Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
9th Edition
ISBN: 9781259290619
Author: Michael Baye, Jeff Prince
Publisher: McGraw-Hill Education
Question
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Chapter 12, Problem 1CACQ

(A)

To determine

The expected value of each option is to be calculated.

(A)

Expert Solution
Check Mark

Explanation of Solution

Expected value is calculated as

  E(x)=q1x1+q2x2+.........+qnxn

Consider an option 1,

  E(x)=116×150+416×300+616×750+416×300+116×150

  E(x)=15016+120016+450016+120016+15016

  = 720016

  = 450.

Consider an option 2,

  E(x)=15×120+15×255+15×1500+15×255+15×120

  = 24 +51 +300 + 51 +24

  = 450.

Therefore, in both the options, expected value is 450.

(B)

To determine

The variance and standard deviation of each option is to be calculated.

(B)

Expert Solution
Check Mark

Explanation of Solution

Variance is calculated as

σ = [ q1(x1 - (E(x))2 + q2(x2 - (E(x))2 + ................+ qn(xn - (E(x))2 ]

Standard deviation is the square root of variance.

SD = σ

Consider an option 1,

σ = 116×(150450)2+416×(300450)2+616×(750  450)2+416×(300450)2+116×(150450)2

  = 116×(300)2+416×(150)2+616×(300)2+416×(150)2+116×(300)2

  = 116×90000+416×22500+616×90000+416×22500+116×90000

  = 116 [90000+900000+540000+900000+90000 ]

  = 252000016

  = 157500.

Consider an option 2,

σ = 15×(120450)2+15×(255450)2 2 +15×(1500450)2+15×(255450)2+15×(120450)2

  = 15×(330)2+15×(195)2+15×(1050)2+15×(195)2+15×(330)2

  = 15×108900+15×38025+15×1102500+15×38025+15×108900

  = 15 [108900+38025+1102500+38025+108900 ]

  = 13963505

  = 279270.

Variance in option 1 is 157500 and in option 2 is 279270.

Standard deviation is the square root of variance.

SD = v σ

Consider an option 1,

  SD = 157500

  = 396.86

Consider an option 2,

  SD = 279270

  = 528.46

Variance of option 1 is 157500 and variance of option 2 is 279270.

Standard deviation of option 1 is 396.86 and standard deviation of option 2 is 528.46.

(C)

To determine

The option that is riskier to be ascertained.

(C)

Expert Solution
Check Mark

Explanation of Solution

Basically, the option with high variability is more risky option.

Higher variability means high variance or standard deviation.In this question, Option 2 has more variance and standard deviation. Thus, it is riskier.

The riskier option is Option 2.

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