Income and Price Effects in Intertemporal Consumer Problems

We study income and price effects for intertemporal consumer problems with monetary and non-monetary dynamic constraints. We focus on short and long-run responses to a permanent change in income or price, and we characterize how such responses depend on the law of motion of non-monetary dynamic constraints and on time discounting. We provide a dynamic analog to the Slutsky equation, and we show the conditions under which the elasticity of demand to income or price is smaller in the long than in the short run, or even has opposite sign.