The Economics Of Managerial Decisions 1st Global Edition Roger Blair - Solutions

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Plot the Van der Pol equation from the initial point (x(0),y(0))5 (0.5,0.5) for the following values of m. Take dt50.01 and t from 0 to 1500 (i) m521 (ii) m50 (iii) m51 What do you conclude?
In each of the following let x(0)50.01, x(0)50.0105 and t from 0 to 50. (i) Show that x(t11)52.5x(t)(12x(t)) is not sensitive to initial conditions. (ii) Show that x(t11)53.62x(t)(12x(t)) is sensitive to initial conditions.
Plot the following function for t50 to 50 x(t11)53.67x(t)(12x(t)) for the initial values (i) x(0)50.2 (ii) x(0)50.2001 Is this function sensitive to initial conditions?
Consider the following quadratic (Berry, 1996, p.117) x(t11)5x2(t)21 (i) What are the fixed points? (ii) What are the values of the attracting two-cycle?
Consider the following function x(t11)52x(t)22x2(t)2l (i) What are the fixed points? (ii) What is the bifurcation value of l? (iii) What type of bifurcation does this function have?
Consider the numerical example in section 9.3. (i) Suppose the debt/income ratio was to be stabilised at b555%. What is the level of the primary deficit/surplus to GDP that will achieve this? (ii) What is the primary deficit/surplus to GDP that will stabilise the debt/income ratio at 60%? (iii)
A country has 2% inflation, is growing at 2.5% and has a nominal interest rate of 6% and a debt/income ratio of 40%. It presently has a budget deficit as a percentage of GDP of 3% and involves no money financing. This budget deficit exists for periods 0 to 5 and is then reduced to 1% for the next
A country is growing at 3% and has a debt/GDP ratio of 50%. Assuming no money financing, what is the primary budget deficit/surplus that keeps the debt/income ratio constant when(i) The real interest rate is 2%? (ii) The real interest rate is 5%?
For the economy in the numerical example in section 9.3, where b(0)550% (i) At what time period does the debt/income ratio equal 100%? (ii) If the nominal interest rate is higher so i2gy52.5%, at what time period does the debt/income ratio equal 100%? (iii) If the primary deficit/GDP is lower at
A country has no inflation, is growing at 2.5% and has a nominal interest of 4%. It is presently running a budget deficit as a proportion of GDP of 6%. (i) What is the expression for b(t) in terms of b(t21)? (ii) What is the equilibrium debt/income ratio? Is this country a creditor or debtor in
Consider the following Dornbusch model under perfect foresight e50.75y12.510.02(s2p) p50.2(e2y) md5p10.75y20.2r md5ms5155 r5r*1se se5s y510, r*512.5 (i) What is the equilibrium exchange rate and price of this system? (ii) Set up the system on a spreadsheet. (iii) Let the money supply fall from 155
For the system x5x1y11 y52x2y15 (i) Find the fixed point. (ii) Transform the system into deviations from the fixed point. What are the characteristic roots of this transformed system? (iii) Derive the equations for the stable and unstable arms. (iv) Set the model up on a spreadsheet and plot, on
Verify that the following two systems have saddle-point solutions at the origin (i) x52x1y y53x (ii) x5x14y y54x27y Plot trajectories for initial point (22,5).
