ECO 359 Practice Problems 6
1. An entrepreneur has access to a project, which generates future revenue of 20 or 4 and
requires an initial cost of 5. When he exerts an effort level AÐ>rás? for the project, the
project generates revenue 20 with probabilityA and revenue 4 with probability sFA. His
utility is reduced by sxA6. The initial cost must be financed by issuing either debt or equity.
The entrepreneur can choose his effort level at will after debt or equity is issued. Both the
entrepreneur and investors are risk neutral and there is no discounting.
(a) Can the project be financed when he issues debt?
(b) Can the project be financed when he issues equity?
2. Miranda is considering running for society-presidency. If she runs and is successful, she
becomes the society's president and gets a payoff of :Lstr. If she's unsuccessful, she
becomes vice-president and gets a payoff of :Lur. The fixed costs of running are F = 50.
The probability of the high outcome depends on the effort that Miranda puts in. Her effort is a
continuous variable in >rás?, and the probability of the high outcome is 2N::L:;LA, for
the low it is 2Nk:L:oLsFAä Now Miranda rather slacks off, since putting in the effort
is costly for her. To be precise, effort costs her ?:A;LvwA6ä
(a) Suppose Miranda has the funds to finance herself. Which effort level will she choose?
(b) Now suppose she seeks to finance her endeavors through credit (=debt). Assume
throughout that effort is non-contractible.
(i) Suppose the debt's face value has the risk-free amount. Show that a risk-free debt
contract would require that Miranda exerts effort ALs.
(ii) Now assume a risky debt contract. In the bad state, all goes to the debtor, 4Lur.
Verify that the debt's face value 4 as a function of A is
(iii) Show that Miranda's optimal effort choice is AÛLsu or AÛLtu.
(c) Show that Miranda cannot finance her campaign with an equity contract. (In an equity
contract she would sell fraction = of future payoffs to her financier.)