EC210. Macroeconomic Principles
London School of Economics and Political Science
Problem Set 3
Lent term 2016
Professor Ricardo Reis
Short question 1: Can we have a bank run on a …nancial insti-
tution, like an investment bank, that is not authorized by law to
accept checking account deposits?
Short question 2: A BBC investigation discovers that while long-
term investment projects earn a return of 10% per year, people
holding their savings in banks from the beginning to the end of
the projects are only paid 8%, if all goes well. Moreover, the
reporters learn that the return may be zero if there is bank run.
Are these two facts necessarily inconsistent with a competitive
banking sector.
Long question 1: This problem asks you to work through a
slightly harder version of the Diamond? Dybvig model, that I
mentioned in class. In an economy, there is one good, three peri-
ods 0, 1 and 2, and N agents, all identical ex ante at date 0 and
with 1 unit of a good. A fraction g of the agents turn out to be
impatient and get utility from consuming in period 1 u(c1 ), and a
fraction 1 g gets utility from consuming in period 2, u(c2 ). Ex
ante expected utility then is:
gu(c1 ) + (1 g)u(c2 )
The utility function is u(c) = 1 1=c.
There are two investments. One, on short-term storage, re-
turns 1 unit at date 1 per unit invested at date 0. Likewise, a unit
stored at date 1 gives one unit at date 2. The other investment is
on a long-term technology that per unit invested at date 0 returns
R > 1 at date 2, but only L < 1 if it is liquidated at date 1.
1
London School of Economics and Political Science
Problem Set 3
Lent term 2016
Professor Ricardo Reis
Short question 1: Can we have a bank run on a …nancial insti-
tution, like an investment bank, that is not authorized by law to
accept checking account deposits?
Short question 2: A BBC investigation discovers that while long-
term investment projects earn a return of 10% per year, people
holding their savings in banks from the beginning to the end of
the projects are only paid 8%, if all goes well. Moreover, the
reporters learn that the return may be zero if there is bank run.
Are these two facts necessarily inconsistent with a competitive
banking sector.
Long question 1: This problem asks you to work through a
slightly harder version of the Diamond? Dybvig model, that I
mentioned in class. In an economy, there is one good, three peri-
ods 0, 1 and 2, and N agents, all identical ex ante at date 0 and
with 1 unit of a good. A fraction g of the agents turn out to be
impatient and get utility from consuming in period 1 u(c1 ), and a
fraction 1 g gets utility from consuming in period 2, u(c2 ). Ex
ante expected utility then is:
gu(c1 ) + (1 g)u(c2 )
The utility function is u(c) = 1 1=c.
There are two investments. One, on short-term storage, re-
turns 1 unit at date 1 per unit invested at date 0. Likewise, a unit
stored at date 1 gives one unit at date 2. The other investment is
on a long-term technology that per unit invested at date 0 returns
R > 1 at date 2, but only L < 1 if it is liquidated at date 1.
1
