The Emotional Intelligence Test, Decision Making - 1270 Words

Leadership style is significant in creating organizational success and being an effective leader. A person’s leadership style is dependent upon a variety of circumstances such as, biases, decision-making abilities, situation, environment, culture, gender, emotional intelligence, and personality. Effective leadership can induce process improvement and performance, maintain a viable gain, and is a strong foundation for organizational development (Jing, Avery, 2016). Research suggests that leadership style and high levels of emotional intelligence is positively associated with employee performance and organizational success (San Lam O Higgins, 2012). To develop one’s personal leadership style, it is important to be introspective. This†¦show more content†¦The PEDW individual weaknesses include having a weak understanding and acceptance of their emotions and personality, no self-awareness, struggles with immediate emotions, does not easily deal with conflict, and rarely tries to reach higher goals than ones initially set up. Decision-Making Assessment The MindTools Decision-Making assessment results: 59, decision-making process is OK. There is good understanding of the basics of decision-making, but there is a need for process improvement, increase ability to be more proactive, and development of a decision-making system that will work for a variety of situations. The quiz was based on six essential decision-making steps: establishing a positive decision-making environment, generating potential solutions, evaluating the solutions, deciding, checking the decision, and communicating and implementing. In order to develop and increase decision-making success, each step must be evaluated for specific areas to improve skills and knowledge. Establishing a Positive Decision-Making Environment The score for this step was 65%. In this stage, everyone must correctly identify and understand the issue at hand, establish the common goal, and have agreement upon the method to implement the decision. The environment must be free of interpersonal issues, create ground rules for respect, honesty, and openness. Last, assure all necessary stakeholders areShow MoreRelatedEmotional Intelligence: Personal Test Results1188 Words   |  5 PagesEmotional Intelligence Personal Test Results The snapshot results from the Queendom emotional intelligence (EQ) test indicate a score of 69 in emotional identification, perception and expression. The test consisted of 146 questions designed to assess an individuals capacity to recognize their own emotions and those of others, understand how to best motivate yourself, establish relationships and manage personal feelings as well as those of others. The results indicate I am reasonably skilledRead MoreEssay on Emotional Intelligence 2.0 Summary and Assessment826 Words   |  4 Pagesbook, Emotional Intelligence 2.0, provides an alternative approach to how a person achieves success. This book does not focus on the conventional determinant of success, such as formal education and training, experience, and intelligence level (IQ). Although all these components contribute greatly to ones achievement of success, these factors are not the only factors to be considered in whether a person will be successful or not. This book focuses on the concept that it refers to as emotional intelligenceRead MoreThe Protection Of Title Vii Of The Civil Rights Act Of 19641135 Words   |  5 Pagesareas such as reproduction, contraception, abortion and marriage. There are no Supreme Court cases which specifically pertain to privacy issues that arise from employee testing, however certain legal scholars have advanced the idea that personality tests should be considered under the Fourth Amendment Search and Seizure Clause. The claim is based on the position that job applicants should have the expectation of privacy from personal questions that are largely not job-related which could constituteRead MoreEmotional Intelligence Performance And The World Of Academia Essay954 Words   |  4 PagesEmotional Intelligence Introduction Traditionally, the applicant with the higher Intelligence Quotients (IQs) places first in the employment arena. However, Human Resource Managers indicate that candidates with high IQs, but less than desirable Emotional Intelligence Quotient (EQ) may be questionable in job performance and the world of academia. The purpose of this paper is to define, discuss, and provide examples of emotional intelligence and theories significant to the subject. AdditionallyRead MoreAnalysis Of Alfred Binet And Lewis Terman On Intelligence Testing1696 Words   |  7 Pagesapproaches to intelligence testing