url
7
Mar
2015

## DISPLACED CAPITAL: Theoretical Framework 3

Our assumption about costly search and matching is related to the large literature on search and matching (e.g. Stigler (1961), McCall (1970), Diamond (1982), Pissarides (1985), Mortenson (1986)). The structure of our model, however, contains a feature not found in other search models (to our knowledge.) In our model, the firm sells multiple units, whose value depends on the total selection available. This feature leads the firm to face a tradeoff between selling early at a low price and preserving the selection available to high-valuation buyers.

For those readers who wish to skip the theoretical details of the model, we briefly summarize the theoretical results to which we allude later in the empirical section. We show that under certain conditions, a firm structures its capital sales to consist of two parts. The first part, which is called the “private liquidation sale,” is a period of search for industry insiders. These sales result in high value matches and a higher sales price for the capital. The second part is a “public auction,” which involves a large auction in which the remaining capital is sold all at once to industry outsiders. The amount of capital sold to insiders is positively related to the firm’s discount factor: more patient firms spend more time searching for high quality matches among industry insiders.

Model

The model analyzes the decision problem of a firm that is selling used capital.7 Consider a firm from sector A (aerospace) that wishes to sell a total of N units of capital so as to maximize the expected present discounted value of revenue from the sale. The units of capital are heterogeneous in that each unit will have a different value for different buyers, but the seller does not know which particular unit the buyer will prefer. For each unit of capital, the firm can decide whether to sell to another firm in sector A or to a firm outside of sector A, called sector O (outsiders). comments

We assume that selling capital to sector A has the following structure:

(i) To take a draw from sector A, the firm must pay a fixed cost C. The firm can only make one draw from sector A per period.

(ii) If the firm takes a draw from sector A, there is a probability в, 0

Our assumption about costly search and matching is related to the large literature on search and matching (e.g. Stigler (1961), McCall (1970), Diamond (1982), Pissarides (1985), Mortenson (1986)). The structure of our model, however, contains a feature not found in other search models (to our knowledge.) In our model, the firm sells multiple units, whose value depends on the total selection available. This feature leads the firm to face a tradeoff between selling early at a low price and preserving the selection available to high-valuation buyers. For those readers who wish to skip the theoretical details of the model, we briefly summarize the theoretical results to which we allude later in the empirical section. We show that under certain conditions,