An easy way to measure price elasticity is to run a regression of log(output or sales) on Log(price). Then the coefficient of price will be the elasticity.
You can run this for the whole service sectors, or for different segments of it as data permits. Also, note that this can now be done with a spreadsheet program such as Excel.
As there are many factors that affect the dependent variable which is usually quantity demanded or sales and independent variables such as own price, prices of substitute and complementary products, income of the consumers etc should be included in the model. As Lall said you can run a multiple regression (log-log model). Then the coefficients of the independent variables are your elasticities.
Is your question in the context of B2B or B2C? If your services are B2B, then be very wary of using price elasticity. When customers are businesses, lower prices is unlikely to stimulate new business like it would in a B2C context. Lower prices may get you a bigger slice but the pie did not get bigger. The demand level of business customers is driven by demand from their customers, which is exogenous to your sales or booking data. Also be wary of using first order arima models in your time series forecasting. It is my opinion your sales/booking process more likely reflect a random walk with respect to prices.