there are some similarities amongst the two. One such similarity would be regarding content. Alfred Binet’s approach to intelligence testing consisted of tests that ranged in difficulty levels from easy to hard. These tests required one to demonstrate his or her own cognitive ability, decision making, and verbal skills. Lewis Terman’s approach to intelligence testing was an updated version of Binet’s. Terman also used cognitive ability, decision making, and verbalRead MoreEmotional Intelligence Essay1188 Words   |  5 Pagesimportance of emotional intelligence. Emotional intelligence is sometimes referred to as EI or EQ. In their article, Colfax, Rivera Perez (2010) stated that â€Å"Regardless though of how it is referred to, emotional intelligence (EQ) is concerned with understanding oneself and others, relating to people, and adapting to and coping with the immediate surroundings to be more successful in dealing with environmental demands† (pg 90). This statement helps us to recognize that understanding emotional intelligenceRead MorePersonal Statement On Emotional Intelligence1593 Words   |  7 Pages Emotional Intelligence Tanveer Vora 1610793 University Canada West Professor: Dr. Michele Vincenti MGMT601 Leadership in the Global Context 16th January 2017 Abstract The paper discusses about the emotional intelligence, which has various factors. The factors are self awareness, motivation, self regulation, social skills and empathy. In case of effective leadership, these factors plays major role. However, emotional intelligence is teachable to improve the personal skills and personality.Read MoreEmotional Intelligence1076 Words   |  5 Pageslevel of smartness or intelligence can be found pretty straightforwardly by a score on a measurement of intelligence such as an IQ test. Find a pen or pencil, have a seat, and take an IQ test. Even better, look one up on the internet. Hours†¦or even minutes later you will receive a score that supposedly tells you how smart you actually are. â€Å"Based on these results, you are ______ smart.† The emphasis is on smart and how well a person’s mental capacity is captured in writing, on a test. Is this really howRead MoreEmotional Intelligence ( Ei ) And Decision Making ( Dm )1123 Words   |   5 PagesThe newest additions to leadership and the traits organizations now seek out to includes Emotional Intelligence (EI) and Decision-Making (DM). Acknowledging the transformation of emotions from a negative unwanted factor to a positive, successful factor in organizational terms is essential in today s’ job market. Moreover, today’s organizational view, EI is indispensable to the effectiveness of leadership (Fambrough, Hart, 2008). The fact that employees with high EI build solid organizationalRead MoreDecision Making, And Leadership : A Self Assessment1125 Words   |  5 PagesEI, Decision-Making, and Leadership: A Self-Assessment The newest additions to leadership and the traits organizations now seek out includes Emotional Intelligence (EI) and Decision-Making (DM). Acknowledging the transformation of emotions from a negative unwanted factor to a positive, successful factor in organizational terms is essential in today s’ job market. Moreover, today’s organizational view, EI is indispensable to the effectiveness of leadership (Fambrough, Hart, 2008). The fact that

Louisiana Purchase - 1013 Words

#65279;Louisiana Purchase I believe that the Louisiana Purchase was one of the greatest impacts on American society because of the large amount of land and how it helped our economy. In this report you will see how lucky that the United States is to have obtained this large piece of land from France. Their are many reasons why Napoleon had to sell this large piece of land. Napoleon thought that this land could be a great asset to the French if they knew what to do with it. He didnt want to sell the Louisiana territory because he still had dreams of having a French empire in America. At this point in time Napoleons dream would never come true because France was almost always at war. They didnt have enough troops to go†¦show more content†¦The Louisiana territory was purchased by Thomas Jefferson from Napoleon on July 14, 1803. The total cost of the whole Louisiana Purchase was about fifteen million dollars. That is about two cents an acre. This land was a very rich farmland that produced many crops. Included in the in the Louisiana Purchase was New Orleans and Floridas two big sea ports. The New Orleans sea port is in the Gulf of Mexico; it imports and exports foreign and domestic goods every day. As I have stated before this is a very big piece of land. This land stretched as far west as the Rocky Mountains and all the way north