In building a multiple regression model based on advertising
expenditures and a price index, based on normal values, I obtained the
following information:  Multiple R = 0.738; R-square = 0.546. By using
lagged values, I came up with Multiple R = 0.755; R-square = 0.570.
Explain the differences in using these different models and how does a
company further optimize this model?

Well, first off I would make sure that I have specified the model
well. A lot of people simply add or subtract variables so that they
can increase the R-squared, which is simply the proportion of variance
that your model explains. In your models (lagged and non-lagged) your
variance explained is about the same (55-57%), so I don't know if
adding the lag variables really does much to improve your model's
explanatory power. Have you checked on some other statistics? Look at
the F-test, and see if your model reaches significance (at an alpha
value lower than .05) and also look at the individual beta
coefficients and see if they are significant. It is hard to tell what
is going on here because I don't have the full regression printout in
front of me.  There are various approaches used when adding parameters
to a model to determine whether they should be included or not. You
might try and build up your model by adding parameters and then doing
cross-comparison F-tests. If the F-tests show that the additional
parameter has not significantly reduced your SSR (sum of squares due
to residuals), you might wish to not add these parameters. Anyways,
this is just scratching the surface.