Consider the following economy. There are two periods, 0 and 1, and a single

consumption good. The economy is populated by two types of agents: financiers (F)

and entrepreneurs (E). There is a mass one of each type. All agents in the economy

have preferences given by U = C1 + C2 , where Ct denotes consumption in period t

and is a parameter between 0 and 1.

Financiers have deep pockets (i.e., they have a large endowment every period).

Entrepreneurs have access to a variable scale project: investing I units in period 0

yields RI units of the consumption good in period 1 in case of success and 0 in case

of failure. If the entrepreneur puts effort, then the probability of success is pH. If

entrepreneur i shirks, then the probability of success is pL < pH but she gets a private

benefit BiI. Assume that Bi

is observable by Es and Fs. Entrepreneurs differ in

their private benefit of shirking Bi

, which is distributed according to the cumulative

distribution function G(Bi) in the compact set [B, B], with E[Bi

] = B.

E's have limited liability at both dates (C1 0, C2 0) and access to initial funds

Ni

, distributed in the population according to cumulative distribution function F(Ni)

in the compact set [N, N] with E[Ni

] = N. Assume that the distribution of private

benefit Bi

is independent of the distribution of net worth Ni

.

Denote the interest rate of the economy by r. Assume that

pHR

1 + r

> 1 >

pLR + B

1 + r

a) State the conditions an optimal contract must satisfy. Let i R

Bi

pHpL

. Show

that iI is the maximum amount an entrepreneur of type i can commit to repaying at

t = 1 (for this reason we will call i as "pledgeability").

b) State the entrepreneurs' problem. Show that Es invest up to the maximum

possible scale, i.e.,

I =

Ni

1

pHi

1+r

.

How does the project scale depend on Bi? Explain. Hint: Since Fs have a large

endowment, the Es keep all the surplus from the project.

c) Let I

R B

B

R N

N

I(Ni

, Bi)dF(Ni)dG(Bi) be the aggregate investment in this economy. Argue that if the financiers' endowment is sufficiently large, then 1 + r =

1

. Let

e0 denote the Fs' endowment in period 0. What is the minimum value of e0 such that

1 + r =

1

in equilibrium?

d) Start from a situation in which there is no heterogeneity so that B = B = B

and N = N = N. Does an increase in heterogeneity in Ni (but keeping the average

6

constant) increase, decrease or not change aggregate investment I? How about an

increase in heterogeneity in Bi (keeping the average constant)? Hint: If X is a random

variable and h(x) is a convex function of x, then E[h(X)] > h(E[X]).

Now suppose that entrepreneurs can hire a monitoring service (at a cost), which

reduces the private return of shirking to biI where bi = Bi with (0, 1). We will

study whether entrepreneurs have an incentive to hire the monitoring service.

e) Suppose that the cost of monitoring is cI and an entrepreneur i hires the service.

How does the contract with Fs change? Show that the scale of the project is larger

with monitoring if and only if

c (1 )pH

R i

1 + r

Discuss the ways in which money can contribute to the smooth working of an economy.

(20 marks)

(b) Explain the likely economic effects if:

(i) the supply of money grows at a faster rate than a country's production of goods and

services

(ii) the supply of money grows at a slower rate than a country's production of goods and

services.

(20 marks)

(c) (i) Explain what is meant by the term price inflation.

(ii) Name the main index used to measure price inflation in the Irish economy.

(iii) Outline the economic consequences of a rise in the rate of price inflation in Ireland.