The variable is the discount rate of the next unit bought compared to the price of the preceding unit.

The variable is the refinement rate (or the rate of subdivision) of the original assets. For example means the original unit asset is split into 10 new unit assets.

and represent the sensitivity of the average price with respect to and , respectively, computed as partial derivatives with respect to and .

We argue that the U.S. government would discover the real price of the Troubled Assets Relief Program's (TARP) troubled assets by becoming a market maker on those assets, if those assets were purchased at a sufficiently refined level of granularity (i.e., with increasing).

The purple line represents the average price paid for each original unit of asset as the government keeps buying units of toxic assets, assuming no additional bargain hunters enter the market.

As the discount factor increases, the unit price decreases very quickly. But it is not desirable for the market to have a very steep discount factor, as this steepness captures a relative lack of liquidity in the market. Instead, liquidity problems can be handled by refining the unit size of the assets, which contributes to a more effective price discovery process.

Furthermore, note that the sensitivity on is structurally of a different order compared to the sensitivity on . In this simplified model, the sensitivity on is polynomial while the sensitivity on is exponential.