We develop and analyze the generalized version of the shallow lake economics model, built upon the initial version of the model as described in a seminal paper by Mäler et al. (2003). The model is able to simulate the coupled economic-ecological dynamics under conditions of the pronounced nonlinearity of the ecological (lake) module leading to hysteresis effects and irreversibility for certain values of model parameters. The decision making in the area of lake water management is parameterized by the social welfare function consisting of two terms: the utility originating from the economic activity in the surroundings of the lake (increasing with the anthropogenic loading on the lake), and the disutility originating from the pollution of the lake (increasing with the pollution level). From economic side, the problem is therefore to find a tradeoff between the level of economic activity in the surroundings of the lake and the pollution level. In the basic version of the model, the disutility related to pollution is quadratic in phosphorous concentration. We replace this quadratic disutility with a more general power low, and explore the sensitivity of the generalized model to its exponent. The numerical analysis performed suggests that the generalized model is quantitatively sensitive to varying the value of the exponent, yet structurally robust.