Knowing the responsiveness of state spending to federal subsidies along different dimensions allows for the optimal design of joint federal-state programs. Welfare is an important case in point: states have the ability to choose both the extent of welfare eligibility and the intensity of benefits provided through the program. This paper estimates the sensitivity of state spending to separate federal subsidies for increasing benefits and for increasing recipients. Because the federal match rate schedule changed several times during the early years that I study, I am able to estimate elasticities in a way that is not biased by the endogenous relationship between income, spending, and federal contributions. I find that state behavior is quite sensitive to these federal subsidies (and much more sensitive than a simple OLS regression would imply). A 10% increase in the cost of benefits causes a 3.8% decrease in benefit amounts, whereas a 10% increase in the cost of recipients causes a 2.8% decrease in the number of recipients. Cross price elasticities are positive, implying a substitutability of extensive for intensive generosity and making an analysis of total spending without such a decomposition misleading. States appear sensitive to their neighbors' benefit levels, and may also use nonincome recipiency requirements to adjust to changes in prices. These results suggest that the federal government has untapped policy instruments at its disposal to affect the nature of welfare spending.