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Two-Good Two-Factor Model (Two-by-two model)There are two factor inputs- labor and capital and only two goods can be produced with the production functions:

The resource constraints are:

For this two-by-two model there are two sets of equilibrium conditions. They are:I. Profit equals zero.

II. Full employment of both resources. or, L1+L2=L

or, K1+K2=K

Factor Intensity ReversalIn this model we assume the cost functions ci (w, r) are non-decreasing and concave in (w, r) as follows:

According to the zero profit condition:

Totally differentiating the above equation and holding prices fixed, we have:

This is the slope of the iso-cost curve.

r dr/dw= -a1L/ a1K= -L1/K1

A dr/dw= -a2L/ a2K= -L2/K2 p2= c2(w, r) p1= c1(w, r) 0 wIndustry 1 is Labor Intensive.Industry 2 is Capital Intensive.In the above figure, the isocost lines only intersect once at point A. The slope of a point on the isocost curve of industry 1 is greater than the slope of a point on the isocost curve of industry 2. There is no factor intensity reversal.In other words, always.The case where isocost lines intersect more than once corresponds to 'Factor Intensity Reversals'. r

A B p1= c1(w, r) p2= c2(w, r) 0 w wA wBIn the above figure, industry 1 is labor-intensive at point A but capital-intensive at point B. This is an example of 'Factor Intensity Reversal'. While FIRs might seem like a theoretical curiosum, they are actually quite realistic.E.g. while much of the footwear is produced in developing nations, the US retains a small number of plants. Some of these plants operate computerized equipment with up to 20 sewing machine heads running at once. Whereas, plants in Asia use century-old, labor intensive techniques.The technology used to make sneakers in Asia is like industry 1 at point A, using labor-intensive technology and paying low wage wA, while industry 1 in US is at point B, paying higher wage wB and using capital-intensive technology.

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