Outside assets and constraints on short sales
As in the previous section, we model a situation when the only reason for asset trade is the desire to avoid taxation when marginal tax rates differ across individuals. But we now assume that the tax exempt asset is an outside asset in fixed total supply, and that this asset (which we for simplicity refer to as land) can not be sold short. We assume that land is productive, in the sense that each land unit produces p units of the consumption good further.
The introduction of land means that there is an additional layer of heterogeneity in the model. Each individual is now identified by the vector (w, X), where X is the initial land endowment.
Asset trade proceeds as follows. At the beginning of the period, individuals exchange land endowments for taxable consumption loans. This exchange takes place at the per unit land price P. For any individual the proceeds from sales/purchases of land can then be written as P(X – X), where X is the holding of land at the end of the period, when production occurs. Due to the restriction on short sales, X > 0.
As there can be no net savings in our one-period model, any change in an individual’s land value is matched by a corresponding transaction of the opposite sign in the taxable asset. Specifically, an individual who spends a positive amount P(X – X) on land increases tax deductible debt with the same amount. As before, r is the interest rate on the taxable asset.