The phrase "comparative statics with" is a correct and usable phrase in written English.
It is often used in economics to describe a method of analyzing changes in economic variables while holding other factors constant. Example: "We can better understand the effects of a minimum wage increase by conducting comparative statics with labor supply and demand curves."
Consider first the comparative statics with respect to (alpha ).
Again, comparative statics with respect to (rho ) might depend on further properties of the out-degree distributions.
Consider now the comparative statics with respect to P. To do so, we assume a fixed value of (alpha in [0,1]) and analyze how different out-degree distributions lead to different outcomes.
This is a general abstract formulation and specializations of it are of interest, either to derive clear cut theoretical properties of migration flows like comparative statics with respect to characteristics of locations, including inequality in the distribution of factors within locations, or for empirical application.
In this section we report some comparative statics results with respect to the effect of the cost asymmetry π.
Comparative statics, however, with respect to (rho ^) might depend on further properties of the out-degree distributions.7.7
In the next section we develop comparative statics results with respect to the in/out-degree correlation (alpha ) and the out-degree distribution P (the two primitives of the influence network).
Samuelson approached the problems of applying individual utility maximization over aggregate groups with comparative statics, which compares two different equilibrium states after an exogenous change in a variable.
This section presents concrete mathematical analysis results on unique existence and comparative statics on τ * with concise proofs.
If the firms are myopic and do not consider the impact of their period 1 decisions on their period 2 profits, then it is clear that the comparative statics would remain consistent with our original model.
This assumption allows us to perform comparative static exercises with respect to the number of HMOs in order to shed light on the effect of vertical integration in health care markets.5 We denote by J providers who offer health care to patients.
