We will use the Edgeworth-Bowley box and results from factor price equalization (FPE) to derive Rybczynski’s theorem It applies to the effect of an increase in the available level of an input, say From FPE we know that if the prices of final goods do not change, then the That, in turn, implies that the capital-intensity with which the two goods are produced (the Suppose that at constant prices for final goods rewards to factors of production do not change labor, capital-labor ratio) does not change good X uses capital relatively intensively K x /L x > K y /L y  Charles van Marrewijk Rybczynski, 1

OxOx OyOy K L0L0 K x /L x K y /L y The capital-labor intensities for goods X and Y determine the allocation of capital and labor (on the contract curve)  Charles van Marrewijk Rybczynski, 2Study Guide Figure 7

More labor available increases the Edgeworth Box The Y-origin is shifted to the right OxOx OyOy K L0L0 K x /L x K y /L y O y’ L1L1  Charles van Marrewijk Rybczynski, 3Study Guide Figure 7

The goods prices do not change, so K/L intensities do not change The equilibrium moves from E 0 to E 1 OxOx OyOy K L0L0 K x /L x K y /L y O y’ L1L1 E0E0 E1E1  Charles van Marrewijk Rybczynski, 4Study Guide Figure 7

Less capital and labor is allocated to produce good X The production of X falls; similarly, the production of Y rises OxOx OyOy K L0L0 K x /L x K y /L y O y’ L1L1 E0E0 E1E1  Charles van Marrewijk Rybczynski, 5Study Guide Figure 7

Rybczynski’s result makes perfect sense. After all the economy-wide K/L ratio must be a weighted average of K x /L x and K y /L y. If the economy-wide K/L ratio falls as a result of an increase in labor, while the sectoral rates K x /L x and K y /L y do not change because the prices of final goods do not change, then the weight attached to the relatively capital-intensive sector (good X) must decrease, pulling capital and labor away and causing a fall in its output. Rybczynski’s result can be nicely illustrated in goods space to show the impact on the production possibility frontier (ppf). In this respect it is important to note that the demonstration of the Rybczynski result above using the Edgeworth Box is exclusively based on straight lines. Any other change in the available labor supply results in changes in produced output equiproportional  Charles van Marrewijk Rybczynski, 6

Capital Rybczynski line Labor Rybczynski line A X Y 0 If the economy produces at point A and labor rises10 units, causing a rise in the output of Y of, say, 4 units and a fall in the output of X by 3 units, then a further increase in labor of 10 units also leads to 4 more Y and 3 less X This process continues until X is no longer produced; it is summarized by the blue Labor Rybczynski line A similar procedure can be used to derive the dotted red Capital Rybczynski line indicating the effect of increasing the supply of capital  Charles van Marrewijk Rybczynski, 7

B X Y 0 We can draw the ppf through the initial production point A; the income line must be tangent there A Labor Rybczynski line As the labor stock increases production moves along the Labor Rybczynski line to the eq. at point B The increase in labor also shifts the ppf outward; it must be tangent to a parallel income line at point B The outward shift of the ppf is biased toward good Y, that is the labor-intensive good  Charles van Marrewijk Rybczynski, 8

 Charles van Marrewijk Rybczynski, 9