998) and Varian (1976)). The second principle is egalitarian equivalence (Panzer and Schmeidler 1978): A reference bundle exists such that each agent is agnostic between her bundle and the reference bundle. These two ideas can be combined to solve the challenge of allocating individual endowments. The principle of no envy in trades holds that no agent favours another agent’s trade over her own. According to egalitarian equivalence between endowments, a reference vector exists. Each agent is indifferent between her bundle and the bundle generated from the sum of her endowment and the reference vector.

For economies with individual endowments, a concept akin to egalitarian equivalence has recently been proposed: an allocation is fair if it is welfare equal to an allocation derived by adding a vector of fair “concessions” to the endowment profile (Pérez-Castrillo and Wettstein 2006). This concept generalises egalitarian equivalence in two ways: first, it allows for disparities in reference bundles based on individual endowments; second, it allows for inequalities in concessions.

Our understanding of fairness is comparable to that of Pérez-Castrillo and Wettstein (2006), but it differs in two respects. First, we take the welfare equivalent of the endowment profile as our reference allocation and add the vector of contributions to it. Second, our contribution vector differs from their concession vector. In addition, our results differ from theirs in format. They demonstrate the existence of fair and efficient allocations; however, we do not acquire a fair and efficient allocation instantly. Instead, we suggest a recursive approach that is fair at each stage and results in an efficient allocation at the limit. We also propose an algorithm for doing it.

4.3 Measuring the Benefits of International Trade

The benefits of international trade are quantifiable. According to Prof. Jacob Viner, traditional economists used three methods to calculate these benefits.

1. Using comparative cost theory to calculate increased real income.
2. An increase in the national income level.
3. Enhancement in terms of trade.

However, since the advent of J.S. Mill’s theory of reciprocal demand,  trade technique has become the most commonly used method of evaluating trade gains.

As a result, three methodologies are employed to measure trade gains.

1. Ricardo’s Method
2. The J.S. Mills Method
3. Samuelson’s Approach or the Modern Approach

Ricardo’s Method

According to Ricardo, a country would export commodities with a lower comparative cost of production.

India: 15 units of cotton or 20 units of wheat

Pakistan: 10 units of cotton or 10 units of wheat                                                    (i)

If, in every country, only two units of the factor are used, the product would be as follows:

India: 15 units of cotton + 20 units of wheat

Pakistan: 10 units of cotton + 10 units of wheat                                                     (ii)

1. Without specialization, if both countries produce both commodities, the total production in the two countries would be as follows:

India + Pakistan = 25 units of cotton + 30 units of wheat (25C + 30W)           (iii)

2. If there is specialization based on comparative cost theory in India, specializing in the production of cotton, total production would be:

India = 25 units of wheat

Pakistan = 20 units of cotton                                                                                      (iv)

India + Pakistan = 40 units of wheat + 20 units of cotton

Comparing situations (ii) and (iii) reveals that due to specialization in the two countries, the production of wheat increases by 10 units, whereas there is a loss of 5 units of cotton.

Net Result = + 10 units W – 5 units C                                                                        (v)

From situation (i), it is revealed that 10 units of wheat in India is equal to 7.5 units of cotton, and in Pakistan, it is equal to 10 units of cotton, i.e.

10 W = 7.5 C or 10 W = 10 C

So, the net result is:

+ 7.5 C – 5 C

or 10 C – 5 C

i.e., + 2.5 C or + 5 Cotton

Thus, specialization produces a net gain of 2.5 or 5 units of cotton distributed between the two countries.

Criticism

The following are the main points of criticism of gains from international commerce as a result of comparative cost, or Richardo’s theory:

1. Later, economists claimed that Ricardo overestimated the benefits of foreign trade. Ricardo’s theory does not apply to countries that cannot produce imported commodities or can only make them at a higher cost.
2. Mill believes that Ricardo’s theory explains why international commerce occurs, but it does not explain the magnitude of the gain or how it is dispersed among different countries.

Mill’s Method

J.S. Mill used his theory of reciprocal demand to examine the benefit and the distribution of the gain from international commerce. According to Mill, reciprocal demand dictates trade terms, which determine the distribution of trade profits among countries. The word ‘terms of trade’ refers to the better terms of commerce between the two countries, i.e., the ratio of a country’s imports to its exports.

Samuelson’s Approach (Modern Approach)

The profits from international commerce are clearly distinguished in modern trade theory as gains from exchange and specialisation. The study is explained in terms of the general equilibrium of a closed economy, which considers demand and supply. The tangency of a community indifference curve with the transformation curve and the equality of the marginal substitution rates between commodities in consumption and production with the domestic terms of trade or commodity price ratio characterise it. “The introduction of international trade allows for the realisation of a gain from exchange as well as a gain from specialisation.” When equilibrium is reached, and these gains are maximised, the new marginal rate of production transformations and the new marginal rate of substitution in consumption equals the international price ratio or terms of trade.” As a result, producers and consumers benefit from global commerce by creating and consuming more than before trade.