Suppose we have following regression models of quantity:
What happens to value when we change price? Since we get following value models:
Now we can dance the usual dance of adding quantities in both sides of the equations:
Thus we get:
So the conclusions are:
- If we have log-linear quantity-price model and the coefficient is negative, then if we increase the price, the value will diminish, unless dominates . This can happen for small values of .
- If we have log-log quantity-price model, then we have a paradox. If , no matter how much we increase the price, the value will increase. In other words, loss of unit sales is compensated by the price increase. The dream of every seller.
- If we have log-quadratic-log quantity-price model, the relationship is more complicated. But unless , negative coefficient of ensures the decrease of value in the event of unreasonable increase of price.