# General A is defending a territory which is accessible by two mountain passes against general B. A

## Question:

General A is defending a territory which is accessible by two mountain passes against general B. A has three divisions at her disposal and B has two divisions. Each general allocates her divisions between the two passes. A wins the battle at a pass if and only if she assigns at least as many divisions to the pass as does B. The payout of a general is the number of battles she wins minus the number of battles that she loses.

a) Formulate this situation as a strategic game, by setting out the strategy sets and payout matrices.

b) Dene a weakly dominated strategy. What are the weakly dominated strategies for each general?

c) Show that this game does not have a pure strategy Nash equilibrium. By iteratively eliminating weakly dominated strategies or otherwise, solve for a

mixed strategy Nash equilibrium.

Developed Machines Corp. (DMC) develops heavy-duty machinery that can be operated remotely. DMC operations are segregated into three industries: roadwork, mining, and reforestation. Each industry branch shares the services of one technology department, which is a cost centre. DMC has an annual innovation competition, and the industry branches commonly compete against each other to come up with the most innovative machinery so that the technology department will want to work with them first before moving on to the other branches. As part of the innovation competition, branch managers are compensated using return on investment (ROI) as the key performance measure. The calculation of each branch's ROI does NOT include the use of the technology department's services. There is NO accountability for the use of those services. DMC currently has an organizational ROI of 9%. DMC has received an offer from Sven Inc. to purchase 1,000 pieces of machinery from the mining or reforestation branches for $3,000,000. Currently, the mining department is the innovation leader and has an ROI of 13%, which is the highest in DMC. The reforestation branch's machinery is very similar to the mining branch's machinery. The reforestation branch is NOT performing as well on innovation and has an ROI of 8%. Each branch that will potentially sell machinery to Syed Inc. will need to purchase additional warehouse equipment in order to meet the increased production levels. The investment in new equipment is estimated to cost $5,000,000. The variable costs of production for the new machinery are $2,000 per unit, and fixed costs are estimated to be $550,000.

Required:

a) Determine the ROI for the Sven Inc. offer.

b) For each of the mining and reforestation branches, discuss whether the branch manager should accept the Sven Inc. offer. Explain why each branch's response might be different.

c) Discuss whether DMC as an organization should accept the offer.

d) Using expectancy theory, explain what DMC needs to do to improve its compensation system.

e) Discuss a long-term concern with respect to the use of the technology department's services, and how this impacts the compensation of the technology department's manager.

f) Recommend an alternative evaluation tool for performance measurement at DMC.

Carol Jones, a single person, has an annual income of $32,200. The principal and interest payment on the $25,000 loan (30 years at 8%) for her condominium is $7.34 per $1000. Annual property taxes are $1,200 and insurance is $280 a year. Ms. Jones would like to purchase a larger unit in a new high rise, but her monthly principal and interest will increase to $330.30, plus annual taxes will be $2,100. Interest on the $45,000 will be 8% as rates are lower than when she purchased her present condominium., given Ms. Jones' situation as described here, answer and discuss the following: [Loan Amount = $25,000, Term = 30 years, Interest Rate = 8%, After Tax Rate = 5.72%, Monthly payment = $183.44, Annual Property Tax = $1,200, Annual Homeowners Insurance = $280] Assuming Ms. Jones falls under the 28% tax bracket and that she is itemizing on her Schedule A, under her current mortgage she is effectively able to deduct an average yearly amount of $385.37 over the life of the loan, in this case over 30 years. Previously, taxpayers were able to deduct interest paid on a 1st or 2nd mortgage amounts capped at 1 million. If filing married or filing separately it was capped at $500,000. *Under the Tax Cuts & Job Act (TCJA) these amounts have changed. Taxpayers can deduct the interest they pay on their mortgages for up to $750,000 in new mortgage debt and up to $375,000 when married filing separate or up to $500,000 filing jointly (Tax Reform, 2019). [Loan Amount = $45,000, Term = 30 years, Interest Rate = 8%, After Tax Rate = 5.76%, Monthly payment = $330.19, Annual Property Tax = Unknown, Annual Homeowners Insurance = Unknown, HOA = Unknown] If Ms. Jones were to purchase the new condominium assuming the same factors above apply, she is itemizing her Schedule A, she can deduct 385.37

