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aleksandr82 [10.1K]

2 years ago

6

Country A has a population of 1,000, of whom 800 work 8 hours a day to make 128,000 final goods. Country B has a population of 2

,000, of whom 1,800 work 6 hours a day to make 270,000 final goods.a. Calculate each country's productivity and real GDP per person.b. Which country is better off?

1 answer:

algol [13]2 years ago

5 0

Answer:

a) Productivity of country A = 20 goods per hour

Productivity of country B = 25 goods per hour

Real GDP per person for country A = 128 goods per person

Real GDP per person for country B = 135 goods per person

b) Country B is better off

Explanation:

Data provided in the question:

For country A

Population = 1,000

Number of workers = 800

Number of working hour per day = 8

Final goods = 128,000

For country B

Population = 2,000

Number of workers = 1,800

Number of working hour per day = 6

Final goods = 270,000

Now,

(a) The Productivity is given as

= [ Total Output ÷ Total Productive Hours ]

Thus,

Productivity of country A

= [ 128,000] ÷ [ 800 × 8 ]

= 20 goods per hour

Productivity of country B

= [ 270,000 ] ÷ [ 1800 × 6 ]

= 25 goods per hour

and,

Real GDP per person = [ Final goods ] ÷ [ Population ]

Real GDP per person for country A

= 128000 ÷ 1000

= 128 goods per person

Real GDP per person for country B

= [ 270000 ] ÷ 2000

= 135 goods per person

(b) Since,

The Real GDP per person for country B is greater than the Real GDP per person for country A

Therefore,

Country B is better off

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Assume that your uncle holds just one stock, East Coast Bank (ECB), which he thinks has very little risk. You agree that the stock is relatively safe, but you want to demonstrate that his risk would be even lower if he were more diversified. You obtain the following returns data for West Coast Bank (WCB). Both banks have had less variability than most other stocks over the past 5 years.

Year ECB WCB

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b. Measured by the standard deviation of returns, by how much would your uncle's risk have been reduced if he had held a portfolio consisting of 60% in ECB and the remainder in WCB? In other words, what is the difference between portfolio's standard deviation and weighted average of components' standard deviations? (Hint: check the example on page 11-12 on my note).

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The estimated return of the stock is the average profit.

So the average of ECB is (40-10+35-5+15)/5

= $\frac{75 percent}{5}$

= 15% expected return

WCB expected return = 40+15-5-10+35

= $\frac{75 percent}{5}$

= 15%

They've had the same planned return.

This is generally defined in the Greek letter Mu, (U) A weighted average may also be used to calculate portfolio volatility.

Standard deviation of ECB is $\sqrt{{ sum [(x-U)^2]/5}}$

so for ECB:

$(40-15)^2$ = $25^2$ =6.25%

$(-10-15)^2$ = $-35^2$ = 0.1225

$(35-15)^2$ = $20^2$ = 0.04

$(-5-15)^2$ = $-20^2$ = 0.04

$(15-15)^2$ =0

now 0.0625+0.1225+0.04+0.04+0=0.265

stdev= $\sqrt{(0.265/5)}$ = 0.23

So WCB is the same except in a different order to make things quick I'm only going to add the median again WCB=0.23

Then the 60/40 portfolio will be the "weighted average" of the returns.

portfolio returns

2004: (60%*40%)+(40%*40%) = 40%

2005: (60%*-10%)+(40%*15%) = 0%

2006: (60%*35%)+(40%*-5%) = 19%

2007: (60%*-5%)+(40%*-10%) = -7%

2008:(60%*15%)+(40%*35%) = 23%

we have an average return of (40+19-7+23)/5 = 75/5 =15%

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we knew they both had expected returns of 15% so we can say

(60%*15%)+(40%*15%)=15% so the portfolio has an expected return of 15%

Now we do the standard deviation for the whole portfolio and get

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