A Note on the Geometry of the Two-by-Two General Equilibrium Model
Bibliographic Data
| ID | 9722738 |
|---|---|
| Authors | Harry G Johnson (corresponding author) |
| Year | 1977 |
| Volume | 44 |
| Issue | 173 |
| Pages | 71 |
| Publication date | 1977-02-01 |
| Open Access | No |
| Type | ARTICLE |
| Venue | Economica (JOURNAL) |
| Journal identifiers | ISSN: 0013-0427 • E-ISSN: 1468-0335 |
| Publisher | JSTOR (PUBLISHER) |
| DOI | 10.2307/2553551 |
| OpenAlex | W1999998484 |
| Language | EN |
| References cited | 3 |
The geometrical representation of two-good-two-factor-twoconsumer general equilibrium model has been fully developed and available for expository use for some years now (Johnson, 1971; Krauss and Johnson, 1974). That geometry, however, has usually been derived from starting point of Edgeworth-Bowley contract box, rather than Lerner-Pearce diagram, which has considerable expository superiority for a number of purposes. A noteworthy exception has been the Melvin (Melvin, 1971), which involves transposition from factor space into commodity space by means of a budget line drawn arbitrarily through endowment point to locate geometrically terminal points of commodity transformation curve. The dependence of this technique on an arbitrarily chosen budget line appears, however, to cause difficulties to some students. This note therefore presents an alternative and (it is hoped) somewhat more readily understandable development along Melvin lines, which permits derivation and representation of both commodity transformation curve and income shares of two factors on Lerner-Pearce diagram. Since that diagram in its original form permits an easy proof of Stolper-Samuelson relationship between commodity and factor prices, and between either of these price ratios and quantities of two goods produced when factor quantities are given, and can be easily extended to prove Rybczynski theorem and analyse effects of neutral and biased technical change, as well as other problems, modification of Melvin technique presented here permits analysis of all such problems, without need for reference to contract-box. Figure 1 is Lerner-Pearce diagram; E is economy's endowment point, with. OCO of capital and OLo of labour; and XX and YY are isoquants for two goods X and Y passing through E and thus representing maximum attainable levels of X and Y production achievable by specialization of economy's endowment of factors on X and Y respectively. With factor-price ratio represented by common slope of two tangents M,M. and MyMy to these isoquants, factor allocations to two industries, obtained by completing parallelogram formed by E and equilibrium factor-utilization ratios OR. and ORy, are depicted by P, and Py. P' and P' are corresponding points on maximum output isoquants XX and YY for given factor-price ratio, and OPxIOP' and OPylOP' proportions of maximum producible outputs of two goods actually produced at initial factor-price ratio. (Note, incidentally, that if two maximum outputs are defined as unit quantities, their costs can be represented by relative distances along a ray OE extended, not shown in diagram, cut off by MxMx and MyMy extended, and starting point of
Boundary (topology) · Commodity · Diagram · Economics · Factor endowment · General equilibrium theory · Geometry · Macroeconomics · Mathematical analysis · Mathematical economics · Neoclassical economics · Point (geometry) · Representation (politics) · Space (punctuation) · Computer Science · Economic Growth and Productivity · Economic theories and models · Economic Theory and Policy · Law · Mathematics
| Highly cited | No |
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