to Canada. It goes to the Mississippi in the east and down in the south to the Gulf of Mexico. There is 827,987 square miles (2,144,476 square kilometers) of land. All this land today makes up parts of 15 states including: Montana, Wyoming, Colorado, New Mexico, Texas, Oklahoma, Kansas, Nebraska, North Dakota, South Dakota, Minnesota, Iowa, Missouri, Arkansas, and Louisiana. The most important dates of the purchase are when they were signed and who they were signed by.Concluded at Paris, Aprill30,1803;Ratification advised by the Senate October 20,1803; Ratified by the President October21,1803; Ratifications exchanged at Washington October 21,1803; Proclaimed October21,1803.These dates are when it was looked over and then it was signed. In conclusion I think that this could have been the most important thing thatShow MoreRelatedLouisiana Purchase And The Louisiana1535 Words   |  7 Pagessignificant occurrence happened. The purchase of 827,000 square miles of land for approximately 4 cents an acre or 15 million dollars was made. This purchase was unlike any other, for it would have the most importance of any other purchase made in the United States. It is referred to as the Louisiana Purchase. The land that was purchased was known as the Louisiana Territory. Also, this territory wasn’t just bought. It was exchanged, for an important reason. The Louisiana Purchase is known as one of the mostRead MoreThe Louisiana Purchase1275 Words   |  5 PagesWhen the Louisiana Purchase was made by Thomas Jefferson in 1802, nobody in the United States knew anything about the territory. Everyone had to know more about the huge land grant that was just purchased by the U.S. People took the challenge and went out to see the great land. Famous explorers are known for their exploration of the Lo uisiana Purchase. Two famous explorers are known by many, Lewis and Clark. Although, there is one explorer that is less known but explored just as much area as LewisRead MoreThe Legacy Of Louisiana Purchase1286 Words   |  6 PagesLouisiana Purchase, more prominently known as an acquisition that doubled the size of the country we reside in, was much more than just a simple purchase, much less an easy one. Thomas Jefferson had to consider all the aspects, consequences, and effects that the decision of buying 2,144,500 square kilometers of land would have on the country (Columbia Electronic Encyclopedia 1). This purchase brought many improvements to the country, but also had unexpected consequences that would transform the countryRead MoreThe Purchase Of Louisiana Posed Essay1103 Words   |  5 PagesName: Title: Institution: Personal Responsibility The Purchase of Louisiana posed several important moral dilemmas for American President Thomas Jefferson; among these were the means of achieving Republican government states’ rights and strict constructionism which he relented. Constructionist and a strong supporter of states rights and, therefore, the action of purchasing Louisiana presented a moral dilemma, he was either to stick to his principle or compromise and save the Republican governmentRead MoreLouisiana Purchase Essay1253 Words   |  6 PagesThe Louisiana Purchase was the most influential and important land purchases in American history. The acquired land in this historical purchase proved to far outweigh what most Americans at the time could imagine. The Louisiana Purchase more than doubled the size of the United States, and lead to many great discoveries and societal benefits. Some of the major and most prominent ways that the Louisiana Purchase influenced the evolution of American were the expeditions of L ouis and Clark on theRead MoreThe Louisiana Purchase1215 Words   |  5 Pagessignificantly with the Louisiana Purchase. The Louisiana Purchase added 828,000 square miles which doubled the land area of the United States (history.com 1). The importance of the Louisiana Purchase can be best appreciated by understanding why this purchase was considered significant to the United States, why France agreed to sell such a sizable amount of land, and how the Louisiana Purchase changed the United States forever. The United States was interested in the purchase of Louisiana for a number ofRead MoreThe Louisiana Purchase By Thomas Jefferson1129 Words   |  5 Pagesthroughout the endeavor of the Louisiana Purchase. The Louisiana Purchase is highly regarded as the greatest achievement of American expansion since the establishment of the country. This transaction between France and America gave the necessary requirements to recover and even advance the weak U.S. economy. America paid France $15 million for an estimated 800,000 acres of land; making this the largest land deal in history. Despite