Abstract: This dissertation develops three essays on dynamic pricing to investigate two important topics in industrial organization: price dispersion and price discrimination. The first essay considers a stylized model of dynamic price competition in which each seller sells one unit of a homogeneous commodity by posting prices in every period to maximize the expected profits with discounting. A random number of buyers come to the market in each period. Each buyer demands at most one unit of the good, and they all have a common reservation price. They know all prices posted by all firms in the market; hence search is costless. I show that when there is a positive probability of excess demand, the model has a unique (symmetric) mixed-strategy equilibrium. In this equilibrium, each seller posts a price in every period according to a non-degenerate distribution, which is determined by the number of sellers remaining in the market in that period. Sellers play mixed strategies as they are indifferent between selling sooner at a lower price and waiting to sell at a higher price later. Thus, price dispersion not only exists in every period among firms, but also persists over time. In the second essay, I consider a monopolist who can sell vertically differentiated products over two periods to heterogeneous consumers. Consumers each demand one unit of the product in each period. In the second period, consumers are sorted into different segments according to their first-period choice, and the monopolist can offer different menus of contracts to different segments. In this way, the monopolist can price discriminate consumers not only by product quality, but also by purchase history. I fully characterize the monopolist's optimal pricing strategy when the type space is discrete and a simple condition is given to determine whether the monopolist should price discriminate consumers by product quality in the first period. When the consumers' type space is a continuum, I show that there is no fully separating equilibrium, and some properties of the optimal menu of contracts (price-quality pairs) are characterized within the class of partition PBE (Perfect Bayesian Equilibrium). The monopolist will offer only one quality in the first period when the social surplus function is log submodular or the firm and consumers are patient. If it is optimal for the firm to offer only one quality in the first period, the optimal market coverage in the first period is smaller than that in the static model. Furthermore, in equilibrium there are some high-type consumers choosing to downgrade the product in the second period, a phenomenon that has never been addressed in the literature. In the second essay, when the consumers' type space is a continuum, the analysis of the optimal menu of contracts is restricted within the class of partition PBE. The third essay provides a justification for this qualification. I ask whether an optimal menu of contracts can induce a non-partition continuation equilibrium by scrutinizing the example constructed by Laffont and Tirole (1988). They construct a non-partition continuation equilibrium for a given first-period menu of incentive contracts and conjecture that this continuation equilibrium need not be suboptimal for the whole game under small uncertainty. I construct two first-period incentive schemes leading to a partition continuation equilibrium and show that, regardless of the extent of uncertainty, their non-partition continuation equilibrium generates a smaller payoff than one of two partition continuation equilibria for the principal. In this sense, Laffont and Tirole's menu of contracts, giving rise to a non-partition continuation equilibrium, is not optimal. I provide an intuition behind this result, hoping to shed light on the problem of dynamic contracting without commitment.