For the system x5x13y y55x13y (i) What is the fixed point of the system? (ii) Set x5lx and y5ly. What are the equations for the two arms of the saddle-point? Which is the stable arm and which the unstable arm? (iii) Use a spreadsheet to plot the trajectory of the system starting at the point
For the system x5x12y y53x1y (i) Establish the fixed point. (ii) Derive the equations for the two isoclines and establish the vector of forces. (iii) Derive the equation for the stable and unstable arms. (iv) Take a point on the stable arm for x52, and show on a spreadsheet that the trajectory
Consider the following three-firm oligopoly model p5202Q Q5q11q21q3 TC152q1 TC252q2 TC352q3 Dynamics of the firm 147 (i) What is the Cournot solution? (ii) Firm i chooses qi (t) to maximise pi (t), assuming qj (t)5qj (t21) for all j°i. What are the dynamic adjustment equations? (iii) Show that no
Consider the following Cournot model with identical quadratic total costs p592Q Q5q11q2 TC150.5q1 2 TC250.5q2 2 (i) What is the Cournot solution? (ii) Firm 1 chooses q1(t) so as to maximise p1(t), assuming q2(t)5q2(t21); and firm 2 chooses q2(t) to maximise p2(t), assuming q1(t)5q1(t21). What are
Consider the following model of oligopoly in which total costs are different p592Q Q5q11q2 TC153q1 TC251.5q2 (i) What is the Cournot solution? (ii) Assume firm 1 chooses q1(t) so as to maximise p1(t), assuming q2(t)5q2(t21); and firm 2 chooses q2(t) to maximise p2(t), assuming q1(t)5q1(t21). What
Consider the following diffusion model for a new product in which at the moment no sales have taken place DF(t11)5(0.00510.02F(t))(12F(t)) (i) What are the fixed points of this system? (ii) At what time will the maximum penetration of the market occur?
Consider the discrete advertising model of section 7.3. A product has present sales of 100,000 with sales declining at a rate of 2% per period. The maximum absorption per period is 250,000. £10,000 is to be spent on advertising over a five-year period or a ten-year period, in each case at a
Use the model in qu. 4, and set the initial values at their equilibrium level. What are the implications of a fall in the natural level of income (a rise in the natural rate of unemployment) from 60 to 50?
Consider the following model Dy(t11)55(102p(t))10.25Dpe(t11) p(t)50.25(y(t)260)1pe(t) Dpe(t11)50.5(p(t)2pe(t)) (i) What is the equilibrium for this model? (ii) Plot on the same diagram income against expected and actual inflation for t50 to 40 starting from point (y(0),pe(0))5 (40,15). (iii) Now
Consider the following model Dy(t11)510(202p(t))10.75Dpe(t11) p(t)50.5(y(t)215)1pe(t) Dpe(t11)52(p(t)2pe(t)) (i) Derive the two fundamental difference equations for this model. (ii) What is the fixed point of the model? (iii) Derive the two isoclines and the vector forces. (iv) Set up the model on
Consider the following two models (i) What are the recursive equations for each model and what is their fixed point? (ii) Compare the adjustment of prices in each model.
Consider the following model in which expected inflation is zero y(t)51210.2(m2p(t)) p(t11)2p(t)51.5(y(t)2yn) m510 yn58 (i) What is the fixed point of this model and is it stable? (ii) If p(0)515, plot the inflation rate for t51 to 20.
Set up model (5.22) using the parameter values in model (5.17), except let b53. What is the new equilibrium and the trajectory of the economy for the following events (i) A fall in G from 25 to 22? (ii) A fall in M from 8 to 5?
Set up model (5.22) using the parameter values in model (5.17). What are the new equilibrium and the trajectory of the economy for the following events (i) A rise in autonomous taxes from 0 to 10? (ii) A fall in the money supply from 8 to 5?
Use model (5.17) to establish the new equilibrium and to construct trajectories for the following events (i) A fall in the money supply from 8 to 5. (ii) A fall in business expectations resulting in a fall in autonomous investment from 10 to 5.(iii) A rise in savings at all levels of income,
Set up a vector force diagram for model (5.14) and illustrate possible trajectories for the economy in (Y,r)-space for each of the following (i) A fall in government spending. (ii) A fall in the money supply.
Set up model (5.8) on a spreadsheet and assume instantaneous money market adjustment and sluggish goods market adjustment. Establish the new equilibrium and plot the trajectory of the economy in (Y,r)- space starting from the initial equilibrium for each of the following. Treat each one separately
(i) Establish the trajectory of the following discrete system x(t11)52210.25x(t)10.4y(t) y(t11)51022x(t)10.5y(t) (x(0),y(0))5(2.5,15) (ii) What is the fixed point of the system and does the trajectory converge on this value? (iii) Plot x(t) and y(t) for t50 to 20. What do you observe?
