11/6/2009

#Credit

The way the market works is that I want to do something with my money.
I can give it to a firm and they will give me it back later with added interest,
  or I can give it to a bank to hold.  In equillibrium, the bank should give
  a rate equal to the interest of investing in a company, or else a competitor
  will supply a more competitive service, etc.

(keep in mind that in perfect market, firms make zero profit)

Neoclassical model
  in equillibrium, capital supply for firms equals the rate of return on investment,
    once supply = demand
  marginal product of capital = mpk = 1 + r
      what you invested --------------^   ^----interest earned over time
  from here on in, let r be 1+r (the gross interest rate)

In the real-world, there's a probability of default (you run away w/ money,
  are unable to pay, etc.).  Let d=default rate
so in reality, MPK = (1-d)r       [should also have -d, since they might 
                                   run away w/ money]

Facts
  - lending rates are high (low bound is 12-20% all the way to 80-120% interest)
  - there's high variance and mean.  mu = 80%, sd = 35%.  The variance is
    high because different people walk in to the bank and get very different
    rates depending on their data
  - profitability?  nope---credit guys in villages run basically at 0 profit
  - default probability? low
  - rich people borrow more, and r for the rich is lower
  - 70% of loans go toward production, not just fun

How do we model this?
Assumptions
  - \rho is cost of capital---money lenders have to walk to big down, borrow from
    big bank, etc.
  - k is capital you need to invest to get income of F(k)
  - w is your current wealth, so you need to borrow k-w
  - borrower must repay (k-w)*r
  - the borrower can shirk (run away) at a cost of \eta per dollar loaned.
  - borrower repays when the profit is greater than cost of shirking
      F(k) - (k-w)r >= F(k) - \eta*k
      rearrange: r/(r-\eta) >= k/w

From this, you can get that firms are credit-rationed
That gives you the reason why microcredit is so wildly popular