Chapter 14, Problem 14.3P

a

To determine

Present value of each student’s income.

Answer to Problem 14.3P

The present value of income is $100,000

Explanation of Solution

Given Information:

  $\text{MRS}\text{for}\text{P}\text{=}{\text{C}}_{\text{1}}/{\text{3C}}_{\text{0}}$

  $\text{MRS}\text{for}G\text{=}{\text{3C}}_{\text{1}}/{\text{C}}_{\text{0}}$

It is known that,

  $(1+r)C_0+C_1=(1+r)Y_0+Y_1$

Above budget constraint shows Consumption in present period and in future period is equal to total income earned.

Since, $r=0.1$

  $1.1C_0+C_1=1.1(50000)+55000$

  $=55000+55000$

  $=110000\mathrm{......}(1)$

The present value (PV) of D$ is $\frac{D}{(1+r)}$

The Income this year is $50000.

So the present value is given below.

  $\frac{50000}{(1+0)}=50000$

The income next year is $55000. Present value using this income is calculated as follows.

  $\frac{55000}{(1+0.1)}=50000$

Therefore, the present value of income is $100,000.

Economics Concept Introduction

Introduction:

Present discounted value means an amount to be paid or invested today to get regular income in future. It is usually done to know the real interest rate in an economy for the investment done.

b)

To determine

Condition for maximizing utility.

Answer to Problem 14.3P

He must consume times of consumption this year in next year.

Explanation of Solution

Given Information:

  $\text{MRS}\text{for}\text{P}\text{=}{\text{C}}_{\text{1}}/{\text{3C}}_{\text{0}}$

  $\text{MRS}\text{for}G\text{=}{\text{3C}}_{\text{1}}/{\text{C}}_{\text{0}}$

For utility maximization, marginal rate of substitution is equal to the price ratio.

For roommate P,

  $MRS=\frac{C_1}{3C_0}$

The price ratio is $1+r$

In equilibrium,

  $\frac{C_1}{3C_0}=1+r$

  $\frac{C_1}{3C_0}=1.1$

  $C_1=3.3C_0$

For utility maximization of roommate P, he must consume times of consumption this year in next year.

Economics Concept Introduction

Introduction:

Utility is the satisfaction dervied from consumption of good or services. To calculate satisfactifaction, it is given numeric form called utils. Util is the unit to measure utility. More the utils, more is the utility derived.

c)

To determine

Way to $C_1$ and $C_0$ choose to get maximum utility and amount to be borrowed or saved by P.

Answer to Problem 14.3P

saving this (present) year is $25000 and there is a dissaving of $27500 in next year.

Explanation of Solution

Given Information:

  $\text{MRS}\text{for}\text{P}\text{=}{\text{C}}_{\text{1}}/{\text{3C}}_{\text{0}}$

  $\text{MRS}\text{for}G\text{=}{\text{3C}}_{\text{1}}/{\text{C}}_{\text{0}}$

Now according to the third condition, put $C_1=3.3C_0$ in equation (1),

  $1.1C_0+3.3C_0=110000$

  $\begin{array}{l}4.4C_0=110000\\ C_0=25000\\ C_1=3.3(25000)\\ =82500\end{array}$

  $\text{Saving in period 0}\left(\text{this year}\right)\text{ = Income this year - Consumption this year}$

Similarly,

  ${\text{S}}_1=Y_1-C_1$

  $S_1=55000-82500$

  $=-27500$

For roommate P, saving this year is $25000 and there is a dissaving of $27500 in next year.

Economics Concept Introduction

Introduction:

Present discounted value means an amount to be paid or invested today to get regular income in future. It is usually done to know the real interest rate in an economy for the investment done.

d)

To determine

Way to $C_1$ and $C_0$ choose to get maximum utility and amount to be borrowed or saved by G.

Answer to Problem 14.3P

G borrows $25,000 in period 0 and save S $27,500 in period 1.

Explanation of Solution

Given Information:

  $\text{MRS}\text{for}\text{P}\text{=}{\text{C}}_{\text{1}}/{\text{3C}}_{\text{0}}$

  $\text{MRS}\text{for}G\text{=}{\text{3C}}_{\text{1}}/{\text{C}}_{\text{0}}$

Here, solve for roommate G. The MRS for Glitter is $\frac{3C_1}{C_0}$ .

In equilibrium,

  $\begin{array}{l}MRS=1+r\\ MRS=1.1\end{array}$

  $\frac{3C_1}{C_0}=1.1$

  $C_0=\left(\frac{30}{11}\right)C_1$

Put this in equation (1).

  $3C_1+C_1=110000$

  $\begin{array}{l}4C_1=110000\\ C_1=27500\\ C_0=\left(\frac{30}{11}\right)27500\\ =75000\end{array}$

  $\begin{array}{l}{S}_0=Y_0-Y_1\\ S_0=50000-75000\\ =-25000\end{array}$

  $\begin{array}{l}{S}_1=Y_1-C_1\\ =55000-27500\\ =27500\end{array}$

G borrows $25,000 in period 0 and save S $27,500 in period 1.

Economics Concept Introduction

Introduction:

Present discounted value means an amount to be paid or invested today to get regular income in future. It is usually done to know the real interest rate in an economy for the investment done.