This thesis concerns three important issues related to the problem of time-inconsistency in decision-making and revealed preference analysis. The first chapter focuses on the welfare properties of equilibria in exchange economies with time-dependent preferences. We reintroduce the notion of time-consistent overall Pareto efficiency proposed by Herings and Rohde (2006) and show that, whenever the agents are sophisticated, any equilibrium allocation is efficient in this sense. Thereby, we present a version of the First Fundamental Welfare Theorem for this class of economies. Moreover, we present a social welfare function with maximisers that coincide with the efficient allocations and prove that every equilibrium can be represented by a solution to the social welfare optimisation problem. In the second chapter we concentrate on the observable implications of various models of time-preference. We consider a framework in which subjects are asked to choose between pairs consisting of a monetary payment and a time-delay at which the payment is delivered. Given a finite set of observations, we are interested under what conditions the choices of an individual agent can be rationalised by a discounted utility function. We develop an axiomatic characterisation of time-preference with various forms of discounting, including weakly present-biased, quasi-hyperbolic, and exponential, and determine the testable restrictions for each specification. Moreover, we discuss possible identification issues that may arise in this class of tests. Finally, in the third chapter, we discuss the testable restrictions for production technologies that exhibit complementarities. Suppose that we observe a finite number of choices of input factors made by a single firm, as well as the prices at which they were acquired. Under what conditions imposed on the set of observations is it possible to justify the decisions of the firm by profit-maximisation with production complementarities? In this chapter, we develop an axiomatic characterisation of such behaviour and provide an easy-to-apply test for the hypothesis which can be employed in an empirical analysis.