their labor services in the market. Entrepreneurs decide how much capital and
labor to demand. Banks are in the business of intermediating between suppliers
of capital, that is, all workers as well as the entrepreneurs with assets in excess of
their investment needs, and demanders of capital, that is, entrepreneurs who want
to expand their business above the level of their accumulated assets. Finally, at
the end of the period, productivities for the period (z0) are realized and production
takes place. Then, workers are paid their wages, entrepreneurs realize profits and
interests are paid on loans and deposits.
If an agent decides to be a worker, he will draw his effective skill, z0 ,froma
fixed distribution ψ(z0). The revenue from working is z0w where w is the wage per
unit of productivity. Each agent who decides to be entrepreneurs will draw his
productivity level from a Markov process with transition function Q(z, z0). The
Markovian nature of the entrepreneurial skills is assumed to reflect the learning
aspects of entrepreneurial activity as documented by Quadrini [21]. Furthermore,
we assume Q to be monotone and to satisfy the Feller property. Entrepreneurs
hire capital (k) and labor (n) in a competitive fashion and produce according to
the production function
y = z0f (k,n)= z0 (kαn1-α/ , (1)
where α ∈ (0, 1) and θ<1. The production function exhibits decreasing returns
to scale which, as in Lucas [17], can be thought of as capturing the presence of
decreasing returns to managerial control. Capital used in production depreciates at
the rate δ ∈ (0,1). The productivity shocks are drawn from the same set Z = [z, z],
both for workers and entrepreneurs. It is assumed that entrepreneurs with the
lowest signal remain with that level of productivity [Q(z,z) = 1], so that those
agents always prefer to become workers. To guarantee that some entrepreneurs
exit that occupation, we also assume that Q(z,z) > 0, for all z ∈ Z.
Given the distribution of assets and productivities among agents, there will be
some of them who will not want to use all their assets. These are all the workers
and the entrepreneurs who expect to have low relative levels of productivity or
who have relative high levels of initial assets. On the other hand, entrepreneurs
who expect to be very skillful but have relatively low levels of assets will like to use
more capital than what they can finance by themselves. The commercial banks
are in the business of connecting people expecting to have idle assets with people
who want to expand their firms above the level of their accumulated assets. One
problem in this economy is that workers cannot take their assets to where they
work. So, some of the workers may be working with an entrepreneur who does not
borrow at all or who borrows from other agents. Also, there may be entrepreneurs