the many advantages that the Louisiana Purchase had to offer, Thomas JeffersonRead MoreThe Louisiana Purchase: Unconstitutional or Not? Essay558 Words   |  3 Pagessense of public spending. In the case of the Louisiana Purchase many political figures at the time it was created, as well as historians argue whether or not it was in fact a violation of the Constitution or not. This debate is still ongoin g, but in order to analyze whether the Louisiana Purchase was unconstitutional or not, one must analyze the sequence of events leading to the acquisition of the territory by the United States. The Louisiana Purchase appeared to be the only solution to the UnitedRead MoreThe Louisiana Purchase : The United States967 Words   |  4 PagesThe Louisiana Purchase The Louisiana Purchase is one of the most important historic events in America. It changed the course of history, raising America’s rank in the world. It all began at a time where the western half of modern day America was not occupied. During the early nineteenth century, Napoleon Bonaparte had intentions to create a new French Empire in the new world. His plan was to take away America’s ability to use the Mississippi River. Thomas Jefferson, president at the time, wasRead MoreThe Louisiana Purchase Shaping America1213 Words   |  5 Pages The Louisiana Purchase shaping America Christopher Richeson East Forsyth High School Mrs. Callendar American History 4th Period December 15, 2015 Abstract The Louisiana Purchase was a major event in the growth of the United States of America. Purchased from France for 15 million by Thomas Jefferson in 1803, it gave America twice the available land, adding 827,000 square miles. Some may argue the Louisiana Purchase is unconstitutional, but Jefferson found a way around that. The

HECUBA Essay Example For Students

HECUBA Essay A monologue from the play by Euripides NOTE: This monologue is reprinted from The Plays of Euripides in English, vol. i. Trans. Shelley Dean Milman. London: J.M. Dent Sons, 1920. HECUBA: Not oneExists, whose sorrows equal mine, unlessYou of Calamity herself would speak.Yet hear the motive why I clasp your knees.If I appear to merit what I suffer,I must be patient; but if not, avengeMy wrongs upon the man who gainst his guestSuch treachery could commit, who, nor the godsOf Erebus beneath, nor those who ruleIn Heaven above regarding, this vile deedDid perpetrate, een he with whom I oftPartook the feast, on whom I showered each bounty,Esteeming him the first of all my friends;Yet, when at Ilions palace with respectHe had been treated, a deliberate schemeOf murder forming, he destroyed my son,On whom he deigned not to bestow a tomb,But threw his corse into the briny deep.Though I indeed am feeble, and a slave,Yet mighty are the gods, and by their lawThe world is ruled: for by that law we learnThat there are gods, and can mark out the boundsOf justice and injustice; if such lawTo you transmitted, be infringed, if theyWho kill their guests, or dare with impious han dTo violate the altars of the gods,Unpunished scape, no equity is leftAmong mankind. Deeming such base connivanceUnworthy of yourself, revere my woes,Have pity on me, like a painter takeYour stand to view me, and observe the numberOf my afflictions; once was I a queen,But now am I a slave; in many a sonI once was rich, but now am I both oldAnd of my children reft, without a city,Forlorn, and of all mortals the most wretched.That band of my heroic sons is now no more,Myself a captive, am led forth to tasksUnseemly, and een now these eyes beholdThe air obscured by Ilions rising smoke.It might be vain perhaps, were I to foundA claim to your assistance on your love:Yet must I speak: my daughter, who in TroyWas called Cassandra, the prophetic dame,Partakes your bed; and how those rapturous nightsWill you acknowledge, or to her showYour gratitude for all the fond embracesWhich she bestows, O king, or in her steadTo me her mother? In the soul of manTh endearments of the night, by darkness veiled,Create the strongest interest. To my taleNow listen: do you see that breathless corse?Each act of kindness which to him is shown,Upon a kinsman of the dame you loveWill be conferred. But, in one point my speechIs yet deficient. By the wondrous artsOf D?dalus, or some benignant god,Could I give voice to each arm, hand, and hair,And each extremest joint, they round your kneesShould cling together, and together weep,At once combining with a thousand tongues.O monarch, O thou light of Greece, comply,And stretch forth that avenging arm to aidAn aged woman, though she be a thingOf nought, O succour: for the good mans dutyIs to obey the dread behests of justice,And ever punish those who act amiss.

