|Commodity prices and factor prices||The SS theorem links commodity prices and factor prices.|
|Competitive markets||If a country suddenly opens up to trade, how will factor
FPE theorem presupposes that all markets are perfectly competitive. Perfect competition implies that in the long run profits are zero in every industry. Specifically,
Π1 = p1y1 - wL1 - rK1 = 0.
Π2 = p2y2 - wL2 - rK2 = 0.
Per unit profits are also zero.
Dividing the two profit functions by the respective outputs, we get the relationship between prices and factor prices.
price = unit labor cost + unit capital cost.
P1 = aL1 w + aK1 r.
P2 = aL2 w + aK2 r.
|It is well known that the unit cost function g1(w,r) = aL1 w + aK1 r is concave in factor prices, w and r. That is, as either factor price rises, unit cost rises at a decreasing rate. Moreover, the iso-unit cost contour of (w,r) is convex to the origin, as shown by two curves in Figure 12.|
|Iso-unit cost curve||An iso-unit cost curve, also known as factor price frontier,
is a locus of factor price combinations along which the unit cost of a good
remains constant. Paul Samuelson first considered this notion and called
it factor price frontier. These are derived from the above
two unit cost equations.
r = p1/aK1 - waL1/aK1 .
Recall that the input-output coefficients are not fixed, but are actually functions of factor prices, i.e., aij = aij(w,r). The slope of the isoprice curve p1 is
aL1/aK1 = L1/y1 ÷ K1/y1 = L1/K1 = 1/k1 ,
where k1= K1/L1.
Thus, a more capital-intensive industry has a flatter curve.
|Recall that the slope is changing as w or r changes. That
is why the iso-unit cost curves are not linear. A
pair of output prices (p1,p2) results in a unique
combination of factor prices, (w,r)e, an equilibrium set of wage
Note that k2 > k1 implies that p2 is flatter than p1 everywhere.
|The SS Theorem||An increase in the price of a capital-intensive good increases the return to capital and decreases the return to the other factor (labor).|
|When does the price of a good rise? Prices of importable goods rise and those of the exportable goods fall dramatically during war. Price changes moderately when tariffs are imposed.|
Corollary: An increase in the price of a capital-intensive good decreases the wage-rental ratio, w/r.
Remark: Free trade increases the domestic price of the
exportable and increases the return to the abundant factor. After
What was the impact of war on the interest rate? (US interest data are available only for a later period.)
|What is it?||
The magnification effect states that an increase in the price of a capital-intensive good increases the return to capital more than proportionately.
p2 = aL2w + aK2r.
Δp2 = aL2Δw + aK2Δr = aL2w(Δw/w) + aK2r(Δr/r).
Here, Δ reads "change in" and the percentage change in x is written as x with a hat. That is, ^x = Δx/x.
Divide both sides by p2:
^p2 = θL2^w + θK2^r = θL2^w + (1 - θL2)^r
for example = 75% × ^w + 25% × ^r
|labor share, capital share||The percentage change in product price is a weighted average
of percentage change factor price changes.)
Note ^w = Δw/w is the "percentage change in" w, and
θL2 = aL2w/p2 = wL2/p2y2 is the share of labor in industry 2. Moreover,
θL2 + θK2 = 1 (For example, labor share 75% + capital
share 25% = 100%). That is, the sum of labor and capital shares is unity in every industry.
Intuitive Reason: If both the rental rate and wage were to double, the product price must also double to breakeven. Recall that if the labor share is 75%, then the capital share is 25%. If the wage rate rises by 20% and the interest rate by 10%, then the product price rises by 10% × 3/4 + 20% × 1/4 = 12.5%. If the rental rate were to remain constant, then a 10% increase in output price must be accompanied by 10%/.75 = 13.33%.
However, by the SS Theorem, we know that a 10% rise in the output price (of a capital-intensive good) results in a reduction in the wage rate, and hence the interest rate must rise even faster than 13.33% (a magnification effect on the interest rate) to more than offset the negative effect of the falling wage rate. Similarly, a rise in the price of a labor-intensive good reduces the interest rate and hence increases the wage rate more than proportionately. This is the magnification effect on the wage rate. The return to the friend factor increases more than proportionately.
|Price and Factor Intensities||An increase in the price of a capital intensive good raises (r/w), and hence all industries become less capital intensive to minimize costs.|