(i) Establish the trajectory of the following discrete system x(t11)5282x(t)1y(t) y(t11)5420.3x(t)10.9y(t) (x(0),y(0))5(2,8) (ii) What is the equilibrium value of the system and does the trajectory converge on this equilibrium?(iii) Plot the path of x(t) and y(t) for t50 to 20. What do you observe?
(i) Use a spreadsheet and Euler’s approximation to construct the trajectory for the following system. Use 0.05 for the time interval and t50 to 200 x52x13y y53x12y (x(0),y(0))5(1,0) (ii) Verify that this trajectory is consistent with the vector forces. (iii) Show that the trajectory for the
(i) Use a spreadsheet and Euler’s approximation to construct the trajectory for the following system. Use 0.05 for the time interval and t50 to 200 x523x1y y5x23y (x(0),y(0))5(2,10) (ii) Verify that this trajectory is consistent with the vector forces
Construct diagrams showing isoclines and vector forces for the following systems (i) x53x y5 y (ii) x5x23y y522x1y
Use the model of section 3.8 embodied in model (3.17) and (3.19). Set initial income at its equilibrium level of 1766.667. Let government spending rise from G5200 to G5300. Plot the resulting dynamic path of net exports, NX(t). Comment on your results.
Use the model of section 3.7 on the multiplier–accelerator. Let b50.7 and v51.5 and let Y(0)5300. Derive the level of income, Y(t), consumption, C(t), and investment, I(t). Form the series C(t)2C* and I(t)2I*, where C* and I * denote equilibrium consumption and investment, respectively. Plot
Use the spreadsheet used to express model (3.9) to analyse the following model C(t)520010.8Yd(t) Yd(t)5Y(t)2Tx(t) Tx(t)51010.25Y(t) I5250 G5500 E(t)5C(t)1I1G DY(t11)50.5(E(t)2Y(t)) (i) Establish the equilibrium level of C, Y, Yd and Tx. (ii) Let Y(0)51500 and plot the path of Yd(t) and Y(t) on the
Use the model in qu. 1 with I15150. Set initial income at the equilibrium level. Derive the dynamic multiplier k(t) as defined by (3.8) for a rise in investment of 50. Comment on your result.
Use the model in qu. 1 to verify the following propositions. Take Y(0) 53000 (i) A rise in autonomous consumption spending or a rise in investment or a rise in government spending by 50 leads to the same impact on equilibrium income and to identical adjustment paths for Y(t).(ii) For a rise in
Use the spreadsheet used to express model (3.7) to analyse the following model C(t)520010.8Y(t) E(t)5C(t)1I1G I5150 G5250 DY(t11)50.5(E(t)2Y(t)) (i) Establish the equilibrium level of Y and C. (ii) Plot the path of Y(t) and C(t) given Y(0)52000; and establish that these approach your results in
Given the cobweb model qd(t)51823p(t) qs(t)521014pe(t) pe(t)5p(t21) q(t)5qd(t)5qs(t) (i) Establish the recursive equation for p(t). (ii) If a ceiling price of pU55 is set, establish the new recursive equation for p(t). (iii) Set up this model on a spreadsheet and establish that the ceiling leads to
Given the following nonlinear cobweb model qd(t)52425p(t) qs(t)52412(pe)2(t) pe(t)5p(t21) q(t)5qd(t)5qs(t) (i) Establish the recursive equation for p(t). (ii) What are the fixed points for this recursive equation and are they all economically meaningful? (iii) If p(0)52.6, establish whether the
For the Goodwin model in section 2.5, set p(0)52 and p(1)52. If r50.5, does the system still exhibit a divergent oscillatory price path? Is this true for r523, 20.1, 0.1 and 1?