Supply and Demand and Marginal Cost free essay sample

Demand function for air travel between the U. S. and Europe has been estimated to be: ln Q = 2. 737 1. 247 ln P +1. 905 ln I where Q denotes number of passengers (in thousands) per year, P the (average) ticket price and I the U. S. national income. Determine the price elasticity and income elasticity of demand (8 points). From Lecture Module 3 Equation 4 we learned the alternative formulation of elasticity. Alternative formulation of elasticity EP = dQ/dP * P/Q = dlnQ/dlnP Natural log: ln, uses the base â€Å"e† How? ?lnQ/? lnP =(d lnQ/dQ) * (dQ/dP) * (dP/dlnP) [ Note: dY/dX = 1/(dX/dY) since, dlnX/dX = 1/X, dX/dlnX = X] Example: Q = AP-? A:Constant0 lnQ=lnA + ln(P-? ) =lnA – ? lnP EP = dlnQ/dlnP = -? ? =? lnQ/? lnP ? =P/Q* (? Q/? K) = Elasticity The coefficients of double log model are the corresponding elasticity Price elasticity = -1. 247 Income elasticity = 1. 905 (1ii) It has been estimated that the price elasticity of demand for U. We will write a custom essay sample on Supply and Demand and Marginal Cost or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page S. manufactured automobiles is -1. 2, while the income elasticity of demand is 2. 0 and the cross price elasticity of demand with respect to the foreign automobiles is 1. 5. The current volume of sales for U. S. manufactured automobiles is 10 million per year. It is expected that over the next year the average income of the consumers in the U. S. will increase by 2. 5 percent. It has been determined that the price of the foreign imports will increase by 6% over the next year. By how much should the U. S. automakers adjust the price of their automobiles if they wish to increase the volume of their sales by 9. 2% next year (8 points)? Price elasticity = -1. 2 Income elasticity = 2 Cross price elasticity = 1. 5 Current volume = 10 million 2. 5% Average income increase We know from Module 3 created by Dr. Ghosh that: EP = %? Qx / %? Px, where only Px changes %? Qx = EP * %? Px if only Px changes Exy = %? Qx / %? Py, where only Py changes %? Qx = Exy * %? Py, if only Py changes EI = %? Qx / %? I, where only Income changes %? Qx = * EI %? I, if only Income changes Total % ? in Demand, %? Qx = EP * %? Px % + Exy * %? Py + EI * %? I We want the new Total % ? in Demand (%? Qx) = 9. 2%. Applying this highlighted formula we can calculate the % change in price for US automobiles to obtain a 9. 2% increase in demand: 9. 2 = -1. 2*%? Px(what we want to solve for) + 1. 5*6 + 2*2. 5 X=4% (1iii) Bright Future, Ltd (BF) is a nonprofit foundation providing medical treatment to emotionally distressed children. BF has hired you as a business consultant to design an employment policy that would be consistent with its goal of providing the maximum possible service given its limited financial resources. You have determined that the service (Z) provided by BF is a function of its medical staff input (M) and sound service input (S) which is given by: Z = M + . 5S + . 5 MS S2 BF’s staff budget for the coming year is $1,200,000. Annual employment costs are $30,000 for each social service staff member (S) and $60,000 for each medical staff member (M). (1iiia) Using the Lagrangean multiplier approach calculate the optimal (i. e. , service maximizing) combination of medical and social staff. Determine the optimal amount of service provided by BF (32 points). Objective function: Z = M + . 5S + . 5 MS – S2 Constraint: 30000S+60000M = 1200000 Lagrangian: L = M + . 5S + . 5 MS S2+? [1200000-30000S-60000M] First we need to calculate the first order conditions from the objective function: dL/dS = 0 implies 0. 5+0. 5M-2S = 30000? or 0. 5+0. 5M-2S-30000? =0 dL/dM = 0 implies 1+0. 5S=60000? or 1+0. 5S-60000? =0 dL/d? = 0 implies 30000S+60000M = 1,200,000 or 30000S+60000M-1,200,000=0 Next we need to equate dL/dS = dL/dM 60000*(0. 5+0. 5M-2S) = 30000*(1+0. 5S) 30000+30000*M-1,200,000S = 30000+15000S M = 4. 5S Substituting this value into the last equation of dL/d? 30000S+60000*4. 5S = 1,200,000 S= 4 = Social Staff M* = 4. 5*4 = 18 = Medical Staff Z = M + . 5S + . 