contestada

Suppose an agent has $100. He opens a demand deposit of S100 with a bank which has asset x where x is a random variable.

Required:
a. Suppose x is uniformly distributed on the interval [100, 200]. The density of x is f(x)=1/100 on [100,200] and f(x)=0 otherwise. What is the expected loss of the depositor?
b. Suppose changes in the economy changes the distribution of x. Now x is uniformly distributed on the interval [60, 200]. The density of x is f(x)=1/140 on [60, 200) and f(x)=0 otherwise. What is the expected loss of the depositor?
c. Suppose x is uniformly distributed on the interval [0, 200]. The density of x is f(x)=1/200 on [0, 200] and f(x)=0 otherwise. Calculate the expected loss of the depositor.
d. Suppose x is uniformly distributed on the interval [0, 200]. Given the macroeconomic environment, the government introduces deposit insurance. There is deposit insurance of an amount I=84. Calculate the expected loss of the depositor.

Respuesta :

Answer:

Following are the solution to the given points:

Explanation:

Any agent has a $100 deposit to an institution of assets X to make a demand deposit of $100.

For point a:

[tex]X \approx U(100,200)\\\\E(X) = \frac{(100+200)}{2} = 150\\\\[/tex]

assume Y is the Loss of depositor  

[tex]Y = X - 100\\\\E(Y) = 150 - 100\\\\[/tex]

The expected loss of depositors [tex]E(Y) = \$50[/tex]

For point b:

[tex]X \approx U(60,200)\\\\E(X) = \frac{(60+200)}{2} = 130\\\\Y = X - 100\\\\E(Y) = 130 - 100\\[/tex]

The expected loss of depositors [tex]E(Y) = \$30[/tex]

For point C:

[tex]X \approx U(0,200)\\\\E(X) = \frac{(0+200)}{2} = 100\\\\Y = X - 100\\\\E(Y) = 100 - 100[/tex]

The expected loss of depositors[tex]E(Y) = \$0[/tex]

For point D:

[tex]X \approx U(0,200)\\\\E(X) = \frac{(0+200)}{2} = 100\\[/tex]  

Here the government introduce deposits insurance, deposit insurance amount (I) is 84

[tex]Y \ becomes\ X+84 - 100\\\\E(Y) = E(X) + 84 -100\\\\E(Y) = 100 + 84 -100= $84[/tex]

Otras preguntas