Set up the following adaptive expectations model on a spreadsheet qd(t)510022p(t) qs(t)522013pe(t) pe(t)5pe(t21)2l(pe(t21)2p(t21)) q(t)5qd(t)5qs(t) (i) If l50.5, what is the equilibrium price and quantity? Are these values the same as those in qu. 1(i)? (ii) If p(0)510, does this system converge on
Set up the following cobweb model on a spreadsheet for t50 to 10 qd(t)51823p(t) qs(t)521014pe(t) pe(t)5p(t21) q(t)5qd(t)5qs(t) (i) What is the equilibrium price and quantity? (ii) Given p(0)53, does the market tend to equilibrium?
Given the model qd(t)510022p(t) qs(t)522013p(t) Dp(t11)50.1(qd(t)2qs(t)) q(t)5min(qd(t), qs(t))(i) Establish the equilibrium price and quantity. (ii) Use a spreadsheet to plot p(t) and q(t), given p(0)510. Do these values tend to their equilibrium values? (iii) Raise the speed of adjustment to 0.2.
Establish the fixed points of the following continuous models and their stability/instability properties (i) x5522x (ii) x5x21x25 (iii) x5x312x22x22
Establish the fixed points of the following nonlinear discrete systems and establish their stability/instability properties (i) x(t11)531x2(t)25x(t) (ii) x(t11)5x3(t)12x2(t)22 (Note: x312x22x225(x21)(x213x12), or plot the function x312x22x22 for 23,x,3)
Represent a phase line for the periodic solution to the linear equation x(t11)532x(t) x(0)51
Establish whether the systems in qu.1 are globally stable or globally unstable.
Establish the fixed points of the following discrete systems and show the path of the system from the given initial condition (i) x(t11)5520.2x(t) x(0)52 (ii) x(t11)52213x(t) x(0)50.5 (iii) x(t11)531 x(0)51
4. Suppose that the Department of Justice catches wind of the predator’s actions and files suit against the predator.Present several examples of false assertions the predator’s managers might make in order to defend themselves against the charge of predatory pricing. In 1911, the U.S. Justice
3. Based on the managers’ estimate that they will make the economic profit of $1.13 million for six years, is the predatory pricing profitable? In 1911, the U.S. Justice Department charged Standard Oil of New Jersey (now ExxonMobil) with unlawfully monopolizing the petroleum industry. More
2. Ignoring the illegality of the act and possible prosecution, for how many years must the predator earn the economic profit of $1.13 million to make the predatory pricing profitable? In 1911, the U.S. Justice Department charged Standard Oil of New Jersey (now ExxonMobil) with unlawfully
1. What is the present value of the firm’s economic loss? In 1911, the U.S. Justice Department charged Standard Oil of New Jersey (now ExxonMobil) with unlawfully monopolizing the petroleum industry. More specifically, Standard Oil allegedly used profits made in its noncompetitive geographic
16.2. Suppose that you are a consultant for a firm like Yoo, a company building apartments and condominiums worldwide. You are charged with determining the number of floors to include in a proposed structure in Quito, Ecuador. Each floor will have 10 separate living spaces. They will be rented as
16.1. Riverside Technologies Incorporated (RTI) is a small firm in North Sioux City, SD, that provides IT solutions for other companies. In addition to providing IT services and computer hardware (i.e., laptops, desktops, and tablets), RTI has decided to add customized computer bags for companies
4.7 Employee Paul was injured at your plant. Last year Paul had $100,000 in medical expenses(which your firm has already paid). This year and every other year in the future those expenses will increase by 10 percent per year.The medical expenses are all paid at the end of the year. The average
4.6 You are deciding whether to send several of your employees to a training session. The cost of the session is $20,000. You estimate that if they receive this training, your firm’s after-tax operating profit will increase by $5,000 per year for five years. If your firm’s discount rate is 7
4.5 A competitor has infringed your patent, so you are entitled to recover lost profits. You have calculated lost profits of $12 million. The jury, in a burst of common sense, has awarded your company the entire $12 million. The defendant threatens to appeal. The appellate process will take five
