Final answer:
State welfare spending is expected to increase with the federal government's shift from a one-for-one to a two-for-one match for state spending, given the elasticity of 0.38 for state spending on benefits per recipient.
Step-by-step explanation:
According to Baicker [2005], the elasticity of state spending on benefits per recipient is 0.38. This means if the price of providing welfare (the share of the costs paid by the state) changes by 1%, we would expect the quantity of welfare spending to change by 0.38%. When the federal government changes its matching rate from a one-for-one basis to a two-for-one basis, the effective price to the state of welfare spending decreases.
With a lower price, we apply the elasticity of spending to predict changes in state welfare spending. Using the provided elasticity, we would expect states to increase their welfare expenditures since for every dollar they now spend, the federal government chips in two dollars, effectively doubling the federal contribution compared to before. States will perceive this as a more favorable condition for supporting their welfare programs and are likely to allocate more funds as a result.