


An efficient allocation is one for which these two isoquants are tangent, as shown at E_{0} for X_{0} and Y_{0}. The set of all such tangencies is the efficiency locus, the curve O_{X}E_{0}O_{Y}. Under the usual assumption of constant returns to scale in both industries, the efficiency locus cannot cross the upwardsloping diagonal of the box, and it must therefore lie either wholly above it, as shown, if industry X is capital intensive compared to industry Y, or wholly below it in the opposite case.
The diagram can be used to illustrate the effects of factor reallocations along the efficiency locus on outputs and factor prices, where the latter appear as via isocost lines tangent to the isoquants. It can also be used to show the effects of changing factor endowments, under the assumption that prices of goods (and therefore factors, due to FPE) are held constant.
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Price Changes  
A price change appears in the diagram as a shift of a unitvalue isoquant. An increase in the price of good X, for example, means that a smaller quantity of good X is needed to be worth one dollar. With linearly homogeneous technologies, the new unitvalue isoquant is just a shrunken version of the old, contracted inward toward the origin by the fraction of the price increase.
As shown, an increase in the price of X, then, shifts the Xisoquant inward, causing the common tangent to rotate clockwise. From the intercepts, the wage rises and the rental falls. A fall in price of X has the opposite effects, while a change in the price of Y is analogous.  
Technological Change  
A technological improvement for producing a good causes the isoquant for the same quantity to be shifted inwards. The shift need not be proportional, but the figure above assumes Hicksneutral progress, for which it is. Thus the picture looks exactly the same as that for an increase in the price of the good. The effects are correspondingly the same, except that one must be careful in distinguishing changes in quantities from changes in values for a good with a changed technology.  
Extensions  
The Lerner Diagram provides a convenient starting point for further analysis of the HeckscherOhlin Model. The figure can be used to determine, essentially in the following order,
The Diversification Cone
Patterns of Specialization
Factor Allocations and Factor Prices Inside the cone, factor prices are given by the common tangent, and the industries employ factors in the ratios k_{X} and k_{Y}. With two factors and two goods, there is only one way that factors can be fully employed given this constraint. It can be found by constructing lines parallel to the k_{X} and k_{Y} rays from the point representing the country's factor endowment to where each intersects the other industry's ray. The point of intersection is the amount of factors allocated to that industry.
Effects of a Price Change 