Lectures week 1: Introduction
Fintech is the utilization of technology in the process of financial innovation. While historical
developments in fintech were mostly lead by financial institutions themselves, recent developments
have been by technology companies (e.g. Facebook with libra). This may be due to the fact that these
types of firms are less strongly regulated than the incumbents. Developments in fintech usually
happen piecemeal and affect different parts of the supply chains of incumbent financial institutions.
Topic: Utility and financial models
Utility measures the total satisfaction received from consuming a good or service. We assume that
the utility function is increasing and concave (thus the first order derivative is positive, while the
second order derivative is negative). This concavity leads to diminishing marginal utility, thus the
marginal utility of each homogeneous unit decreases as the supply of units increases. A temporal
utility function gives you the amount of utility gained in one period, while an intertemporal utility
function can be used to calculate the utility of more periods. An example of an intertemporal utility
function is shown below:
Budget constraints represent a constraint on for example the agent’s budget for consumption. These
can be used to calculate the optimal division of income. An example of a budget constraint is shown
below:
Indifference curves consist of all combinations that make you indifferent between the two.
,If you are given a budget constraint and a utility function, you can compute the optimal level of
consumption to give a maximum utility level.
Topic: Autarky world and Technology world
Suppose we have the model below to represent the setting of the worlds we are going to research:
Model I Autarky world:
In an Autarky world the actor can only consume what you have in each period. In this model it is easy
to see that to maximize his or her utility, the actor will consume such that all income in each period is
consumed in that period: . Thus, in conclusion, in this type of world individual agent’s
consumption is constrained by their own production probabilities (Y1 and Y2).
Model II with storage technology:
If we add storage technology to this world, such that agents can store a unit in period one which they
can then consume in period two for gamma units (with gamma being larger than 0 but smaller than
1). An agent is always better off in this model, since their opportunity set is larger, because the agent
can always choose to store nothing and we would have the same model as in Autarky world. The
figure below compares this setting to the Autarky world and computes the optimal value of x. We
can see that the opportunity set has been increased from a point to a line.
,Thus, we can see that with the assumptions above the storage technology has improved the agent’s
utility. The utility is higher than in Autarky world, which is also evidenced by the fact that the
indifference curve in the technology world is more to the upper right-hand corner (thus signifying
higher utility).
Model III with production technology:
Now there is a world with production technology, such that you can use some of your income in
period 1 to produce and get more income in period 2 (difference with storage technology is that you
get more income in period 2 for a unit of period 1 income). With deriving the utility function subject
to the budget constraints and setting it equal to zero, we can calculate that with the production
technology the utility of the agent has increased as compared to the other two worlds.
, Model IV with financial markets:
We can also extend the model to include a financial sector in which you can borrow or lend in the
financial market with an interest rate R = (1+r). Thus the agent can now borrow money to consume
more in period one (at the cost of being able to consume less in period two) or he can lend money to
consume more in period two (at the cost of being able to consume less in period one). The model is
set up as shown below:
We can now again solve an optimization problem with budget constraints to get the optimal amount
to lend/borrow in this model and calculate the maximum utility to see if the agent is better off. With
some examples it can be shown that with a high discount factor beta, the financial market adds
utility, since it allows the agent to borrow money to consume more in period 1 (for which there is no
discount).
As we can see in the model above, a model with financial markets can increase our opportunities
(see the blue line) by allowing the agents to consume more in period 1 through borrowing or
consumer more in period two by lending. It can also be shown that with financial markets, a model
with production technology can lead to more utility, such that we can argue that financial markets
are complementary to production, not a substitute.
Summary:
• Agents are risk averse individuals and like smooth consumption
• Financial markets help individuals to transfer wealth across periods and states (e.g.
insurance) and thereby smooth their consumption, stabilize lives and maximize utility for
risk-averse agents.
Fintech is the utilization of technology in the process of financial innovation. While historical
developments in fintech were mostly lead by financial institutions themselves, recent developments
have been by technology companies (e.g. Facebook with libra). This may be due to the fact that these
types of firms are less strongly regulated than the incumbents. Developments in fintech usually
happen piecemeal and affect different parts of the supply chains of incumbent financial institutions.
Topic: Utility and financial models
Utility measures the total satisfaction received from consuming a good or service. We assume that
the utility function is increasing and concave (thus the first order derivative is positive, while the
second order derivative is negative). This concavity leads to diminishing marginal utility, thus the
marginal utility of each homogeneous unit decreases as the supply of units increases. A temporal
utility function gives you the amount of utility gained in one period, while an intertemporal utility
function can be used to calculate the utility of more periods. An example of an intertemporal utility
function is shown below:
Budget constraints represent a constraint on for example the agent’s budget for consumption. These
can be used to calculate the optimal division of income. An example of a budget constraint is shown
below:
Indifference curves consist of all combinations that make you indifferent between the two.
,If you are given a budget constraint and a utility function, you can compute the optimal level of
consumption to give a maximum utility level.
Topic: Autarky world and Technology world
Suppose we have the model below to represent the setting of the worlds we are going to research:
Model I Autarky world:
In an Autarky world the actor can only consume what you have in each period. In this model it is easy
to see that to maximize his or her utility, the actor will consume such that all income in each period is
consumed in that period: . Thus, in conclusion, in this type of world individual agent’s
consumption is constrained by their own production probabilities (Y1 and Y2).
Model II with storage technology:
If we add storage technology to this world, such that agents can store a unit in period one which they
can then consume in period two for gamma units (with gamma being larger than 0 but smaller than
1). An agent is always better off in this model, since their opportunity set is larger, because the agent
can always choose to store nothing and we would have the same model as in Autarky world. The
figure below compares this setting to the Autarky world and computes the optimal value of x. We
can see that the opportunity set has been increased from a point to a line.
,Thus, we can see that with the assumptions above the storage technology has improved the agent’s
utility. The utility is higher than in Autarky world, which is also evidenced by the fact that the
indifference curve in the technology world is more to the upper right-hand corner (thus signifying
higher utility).
Model III with production technology:
Now there is a world with production technology, such that you can use some of your income in
period 1 to produce and get more income in period 2 (difference with storage technology is that you
get more income in period 2 for a unit of period 1 income). With deriving the utility function subject
to the budget constraints and setting it equal to zero, we can calculate that with the production
technology the utility of the agent has increased as compared to the other two worlds.
, Model IV with financial markets:
We can also extend the model to include a financial sector in which you can borrow or lend in the
financial market with an interest rate R = (1+r). Thus the agent can now borrow money to consume
more in period one (at the cost of being able to consume less in period two) or he can lend money to
consume more in period two (at the cost of being able to consume less in period one). The model is
set up as shown below:
We can now again solve an optimization problem with budget constraints to get the optimal amount
to lend/borrow in this model and calculate the maximum utility to see if the agent is better off. With
some examples it can be shown that with a high discount factor beta, the financial market adds
utility, since it allows the agent to borrow money to consume more in period 1 (for which there is no
discount).
As we can see in the model above, a model with financial markets can increase our opportunities
(see the blue line) by allowing the agents to consume more in period 1 through borrowing or
consumer more in period two by lending. It can also be shown that with financial markets, a model
with production technology can lead to more utility, such that we can argue that financial markets
are complementary to production, not a substitute.
Summary:
• Agents are risk averse individuals and like smooth consumption
• Financial markets help individuals to transfer wealth across periods and states (e.g.
insurance) and thereby smooth their consumption, stabilize lives and maximize utility for
risk-averse agents.