4.4 You are the manager of a large printing shop.You have the opportunity to buy a used six-color offset press for $1,000,000. Transporting and installing the press costs another $1,500,000 and will take a year to accomplish.Once installed, the press will create additional operating profit of
4.3 Noting the success of Energizer’s long-running advertising campaign featuring a robotic rabbit and AFLAC’s campaign showcasing a duck, you decide to combine the two ideas and run a two-year advertising campaign for your company featuring a robotic duck. You forecast that at the end of the
4.2 You have sold bonds that promise to pay $400 in interest at the end of each year until the end of the year in which the bond matures. At that time you will also pay the $12,000 in principal.a. If the bond has 10 more years until it matures and the discount rate is 5 percent, what is the price
4.1 Say that you work for a bank that has purchased a bond issued by Verizon. The bond promises to make interest payments of$500 at the end of each year for the next six years. At the end of the sixth year, the bond also pays the $12,000 principal. If the discount rate is 6 percent, what is the
3.4 As a manager at BMW, you are considering leasing a plant to build batteries for your electric-powered BMW i3 vehicle. Suppose that BMW’s current cost of batteries is $8,000 per car. You predict sales of 10,000 cars per year for this year and each of the following six years. If BMW leases the
3.3 Say that you are manager at a firm like LGI Technology, a lighting company that produces LED lights. Currently, your firm manufactures the LEDs it uses in-house. Technological advances have led to a new type of LED. Your firm can continue to produce the more advanced LEDs by buying new
3.2 As a manager at AbbVie, a major pharmaceutical company, you work in the division responsible for the best-selling drug Humira. Humira is administered in preloaded syringes. To investigate the sort of calculation you might make, let’s explore a hypothetical case. Suppose that AbbVie buys 3
3.1 You are a manager at a firm like Terrapin Ridge Farms, a company that produces dressings, dips, sauces, and jams. One of the jams is strawberry and fig. Currently, your company buys 20,000 pounds of strawberries from local farmers at a price of $2.00 per pound. One local farmer has offered you
2.3 Your company owns a minor league baseball team and is considering building a new stadium.The local governments refuse to help build the stadium, so you must fund it yourself.The stadium will cost $10 million and will have a 20-year life span, after which it will be valueless. It will take a
2.2 Why does including the depreciation allowance as another cost increase the net present value of an investment?
2.1 You can make an investment that will immediately cost $52,000. If you make the investment, your after-tax operating profit will be $13,000 per year for five years. After the five years, the profit will be zero, and the scrap value also will be zero. You will finance the investment with
1.9 In your role as a manager, you are negotiating a contract with a construction company to build part of a new plant. The construction will take three years and will cost $9 million.Would you prefer a contract that calls for equal payments of $3 million over three years or one that specifies
1.8 The New York Yankees signed pitcher Masahiro Tanaka to a seven-year contract. Because Mr. Tanaka was under contract in Japan with the Golden Eagles, the Yankees paid them $20 million to release him. Mr. Tanaka’s contract calls for payments of $20 million per year for six years and $23 million
1.7 What is the present value of $15,000 received at the end of the year for the next seven years at a discount rate of 6 percent? Now suppose that the payments are delayed for a year, so that the seven payments will be made at the end of the second year, the third year, and so on until the end of
1.6 Use the discount factors presented in Table 16.1 to answer the following questions:a. What is the present value of $1,000 received at the end of four years if the discount rate is 6 percent?b. What is the present value of $1,000 received at the end of eight years if the discount rate is 6
1.5 The longer the time until an amount of money will be received, the larger the discount factor.Why?
1.4 When the discount rate rises, what happens to the present value of an amount of money you will receive in the future? Why?
