 by Steven M. Suranovic

# The Magnification Effect for Prices

The magnification effect for prices is a more general version of the Stolper-Samuelson theorem. It allows for simultaneous changes in both output prices and compares the magnitudes of the changes in output and factor prices.

The simplest way to derive the magnification effect is with a numerical example.

Suppose the exogenous variables of the model take the following values for one country:  PS = 120  PC = 40

With these numbers which means that steel production is capital-intensive and clothing is labor-intensive.

The zero-profit conditions in the two industries are,

Zero-profit steel: Zero-profit clothing: The equilibrium wage and rental rates can be found by solving the two constraint equations simultaneously.

A simple method to solve these equations follows.

First, multiply the second equation by (-4) to get,  Adding these two equations vertically yields, which implies, . Plugging this into the first equation above (any equation will do) yields, . Simplifying we get, .

Thus the initial equilibrium wage and rental rates are: w = 8 and r = 24.

Next suppose the price of clothing, PC, rises from \$40 to \$60 per rack. This changes the zero-profit condition in clothing production but leaves the zero-profit condition in steel unchanged. The zero-profit conditions now are,

Zero-profit steel: Zero-profit clothing: Follow the same procedure to solve for the equilibrium wage and rental rates.

First, multiply the second equation by (-4) to get,  Adding these two equations vertically yields, which implies, . Plugging this into the first equation above (any equation will do) yields, . Simplifying we get, .

Thus the new equilibrium wage and rental rates are: w = 24 and r = 12.

The Stolper-Samuelson theorem says that if the price of clothing rises, it will cause an increase in the price paid to the factor used intensively in clothing production (in this case the wage rate to labor) and a decrease in the price of the other factor (the rental rate on capital). In this numerical example w rises from \$8 to \$24 per hour and r falls from \$24 to \$12 per hour.

The magnification effect for prices ranks the percentage changes in output prices and the percentage changes in factor prices. We'll denote the percentage change by using a ^ above the variable. (that is, = % change in X).

Percentage Changes in the Goods and Factor Prices The price of clothing rises by 50%. The wage rate rises by 200%. The rental rate falls by 50%. The price of steel is unchanged

The rank order of these changes is the Magnification Effect for Prices, The effect is initiated by changes in the output prices. These appear in the middle of the inequality. If output prices change by some percentages, ordered as above, then the wage rate paid to labor will rise by a larger percentage than the price of steel changes. The size of the effect is magnified relative to the cause.

The rental rate changes by a smaller percentage than the price of steel changes. Its effect is magnified downward.

Although this effect was derived only for the specific numerical values assumed in the example, it is possible to show, using more advanced methods, that the effect will arise for any output price changes that are made. Thus if the price of steel were to rise with no change in the price of clothing, the magnification effect would be, This implies that the rental rate would rise by a greater percentage than the price of steel, while the wage rate would fall.

The magnification effect for prices is a generalization of the Stolper-Samuelson theorem. The effect allows for changes in both output prices simultaneously and provides information about the magnitude of the effects. The Stolper-Samuelson theorem is a special case of the magnification effect when one of the endowments is held fixed.

Although the magnification effect is shown here under the special assumption of fixed factor proportions and for a particular set of parameter values, the result is much more general. It is possible, using calculus, to show that the effect is valid under any set of parameter values and in a more general variable proportions model.

The magnification effect for prices can be used to determine the changes in real wages and real rents whenever prices change in the economy. These changes would occur as a country moves from autarky to free trade and when trade policies are implemented, removed or modified.

International Trade Theory and Policy - Chapter 60-6: Last Updated on 7/31/06