Menu | <<<< | >>>> | Symmetry in Elasticity Matrices Symmetry is the relationship between cross prices in a price elasticity matrix as shown above (matrix for BL, NUT, W).  The equations in gray are calculated by formula as shown in cell C16 where the formula calculates the elasticity in cell C16 as the elasticity in cell D15 times the base value (price times quantity) of NUT divided by the base value of W (cells containing formulas calculated by VORSIM are gray).  The point of this relationship is to have a reasonable, and in this case, a positive sum of the qp (supply) cross price elasticities (sum of current qp elast.).  If any sum for a product is not positive, you have a downward sloping supply schedule and the model is likely to be unstable or give odd results for the product.  Applying symmetry calculations to the lower half of the matrix and then adjusting the cross price elasticities in the top half of the matrix can assure you of a positive sum for supply.  You have to determine which products have cross price elasticities of a certain magnitude in the top half of the matrix and enter them.  Then clicking the [Symmetry] button brings up the menu shown below with three options for you to consider :  1. – You enter elasticities in top half of the matrix and VORSIM enters the formulas in the lower left half.  Then you have to manually adjust the top half elasticities (with the formulas adjusting the lower half) to achieve satisfactory row sums.  2. – The same procedure as 1. except that VORSIM adjusts the top half elasticities until satisfactory row sums are obtained.  3. – VORSIM guesses at top half cross price elasticities for all products and adjusts them to obtain satisfactory row sums.  In cases 2 and 3, you will have to make final judgments about the elasticities that VORSIM came up with.  Basically, if you have a good idea of what products should have cross price elasticities and what those elasticities should be, use procedure 1 or 2 (carefully).  Procedure 3 involves VORSIM guessing at cross price elasticities and the results could turn out good or bad from an economic viewpoint.  These symmetry routines are useful because one typically spends a lot of time and judgment entering and adjusting cross price elasticites; anything that can help speed up the process is welcome.