1\newcommand{\WPabstract}{%2This paper studies how search frictions, heterogeneous seller urgency, financing frictions and bargaining jointly determine3the liquidity discount, transaction prices, sale hazards and price dispersion in a local housing market. In a continuous-time4matching model with free entry of buyers, sellers differ in a permanent carrying cost, buyers draw match-specific valuations, and5prices are set by Nash bargaining. The urgency discount, defined relative to the most patient seller, is nonnegative and6increasing in the carrying cost, and the expected price falls by less than the reservation price. A fall in buyer arrivals or7in mortgage qualification lowers prices, lengthens time on market and widens the discount when the valuation distribution has8an increasing failure rate; with heavy-tailed valuations a more liquid market can lengthen time on market, under an explicit9condition on the carrying cost. Liquidity shocks move prices, volume, inventory and durations with no change in housing-service10values, and buyer entry amplifies them. The gap between mortgage and cash prices decomposes into a delay-bargaining term that11rises with urgency, an outside-option term, and a selection term that can be negative. The composition of transactions shifts12after a liquidity shock in a direction governed by the shape of the valuation distribution, and its effect on a13transaction-price index is an order of magnitude smaller than the within-type liquidity effect, which no quality adjustment14removes. The Walrasian free-entry price is shown not to be a liquidity premium benchmark, since search prices exceed it in thick15markets. Results are illustrated numerically with a documented parameterisation and reproducible code; no data are used.%16}17