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