Bundle: Microeconomic Theory: Basic Principles and Extensions, 12th + MindTap Economics, 1 term (6 months) Printed Access Card
Bundle: Microeconomic Theory: Basic Principles and Extensions, 12th + MindTap Economics, 1 term (6 months) Printed Access Card
12th Edition
ISBN: 9781337198202
Author: NICHOLSON, Walter, Snyder, Christopher M.
Publisher: Cengage Learning
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Chapter 18, Problem 18.1P

(a)

To determine

The expected utility if shareholder offered to share half of the store’s revenue and the lowest share one would accept to manage the firm.

(a)

Expert Solution
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Explanation of Solution

Given the utility function, Utility= w-100

If a shareholder’s share is 50% of the gross profit with C, then expected utility can be derive by inserting the value of the half of gross profit in C’s utility function, we have

EU=0.5(500-100) + 0.5(200-100)EU=0.5(400) + 0.5(100)EU=200+50EU=250 (when half reserve is shared with shareholders)

Yes, C will accept when shareholder offered to share half of the store revenue with her.

EU (when receiving quarter share)EU=0.5(250-100) + 0.5(100-100)EU=0.5(150)EU=75

Lowest share that would accept: EU00.5(1000k100) + 0.5(400k100)0Where k: Clare’s share in profits700k1000K17

The lowest value C would accept is 17th reserve with shareholders.

(b)

To determine

The most C would pay to buy out the store if shareholders decided to sell it off.

(b)

Expert Solution
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Explanation of Solution

Maximum C is willing to pay to buy out the store= Expected Value of the store=12×1000+12×400=$700

The maximum amount she is willing to pay to buy is $700.

(c)

To determine

The fixed salary she would accept instead of $100 bonus.

(c)

Expert Solution
Check Mark

Explanation of Solution

Let fixed salary be M

0.5(100+M+100)+ 0.5(M100)0M500M50

(d)

To determine

The lowest share that would induce her to exert effort.

(d)

Expert Solution
Check Mark

Explanation of Solution

  1. Let the required share be K

One must have

      EU(effort)>EU(no effort)       0.5(1000K100) + 0.5(400K100) > 400K       700K100>400K       300K>100        K>13

Therefore, the lowest share that she would induce her to exert effort is 13 .

  1. Maximum expected profit along with fixed salary and bonus.

M=Fixed salary, B= BonusMaximize profit (π)= Revenues- fixed salary-expected bonus         π= 0.5(1000) + 0.5(400)-M-0.5B         π=700-M-0.5B        M+0.5B=700        2M+B=1400

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