Chapter 14A, Problem 1E

To determine

To evaluate the effect on capacity reallocations of advance sales data indicating mean demand of 55 rather than 60 during a slow travel week for business class.

Explanation of Solution

Following are the effects if mean value is assumed to be 55 instead of 60:

  $\begin{array}{c}\left(\text{Price}\left(\text{Business}\right)\text{-}\text{Marginal}\text{Cost}\left(\text{MC}\right)\right)\left(\text{Prob}\text{Shortage}\right)\\ =\left(\text{Price}\left(\text{Non}\text{Business}\right)\text{-}\text{Marginal}\text{Cost}\left(\text{MC}\right)\right)\\ =\left(\$261-\$130\right)\left(\text{Prob}\text{Shortage}\right)=\left(\$188-\$130\right)\\ =\$131\left(\text{Prob}\text{Shortage}\right)=\$58\\ \text{Prob}\text{Shortage}=\frac{58}{131}\\ =\boxed{0.442}\end{array}$

The mean value has been assumed to be 55. Thus optimal level can be calculated in the following way:

Optimal level of seats for business class

  $\begin{array}{l}=\text{Mean}\text{Value}\left(\mu \right)+Z\text{Value}\times \text{Standard}\text{Deviation}\left(\sigma \right)\\ =55+0.146\times 20\\ =57.92\\ =58\end{array}$

Now,

(63-58)= 5 extra will be allocated to the non business class.

Economics Concept Introduction

Introduction:A data set's average absolute deviation, or mean absolute deviation, is the sum of the absolute deviations from the center. It is a mathematical overview of dispersion or variability.