5 MS S2 Z= 18+0. 5*4+0. 5*18*4-42 = 40 = Optimal amount of service (1iiib) Calculate BF’s marginal cost. Explain your answer. Dr. Ghosh†¦I couldn’t find much in our text regarding the interpretation of this in relation to MC. I did find that the multiplier should equate to the marginal cost from research online and inferred from the definition of the multiplier itself in your notes. Applying this, I believe the marginal cost would be calculated as follows: BF’s Marginal Cost = The reciprocal of Lagrangian multiplier Using equation calculated in problem above: ? = 1+0. 5S/60000 = (1+0. 5*4)/60000 = 0. 00005 = 1/0. 00005 = $20000 = BF’s Marginal Cost (1ciii) Using Excel-Solver verify your answer to (a). (Show your work. Show the spreadsheets in detail. Provide print outs with Solver window. To print the solver window, use print screen command on your key board and then create a MS Word document using paste. (12 points) Snapshot: Clickable Excel spreadsheet detailing work: (1iv) The own price elasticity of demand for a pack of cigarettes is estimated to be -. 4. Current price and consumption are $4. 00 and 2 million units per year. Assuming a linear demand relationship determine the demand equation for cigarettes. Show all your calculations (12 points). From Module 3 created by Dr. Ghosh we can determine the following: If we believe that the demand equation can be captured by a straight line graph, then we can proceed as follows to estimate a linear demand function. Let the demand equation be described by the following linear equation, Q=a bP where a0, b0 Our task is to estimate the parameters a and b. From the definition of EP we can write, EP = (? Qx/? Px) * Px/Qx Current Price = P = $4 Current quantity sold = 2,000,000 Ep= -. 4 From the definition of Ep we can write, EP = (? Qx/? Px) * Px/Qx = -. 4 = -b*4/2,000,000 b = 200,000 Substituting in the equation for the demand function we obtain, Q= a 200,000P Using Q = 2,000,000 and P = 4 2,000,000 = a- 200,000*(4) a = 2,800,000 Thus the demand equation can be determined to be Q = 2,800,000 200,000P (2i) The production function for a firm is given by Q = LK where Q denotes output; Land K labor and capital inputs. Wage rate and rental rate are given by w and r respectively. (2ia) Show whether or not the above productions function exhibits diminishing marginal productivity of labor (8 points). We know from our test and from the notes by Dr. Ghosh that: Q = LK MPL= ? Q/? L = K MPL does not fall with respect to L and the second order derivative did not give a negative value thus does not reflect diminishing marginal productivity. (2ib) Determine the nature of the Return to Scale as exhibited by the above production function (12 points). We know from module 4 created by Dr. Ghosh that: Cobb-Douglas Production Function: Q = AL? K? , A 0, ? 0, ? 0 if ? + ? = 1, CRS if ? + ? 1, IRS if ? + ? 1, DRS Note if A =1 and ? = ? = 1, we have the production function, Q = LK As such the production function results in increasing Returns to Scale as ? + ? 1 and 1+ 1 1. (2ic) Using the Lagrangean Multiplier method, calculate the least cost combinations of labor and capital and the resulting long run total cost function for the above production function. Explain the economic significance of the Lagrangean Multiplier and calculate its value (32 points). Q = LK TC = wL + rK L = wL + rK + ? (Q-LK) ?L/? L = w + ? (K) =0 therefore w = ? k ?L/? K = r + ? (L) =0 therefore r = ? L ?L/ = 0 therefore Q=LK As such K = (w/r)L Q=L2(w/r) and least cost value of L =(rQ/w)1/2 K = (wQ/r)1/2 least cost value of K Lagrangean multiplier: ? = (wr/Q)1/2 The Lagrange multiplier allows us to treat constrained problems as though they were unconstrained. From this we can determine the cost function as: C(Q) = wL + rK =w*[(rQ/w)1/2)] + r*[(wQ/r)1/2)] = 2vwrQ (long run total cost function) (2id) Using the above cost function, calculate the numerical value of long run total cost when Q =224, w = 16 and r = 144. Using our cost function above we can determine that: 2*(16*144*224)1/2 = 1,436. 