Essay on the Marshall-Edgeworth Offer Curves of Trade

Mill’s theory of reciprocal demand has been expressed graphically by Edgeworth and Marshall in terms of “offer curves”, also called “reciprocal demand curves.”

The offer curve of a country denotes the amount of commodity (x) it is willing to offer for a given amount of some other commodity (y). It is based on the relative prices of the two commodities.

For deriving an offer curve of a country, first we have to take the production possibility curve (TT) and a set of community indifference curves featuring demand in that country.

Under pre-trade situation, equilibrium is established at point a where the indifference curve is tangent to the production possibility curve (Figure 10.1). At this point, marginal rate of transformation (MRT) in production equals to the marginal rate of substitution (MRS) in consumption. Indifference curve CIC represents the highest level of satisfaction attainable under given constraint. The ruling price ratio is shown by the line P₁ which is tangent to the production possibility and the indifference curve at a. It has a negative slope.

As Professor Staley suggests, it can be represented with a positive slope by placing the origin of the indifference map in the southeast corner, so that the offer curves will have their origin in the southwest corner of the graph.

Suppose, England has all cloth and no wine and P_{ is the line of terms of trade (international price line) and when the trade begins with Portugal, then equilibrium point a implies that to go from O to point a, On of cloth is exported and an of wine is imported. Similarly, the other price lines P₂, P₃ etc. involve higher price of cloth relative to wine and lead to different quantities of imports and exports. Thus, the price line which is revolving a in a counter-clockwise direction, indicates a higher and higher price of cloth in terms of wine, as more and more of wine is being exchanged for the given amount of cloth. Alternatively, it means a lower and lower price of wine in terms of cloth. The curve OE adjoining the equilibrium points a, b,… etc., is the offer curve of England. An offer curve thus may be defined as the locus of the pairs of export and import quantities desired at each possible ratio.

The domestic price line (or price ratio curve) is a limit beyond which the offer curve cannot go, because no country will export goods for less by way of imports than what it can produce domestically. Thus, the offer curve of a country starts from its domestic price ratio.

The offer curve, however, may follow for a distance the price line in the absence of trade, indicating that in case of small amounts of imports the country may be indifferent as to whether, it produces them at home or buys them at the same price in a foreign market. Beyond this distance, the offer curve moves away from the price line.

The offer curve OE may thus be interpreted either as England’s demand for wine against cloth or her supply of cloth against wine.

In fact, the offer curve is a typical demand curve as it denotes the demand for one commodity (imports) in terms of the supply of another (exports).

Derivation of Portugal’s Offer Curve of Wine (Demand for Cloth)

Like England’s offer curve, we can also draw Portugal’s offer curve. It expresses Portugal’s demand for English cloth which will represent the quantities of wine which Portugal is willing to exchange for English cloth. It is quite obvious that, so long as Portugal imports smaller quantity of cloth, it will be willing to exchange more wine for less cloth. But as the quantity of cloth is increased, lesser amount of wine will be exchanged, and hence, the ratio of exchange will go on falling. Thus, the curve OP is Portugal’s offer curve of wine for cloth.

Now, when we take the offer curves of England and Portugal on the same basis they will cross. These two curves are called the reciprocal demand curves of the two countries. The intersecting point of these two demand curves determines the terms of trade, called net barter commodity terms of trade.

The term of trade in this case is more favourable to Portugal as more of cloth is exchanged against a given amount of wine. This implies that England’s demand for Portuguese wine is more urgent than Portuguese demand for English cloth.

Assuming constant costs, the lines Op_] and Oq_t represent the ratio of domestic costs o production of cloth and wine in England and Portugal respectively. The offer curves must lie within the limits set by these lines, and so the terms of trade. When the terms of trade lie at a point between these two lines, both the countries gain, though one may get a larger share than the other. But if the terms of trade are set outside these lines, it will be advantageous for one country to produce both; wine, and cloth domestically rather than entering into foreign trade, and hence, there will be no trade between the two countries. Thus, the equilibrium terms of trade must fall within these two lines upon which the offer curves are based.

Further, the terms of trade will not be equal so long as there is no equilibrium in the balance trade account. The money value of cloth imported by Portugal must be equal to the money value of wine exported by her. So long as there is disequilibrium in the balance of trade, some country will have an adverse balance of trade. Say, when Portugal’s value of imports is equal to her value of wine, she will be required to reduce the price of wine to induce England to buy more wine so the terms of trade will fall for Portugal. This will go on upto the point when Portugal’s value imports are equal to her value of exports.

The same will be the case with England. Thus, under from trade, stable equilibrium terms of trade will be established at point N, the point of intersection of the two offer curves, Point N, therefore, denotes a position of stable equilibrium. Any displacement terms of trade from equilibrium could set in motion forces inducing a return to the equilibrium.

For instance, a deviation in the terms of trade to the left of ON would create an excess supply England’s exports of cloth at a higher price, and the relative price of her exports will therefore, fall On the other hand, a deviation to the right of ON would create an excess supply of England’ s exports of cloth at a higher price, and the relative price of her exports at a lower price, and relative price of Portuguese wine must then rise.

As a result, equilibrium will be restored at point again. At point N the community indifference curves of two countries are tangent to each other the same price line OT. Thus, line OT represents an equilibrium terms of trade.

However, it goes without saying that a shift in the terms of trade takes place when there is change or shift in the offer curve of any country. Thus, reciprocal elasticities of demand are significant in the determination of terms of trade and the distribution of gains from trade.