allows us to study how the elasticity of substitution between wealth and consumption affects
the equilibrium outcome. In particular, we are able to derive a simple condition that ensures
that higher substitutability leads to a higher intensity of extraction from the common property
asset and therefore to a smaller growth rate of the public capital stock. The combination of
the wealth effect and positive appropriation costs has also another interesting consequence.
Whereas in the model of Tornell and Velasco [11] and Tornell and Lane [10] the equilibrium
money returns on both types of assets must coincide, this is no longer true in our model with
wealth effects and positive costs of transferring resources from the public to the private asset.
As a matter of fact, depending on the parameter values, the private asset can have either a
lower or a higher money rate of return than the public one.3
Considering the domestic capital stock as a common property asset makes the model formally
similar to one in which agents have common access to a natural (renewable or non-renewable)
resource. There is a large literature on these models and the paper that is closest to ours in this
respect is the one by Sorger [8]. Resource extraction models that allow for private storage of the
extracted resource have been studied, for example, by Sinn [7], Kremer and Morcom [4], Gaudet
et al. [3], or Dutta and Rowat [2]. Whereas Kremer and Morcom [4] and Gaudet et al. [3] study
competitive resource markets, Sinn [7] and Dutta and Rowat [2] deal with oligopolistic markets.
The paper by Dutta and Rowat [2] uses a setup that is very close to ours except that it does
not include wealth-dependent utility. Their focus, however, is quite different from ours since
they are mostly interested in whether or not extinction can occur as an equilibrium outcome.
In our model, the marginal utility of wealth becomes infinitely large as wealth approaches 0,
which implies that agents will never run down their wealth in finite time, i.e., extinction is not
possible in equilibrium.
The paper is organized as follows. In section 2 we formulate the model and state all assumptions.
Section 3 characterizes the interior equilibrium under the assumption of homogeneous players.
We discuss how the structure of the equilibrium is affected by the presence of appropriation
costs and wealth effects. Furthermore, we study how changes in one or more model parameters
influence the intensity of appropriation and the net growth rate of the public capital stock.
Section 4 introduces heterogeneity of the power groups. We characterize again an interior Nash
equilibrium of the game and analyze how the growth rate of the economy depends on the degree
of heterogeneity. Finally, in section 5 we impose an additional constraint on the intensity of
extraction from the public capital stock. Such a constraint can be interpreted in terms of
capital controls. We show that, in general, there exists a pessimistic equilibrium in addition to
the interior equilibrium discussed in section 3. In the pessimistic equilibrium all players transfer
resources from the public capital stock into their private asset holdings as quickly as possible.
Finally, section 6 presents concluding remarks.
and I am a material girl.”
3Of course, if one defines appropriate concepts such as ‘full rates of return’, then, by definition, they must be
equalized in equilibrium.