We present a model of economic growth of an agricultural household that is faced with an exogenous water availability constraint. We examine the long-run investment and consumption choices under two scenarios: (i) when the water availability constraint is binding and (ii) when it is not binding. We then compare the two scenarios to derive conditional convergence hypotheses regarding the impact of water availability on long-run agricultural growth. Panel data from Wyoming are used to test these conditional convergence hypotheses. We find that Wyoming counties exhibit strong conditional convergence in agricultural growth. Our theoretical and empirical results demonstrate that water availability is not a determinant but can be a constraint on long-run agricultural growth. Higher water use leads to higher growth in agricultural yield per capita but when water rights constrain water use in a county, as we found in southeastern Wyoming, there are significant losses in agricultural growth.