Determine the time period that you want to use to calculate welfare changes. As an example, calculate the change over a one year period.
Subtract the initial cost of welfare by the final cost of welfare over the time period determined in Step 1. For example, at the beginning of the year, a government's welfare program costs $100 million to run. Because of administrative cost cutting, at the end of the year the welfare program now only costs $90 million to run. Subtracting $90 million from $100 million equals $10 million.
Divide the result from Step 2 by the initial cost of welfare to determine the percent change in welfare price. In the example, dividing $10 million by $100 million equals 0.1.
Subtract the number of people who used welfare when it was at its initial cost from the number of people who used welfare when it was at its final cost. As an example, 50 million people used welfare when it cost the government $100 million to run the program. The cost-cutting measures revealed that the government could now offer welfare to 60 million people. 60 million minus 50 million equals 10 million.
Divide the result from Step 4 by the number of people who used welfare at its initial cost. In the example, dividing 10 million by 50 million equals 0.2
Divide the result from Step 5 by the result from Step 3 to calculate the elasticity of welfare changes over the period determined in Step 1. In the example, 0.2 divided by 0.1 equals 2. When the government's welfare program changed from $100 million to $90 million over a one year period, its elasticity coefficient was 2. We can interpret this result to mean that the welfare changes were elastic since the change in welfare price meant a large increase in the number of people who used welfare. If the elastic coefficient were a negative number, the welfare changes would be inelastic, meaning the change in welfare price meant a small change in welfare demand.