Product-market competition and financing:-
Two firms, i = 1, 2, compete for a new market. To enter the market, a firm must develop a new technology. It must invest (a fixed amount)
I. Each firm is run by an entrepreneur. Entrepreneur i has initial cash Ai private benefit B from shirking and 0 when working. The probability of success is pH and pL = pH - ?p when working and shirking. The return for a firm is
where M>D> 0.
Assume that pH(M - B/?p) < I. We look for a Nash equilibrium in contracts (when an entrepreneur negotiates with investors, both parties correctly anticipate whether the other entrepreneur obtains funding). In a first step, assume that the two firms' projects or research technologies are independent, so that nothing is learned from the success or failure of the other firm concerning the behavior of the borrower.
(i) Show that there is a cutoff A such that if Ai < A, entrepreneur i obtains no funding.
(ii) Show that there is a cutoff A such that if Ai > A for i = 1, 2, both firms receive funding.
(iii) Show that if A
That is, the entrepreneur is infinitely risk averse below c0 (this assumption is stronger than needed, but it simplifies the computations). Suppose, first, that only one firm can invest. Show that the necessary and sufficient condition for investment to take place is
(v) Continuing on from question (iv), suppose now that there are two firms and that their technologies are perfectly correlated in that if both invest and both entrepreneurs work, then they both succeed or both fail. (For the technically oriented reader, there exists an underlying state variable ω distributed uniformly on [0, 1] and common to both firms such that a firm always succeeds if ωpH, and succeeds if and only if the entrepreneur works when pL
then it is an equilibrium for both entrepreneurs to receive finance. Conclude that product-market competition may facilitate financing.