# Violations of Assumptions

 1. Factor Intensities Expansion paths In competitive markets, wage and interest rates depend on factor productivity, i.e., marginal products of labor and capital, which in turn depend on the combination of capital and labor used. Efficient use of capital and labor inputs occurrs only on the expansion paths, the slope of which are capital-labor ratios, (K1/L1 and K2/L2). When the production functions exhibit constant returns to scale (CRS), the expansion paths are rays from the origin, and their slopes show the capital-labor ratios. One can readily see which industry is capital- or labor-intensive. Along each expansion path, production costs are minimized. It follows that each industry can expand or contract its output only along its expansion path. Of course, the expansion paths are not permanently fixed, but they respond to changes in input prices, which in turn depends on output prices. capital intensity Definition: Let ki = Ki/Li. Industry 2 is said to be capital intensive if k2 > k1 for all (w,r). Remark: If industry 2 is capital intensive, then industry 1 is labor intensive. This definition works only in a two-commodity case. As long as a country's factor endowment falls within the cone generated by k1 and k2, the country will produce both goods. Evaluation A FIR can occur between two industries in different countries when factor prices are different. If either industry is small, this may not be a serious issue empirically.

 2. Factor Intensity Reversal (FIR) FIR A FIR occurs if k2 > k1 for some (w,r) and k2 < k1 for another pair (w',r'). If there is a FIR as shown in the Figure below, then free commodity trade may not equalize factor prices. When FIR is possible, the endowments of both countries must belong to the same cone of diversification in order to guarantee FPE. For instance, when FIR is a latent possiblity, free trade between America and Europe may equalize factor prices, but trade between America and China may not. Example Burma Road (a labor=intensive method) The Burma Road links Kunming, China and Lashio, Burma (now Miyanmar), which was a colony of the United Kingdom. Japan invaded Shanghai in 1937, and blockaded South China Sea around Hong Kong and their submarines sank 400 ships during the war. As a result, China had to find an alternative route to receive food and supplies from the Allies. Western engineers were consulted, and they suggested that it would take six years and Western equipment to build the Burma road, which was about 700 miles through the mountains. China mobilized about 200,000 laborers and completed the road in 12 months. The Burma road served for three years as a vital link, bringing supplies from the United States, but as Japan expanded its military operation further into inland regions, it was closed again in April 1942.

 3. Input Allocations Adding input requirements Aggregate demands for capital and labor are obtained by adding factor demands of two industries. Figure 9. Adding input demand vectors. Input allocation

 4. Unemployment of Factors FPE is based on the assumption that factor markets are competitive, and hence capital and labor inputs are fully employed. Unemployment If some unemployment exists in either the labor and capital market, no positive combination of the two expansion paths will be equal to the resource endowment vector. That is, any positive output combination of the two industries will always yield some unemployment. In this case, the endowment vector can generate a paralleogram, using the expansion paths of the two industries, but one of these two vectors have to be negative. However, a negative input vector implies destruction, rather than production. Negative inputs must be excluded, because they are not economically meaningful. If we limit the production process to use up inputs, rather than produce inputs, then the resource endowment is simply the sum of the input vector of one industry and the residual input that is not used or unemployed. Geometrically, if the endowment does not belong to the cone of diversification — which is a cone-shaped region trapped between two expansion paths, k2 and k2, then the country specializes in one good and one factor will not be fully employed. degenerate parallelogram Specifically, the parallelogram reduces to a flat line (a brown and blue line on k1, a parallelogram with no depth) as shown in Figure. In this case, the country specializes in good 1 and the pink line represents labor unemployment. Figure10. Unemployment Using two rays k1 and k2, one can generate a parellogram, but it must have an accute angle to permit positive production of both goods. If the endowment (L,K) is outside the cone of diversification, one can generate a parallelogram through that point, but it will have an obtuse angle at the origin. Moreover, one of the two rays will be a negative vector, which means a negative output and hence is infeasible. When the factor endowment lies outside the cone of diversification as in Figure 10, the parallelogram (with an acute angle) shrinks to a single line. The horizontal blue line shows the magnitude of unemployed labor. Unemployment requires an adjustment in the wage and interest rates. If specialization persists, the wage/rent ratio converges to that consistent with full employment of both factors. Hence, there will be no factor price equalization.

 Ancient Greek economy Symposium means "drinking party," syn (together) + posis (drinking) in Greek. Potare (drink) in Latin, from which we also get the word "potable" (drinkable).