796 (2ie) Using Excel- Solver verify your answer to (d) above (12 points). The snapshot of the solver window minimizing the cost function is: The clickable excel workbook showing my work is: (ii) As the manager of an 80-unit motel you know that all units are occupied when you charge $60 a day per unit. Each occupied room costs $4 for service and maintenance a day. You have also observed that for every x dollars increase in the daily rate above $60, there are x units vacant. Determine the daily price that you should charge in order to maximize profit (12 points). From learning module 2 created by Dr. Ghosh we know the following: Profit = Total Revenue – Total Cost ? = TR – TC Then we calculate the first order condition, and calculate optimal P and Q for resulting profit. Note: ? TC/? Q = dTC/dQ = Marginal Cost ?TR/? Q = dTR/dQ = Marginal Revenue From these concepts we can apply this to the problem: Fully occupied profit = 80*60 -80*4 = 4480 Price per unit = 60 + x Number of units occupied = 80 x Cost = 4*(80-x) Revenue = P*Q= (60+x)*(80-x) Profit = TR TC Therefore profit = (80-x) (60+x) – 4*(80-x) = (80-x) (56+x) = 4480 + 24 x – x2 In order to maximize profit we obtain the derivative of 4480 + 24 x – x2 as 24 – 2x and set it equal to 0. dQ/dY = 24 – 2x 24 2x = 0 2 x = 24 x = 12 Substitute the value of X into the price equation to arrive at: Price = 60 + 12 = 72 (3i) Sleak Teak builds yard furniture using hardwoods and (in a smaller shop) handcrafted knick-knacks from the same sort of wood. The hardwood usage in the two lines of product are Yard Furniture: Y = 2 Ty . 001Ty2 Knick-knacks: Z = 20Tz . 01 Tz2 where Y and Z are units of furniture and knick-knacks respectively. Ty and Tz are the amounts of hardwood used in Y and Z production respectively. Yard furniture can be sold at a profit (i. e. , net of costs) of $100 per unit and knick-knacks can be sold at a profit of $25 per unit. Sleak Teak has 1300 units of hardwood available that can be allocated between these two lines of production. (3ia) Using the Lagrangean Multiplier method, determine how should the hardwood be allocated between the two lines of product so that total profit can be maximized. Also calculate the optimal amounts of Y and Z and total profit from each product line (32 points). We are provided the following information: Yard Furniture: Y = 2Ty . 001Ty2 Knick Knacks:Z= 20Tz . 01 Tz2 We need to obtain the derivatives of each of these functions: Y (derivative) = 2 -. 002Ty Marginal Profit = is 100(2-. 002Ty) Z'(derivative) = 20 -. 02Tz Marginal Profit = 25(20-. 02Tz) Next we need to set the equations equal to each other: 100(2 . 002Ty) = 25(20 . 02Tz) 200 . 2Ty = 500 . 5Tz .5Tk . 2Ty = 300 We know the constraint as it is given in the equation as Tz+Ty= 1300 5Tz -2Ty= 3000 2Tz +2Ty= 2600 7Tz = 5600 Tz = 800 Ty = 1300-800=500 Production should be allocated to 500 for Ty and 800 for Tz Substituting these values into the given functions we can obtain the optimal amounts of Y and Z: Yard Furniture: Y = 2Ty . 001Ty2 Yard Furniture: Y = 2(500) . 001(500)2 Yard Furniture: Y = 750 Knick Knacks:Z= 20Tz . 01 Tz2 Knick Knacks:Z= 20(800) . 01 (800)2 Knick Knacks:Z= 9,600 Profit can be calculated as = ((100*500) + (25*800)) = 315,000 (3ib) Using Excel Solver verify your answers to (a) above. (12 Points- Show work. ) A screen shot of the solver parameters can be seen below. The clickable excel workbook can be found below for equations: (3ii) You manage Dirt Diggers, an excavating firm that excavates roadside ditches for laying drainpipes. Its output follows the production function: Q = 10L -. 