Answer to Question #228451 in Macroeconomics for birhanu

Question

Assume you are making business decision on alternative two businesses under determined
risks. Given the following probability of the risks and estimated profit, (5 marks)
a. Calculate the expected profit you could get under each risk probabilities for the
business alternatives.
b. Which business do you select based on the expected profit?
c. By constructing a discrete probability distribution, which business do you select?
d. By calculating the expected mean values, variance, standard deviation and
coefficient of variation, which business do you select?
Business Economic Condition Probability Outcome/
Profit
Expected
Profit
Y
Good economic condition/boom 0.2 900
Normal economic condition 0.5 800
Bad economic condition/recession 0.3 700
Expected Profit
Z
Good economic condition/boom 0.2 1000
Normal economic condition 0.5 800
Bad economic condition/recession 0.3 600
Expected Profi

Answer 1

a. Expected profit

Business Y

Boom 0.2 x 900 = 180

Normal 0.5 x 800 = 400

Recession 0.3 x 700 = 210

Total expected Profit for Y = 790

Business Z

Boom 0.2 x 1000 = 200

Normal 0.5 x 800 = 400

Recession 0.3 x 600 = 180

Total expected Profit for Z = 780

b.

I will select business Y because it has a higher expected profit as compared to business Z.

c.

Discrete Probability distribution of Y

y p(y)

180 0.2

400 0.5

210 0.3

Discrete Probability distribution of Z

z p(z)

200 0.2

400 0.5

180 0.3

I will select business Z

d.

Expected Mean

Expected mean for business Y

y p(y) y*p(y)

180 0.2 36

400 0.5 200

210 0.3 63

Expected mean for Y = 299

Expected mean for Z

z p(z) z*p(z)

200 0.2 40

400 0.5 200

180 0.3 54

Expected mean for Z = 294

Based on the expected mean I will choose business Y

Variance

Variance for Business Y

(y – μ)² * P(y)

(180-299)² * 0.2 =2832.2

(400-299)² * 0.5 =5100.5

(210-299)² * 0.3 =2376.3

Total variance for Y = 10309

Standard deviation

Standard deviation of Y is the square root of the variance = 101.53

Variance

Variance for Business Z

(z – μ)² * P(z)

(200-294)² * 0.2 =1767.2

(400-294)² * 0.5 =5618

(180-294)² * 0.3 =3898.8

Total variance for Z = 11284

Standard deviation

Standard deviation of Z is the square root of the variance = 106.23

Coefficient of variation

Coefficient of variation is given by the standard deviation divided by the mean

Coefficient of variation of Y is 101.53 / 299 = 0.34

Coefficient of variation of Z is 106.23 / 294 = 0.36

Based on the variance, standard deviation and coefficient of variation I will choose business Y.