1.3 What is the impact of an increase in the discount rate on the discount factor? Explain your answer.
1.2 What is the present value of $80,000 per year for 10 years at a discount rate of 9 percent?Explain your answer.
1.1 What is the present value of $500,000 received at the end of 5 years at a discount rate of 6 percent?
You have seen how managers can decide whether to make or buy the containers they need. Let’s modify the example by supposing that the more carafes the company produces, the more the workers learn how to operate the machine efficiently. If the company buys the blow-molding machine, say that these
Suppose that you and the other managers of an electric car maker like Tesla, Inc., have announced your plan to build a huge, 10-million-square-foot battery factory at a cost of$5 to $6 billion. The factory is so big that it will take three years to construct. Your firm will share the cost of
Say that you are the owner of a firm like the local H&R Block and you are deciding the timing of an expenditure of $75,000 on new computers. You will buy the computers with your own internally generated funds. The computers will increase your before-tax operating profit by $32,000 per year for
You are a manager at a car rental company similar to Avis Car Rental. You can buy a Ford Focus for $21,000, rent it for two years, and make an operating profit of $4,500 per year, which you receive at the end of each year. After two years, you can sell the car for $15,000. If your discount rate is
You are negotiating a $1 million loan for your employer. The lender offers you a choice:• Payment schedule A requires you to pay $100,000 at the end of the year for the first five years, with a final payment of $1,000,000 at the end of the sixth year, for a total of $1.5 million in payments.•
16.4 Apply the concepts of present value and the net present value rule to make profitmaximizing managerial decisions
16.3 Use present value calculations to answer the make-or-buy questions that managers face.
16.2 Describe how salvage values, taxation, debt financing, depreciation, and risk affect capital budgeting.
16.1 Explain the importance of present value calculations to managerial decision making.
15.2. The Weinandt Family Farm in Wynot, NE, raises livestock and grows crops. Commonly grown crops in Nebraska are corn and soybeans.Suppose that you are helping a farm similar to the Weinandt Family Farm make decisions about how much corn to grow this year. The market for corn, an agricultural
15.1. Alorica is a customer relationship management firm that provides customized customer support via phone, Internet, and social media for companies in a variety of industries.It has many locations in North America, Latin America, Asia Pacific, and Europe.It also allows some employees to work at
5.5 Suppose that you are in charge of security at the Museum of Modern Art in New York. You have hired guards to protect the art overnight while the museum is closed.a. Carefully explain the principal–agent problem you face.b. What actions might you take to overcome the principal–agent problem?
5.4 The Federal Motor Carrier Safety Administration(FMCSA) regulates the hours a truck driver may drive. One regulation limits the time a driver may drive to a maximum of 11 hours and then only after taking 10 consecutive hours off. The FMCSA can fine a company up to $16,000 for violating this
5.3 Professional athletes are incredibly competitive, even outside their own sports. Many professional baseball players, for example, would eagerly play pickup basketball games.a. Because he fears injury, a baseball player does not play pickup basketball games before he signs a long-term contract.
5.2 When Nortel Networks, a bankrupt data-networking equipment manufacturer auctioned its patents, it allowed all the potential bidders to thoroughly examine the patents. Why did Nortel’s managers make the decision to allow bidders to do this?
5.1 Suppose that you are an executive with the North Dakota Department of Trust Lands, the state government agency that manages the lands given to the state by the federal government when North Dakota achieved statehood.One of your tasks is managing the auctions for mineral rights, such as natural
4.8 The bonuses of midlevel bank loan managers are often based on the profits but not the losses of the loans they approve. Suppose that an executive can make two types of loans: risky loans, which yield a large profit if they are successful and incur a large loss if they fail, and safe loans,
4.7 Explain the difference between moral hazard and adverse selection.
4.6 Corporations sometimes buy back shares of their stock, which they then cancel, so that the number of outstanding shares is smaller.For example, in 2017, American Airlines Group announced that it would buy back$2 billion of its shares. What signal are managers sending when they announce a share

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The Economics Of Managerial Decisions 1st Global Edition Roger Blair - Solutions

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