1. General A is defending a territory which is accessible by two mountain passes against general B. A has three divisions at her disposal and B has two

divisions. Each general allocates her divisions between the two passes. A wins the battle at a pass if and only if she assigns at least as many divisions to the pass as does B. The payo¤ of a general is the number of battles she wins minus the number of battles that she loses.

a) Formulate this situation as a strategic game, by setting out the strategy sets and payo¤ matrices.

General A is defending a territory which is accessible by two mountain passes against general B. A has three divisions at her disposal and B has two

divisions. Each general allocates her divisions between the two passes. A wins the battle at a pass if and only if she assigns at least as many divisions to the pass as does B. The payo¤ of a general is the number of battles she wins minus the number of battles that she loses.

a) Formulate this situation as a strategic game, by setting out the strategy

sets and payo¤ matrices.

b) Dene a weakly dominated strategy. What are the weakly dominated strategies for each general?

c) Show that this game does not have a pure strategy Nash equilibrium.By iteratively eliminating weakly dominated strategies or otherwise, solve for a

mixed strategy Nash equilibrium.

The problem of the firm given in class was to maximize the nominal firm value subject to technology and capital law of motion constraints. Note that the class derivation used net investment as the investment concept and the optimal condition that implicitly defines capital/investment demand was given by, mpkt = r (1) where r > 0 is the real interest rate. If instead I had used gross investment as the investment concept, the optimal condition that implicitly defines capital/investment demand would be given by, mpkt = r + δ (2) where 0 ≤ δ ≤ 1 is the depreciation rate of capital. Note that the object (firm value) that would need to be maximized under the gross investment concept in real terms would be given by max n1,n2,k2 f(k1, n1) − w1n1 − [k2 − k1(1 − δ)] + 1 1 + r [f(k2, n2) − w2n2 + k2(1 − δ)] Let the production function for all t = 1, 2 be given by, f(kt , nt) = k α t n 1−α t , 0 < α < 1 (3)

Answer the following questions:

Which of these statements about bank runs are true? More than one answer is possible.

(a) The Fed today tries to prevent bank runs by attempting to reduce the amount high-powered money. (b) Bank runs are impossible on a bank that holds 100% reserves. (c) Bank runs stopped altogether with the advent of federal deposit insurance (FDIC). (d) Bank runs tend to be isolated and have no effect on overall confidence in the economy. (e) The Fed today tries to bail out certain large banks thought to be "too big to fail." (f) Federal deposit insurance (FDIC) was the first attempt to protect depositors against the consequences of bank runs.

Which of these statements about moral hazard are ? More than one answer is possible.

(a) The reckless behavior of some teenagers can be considered a case of moral hazard.

(b) The risk-taking of an entrepreneur who has invested his life savings in a project can be considered a case of moral hazard.

(c) The Fed bailing out banks deemed "too big to fail" creates a moral hazard.

(d) Moral hazard is a type of principal-agent problem.

(e) Moral hazard facilitates irresponsible behavior.

(f) When economic functions, roles, and duties are determined on a private property basis rather than a socialized basis, moral hazard is more prevalent.

(g) Moral hazard entails the consequences of an agent's behavior being partially shared by his principal.

(h) Moral hazard occurs when an individual fully suffers the consequences of his actions; thereby, the alleged "morality" of full individual responsibility is hazardous to individual actors having to bear the brunt of it.

**Related Book For**

## Accounting

ISBN: 978-0324662962

23rd Edition

Authors: Jonathan E. Duchac, James M. Reeve, Carl S. Warren