Academic journal article Economic Quarterly - Federal Reserve Bank of Richmond

# When Geometry Emerged: Some Neglected Early Contributions to Offer-Curve Analysis

Academic journal article Economic Quarterly - Federal Reserve Bank of Richmond

# When Geometry Emerged: Some Neglected Early Contributions to Offer-Curve Analysis

## Article excerpt

In his 1952 A Geometry of International Trade, Nobel Laureate James Meade presented the definitive modern version of the celebrated reciprocal demand, or offer-curve, diagram of the trade theorist. The diagram features curves depicting alternative quantities of exports and imports countries are willing to trade at all possible prices (see Figure 1).(Figure 1 omitted)

Let two countries, home and foreign, trade two goods, x and y. Measure quantities of these goods along the horizontal and vertical axes, respectively. Suppose the home country exports good x and imports good y while the foreign country does the converse. The slope of any ray from the origin expresses the relative price of x in terms of y. That is, it expresses the quantity of y exchanged per unit of x, or y price of x. Curve H is the home country's offer curve. Curve F is the foreigner's. Each curve shows alternative quantities of imports demanded and exports supplied at all price ratios or terms of trade.

As drawn, the curves display declining elasticity, or price responsiveness, throughout their length. They slope upward from left to right when the demand for imports in terms of exports is elastic--that is, when more exports are offered for imports at successively lower import prices. They cease to slope upward when import demand becomes unit-elastic. At such points, the quantity of exports offered for total imports remains unchanged as import prices fall. They bend backward (or downward) when import demand is inelastic. Along such segments, fewer exports are offered for total imports when import prices fall.

World trade equilibrium occurs at point P, where the offer curves intersect. At that point, the market-clearing price ratio, or terms of trade, given by the slope of the ray 0P equates each nation's import demand with the other's export supply. The supply of both commodities equals the demand for them, and the coordinates of point P show the resulting equilibrium volume of world trade.

The foregoing diagram has proved indispensable in illuminating the central ideas of trade theory. Generations of professors and their students have employed it to demonstrate how the strength and elasticity of each country's demand for the other's product determine the equilibrium volume and terms of world trade. Likewise, scores of textbooks use it to illustrate how tariffs, technological advances, resource discoveries, taste changes, and other such disturbances shift the offer curves and thereby alter world trade equilibrium.

That a simple geometrical diagram would prove so useful is hardly surprising. Other economic diagrams, including the Keynesian cross, Marshallian scissors, Hicksian IS-LM, Knightian circular flow, Vinerian cost envelope, Fisher-Haberler production possibility frontier, and expectations-augmented Phillips Curve, or zero long-run trade-off between inflation and unemployment, have proved equally indispensable. Indeed, as long ago as 1879, Alfred Marshall insisted that diagrams are absolutely essential to exact reasoning in economics because they yield many of the same results as higher mathematics while being accessible to the mathematically untrained.

What is surprising is how little has been written on the doctrinal history of offer curves. Few systematic surveys of that topic exist. Textbooks scarcely do it justice. Even history-of-thought treatises spotlight at best only a handful of the chief contributions. Meade himself was largely silent on the diagram's history even though it was more than 100 years old when he published his Geometry.

The development of offer-curve analysis involves some of the leading names in classical and neoclassical economics. John Stuart Mill, Robert Torrens, Alfred Marshall, Francis Ysidro Edgeworth, and Abba Lerner all contributed to the diagram's development and policy applications. Mill invented reciprocal-demand schedules. He used them to determine precisely where, within the limits set by comparative-cost ratios, the terms of trade, or quantity of imports bought by a unit of exports, must fall. …

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