1L2 where L denotes labor hours and Q the length of the ditch in meters. You can hire labor at the going wage rate of $12 per hour. As the manager of DD you want to earn as high a profit as possible. (3iia) You have received an offer to excavate 250 meters for a lump sum payment of $500. Should you accept the offer? Explain with appropriate calculations (12 points). According to Module 4 created by Dr. Ghosh: Incremental measure of productivity or Marginal Product of Labor MPL = ? Q/? L = ? Q/? L = fL = slope of total product curve in the short run when K is fixed. Application: Optimal Business Decisions: Hiring of workers Consider the short production function: Q=f(L,K) Price = P TR = P*Q = P*f(L,K) = TR(L) TC = W*L +F, where F is the fixed cost and W the wage rate Focus on how many workers you need to use to maximize ? = TR-TC = PQ – WL = Pf(L,K)-W*L FOC for Profit Maximization: d? /dL=0 = PfL – W = 0 Marginal Revenue Productivity = Marginal Expenditure on Labor (or marginal input cost) (This is nothing but MR = MC in terms of labor and not output) Additionally from the text we know that MRPL = (MR)*(MPL) in equation 5. 2 The text goes on to detail that â€Å"to maximize profit, the firm should increase the amount of a variable input up to the point at which the input’s marginal revenue product equals its marginal cost. † Therefore equation 5. 3 in the text states MRPL = MCL Applying these concepts to the problem: First you can determine that the initial offer is at a Price of $2 per meter as 500/250=$2 P=$2 (current offer of $500 for 250 meters) We know that the firm maximizes profit when it equates MRPL = (MR)*(MPL) =MCL MPL = dQ/dL = 10 . 2L. Therefore, ($2)(10 . 2L) = 12 and L=20. In turn, Q = 10L -. 1L2 and as such Q = (10)(20) . 1(202) and Q=160 Since the optimal quantity of meters dug at a price of $2 is 160 meters, Ditch Diggers should not accept the offer of $250 meters for $500. This is not the profit maximizing quantity at this price- reject the offer. You can also approach this problem from another angle. Specifically, since we are provided with the production function of Q = 10L -. 1L2 and we know the offer is to dig 250 meters, we can determine the labor and cost required to achieve this result at 250 = Q = 10L -. 1L2 resulting in L of 50. Since the Marginal Cost of labor is $12 we can multiply this by the L of 50 to arrive at a cost of $600 to perform the job, while the offer is only $500 for completion. From this perspective we would still reject the offer as the revenue is less than the cost to perform $500 (revenue) $600 (Cost). (3iib) Suppose that instead of the previous offer, you are now offered as much or as little excavation work at a price of $2. 00 per meter dug. Should you accept the offer? Why or why not? If you accept the offer calculate DD’s resulting profit. Also, calculate the optimal level of output (meter dug) and the level of labor usage (16 points). From our calculation above we already know the following: We know that the firm maximizes profit when it equates MRPL = (MR)*(MPL) =MCL MPL = dQ/dL = 10 . 2L. Therefore, ($2)(10 . 2L) = 12 and L=20 (level of labor usage). In turn, Q = 10L -. 1L2 and as such Q = (10)(20) . 1(202) and Q=160 (optimal output, meters dug) The optimal quantity of meters dug at a price of $2 is 160 meters at a level of labor usage of 20. The firms profit is = PQ – (MC)L= $2(160) $12(20) = $80 Therefore, Ditch Diggers should accept the offer and will receive a resulting profit of $80. (3iii) As a manager of a firm you find the marginal cost of the firm to be $10 and the fixed cost $100. For the range of prices that you are planning to charge, own price elasticity of demand is believed to be –1. 5. Calculate the optimal (profit maximizing) price that you should charge. Show all calculations (8 points). In order to solve this we need to apply the markup rule. Specifically the size of a firm’s markup (above marginal cost and expressed as a percentage of price) depends inversely on the price elasticity of demand for a good or service. According to equation 3. 13 from the text, the optimal markup rule is: P = Ep/(1+Ep)MC And from Module 3 created by Dr. Ghosh we know: Optimal Pricing (for profit maximization): Inverse Elasticity Rule Rule for profit max: Produce output up to a point so that MR = MC MR = MC P[1 1 / | EP |]=MC MC/P = 1-1/| EP | If adding 1 1 MC/P = 1-[1-1/| EP |] (P-MC)/P = 1-1+1 / | EP | (P-MC)/P (Price-Cost Margin) = 1 / | EP |: Inverse Elasticity Rule The lower the value of elasticity, the higher the price-cost margin For a competitive firm, |E|=infinity, therefore (P-MC)/P = 0 (rule for profit maximization, P=MC) Additionally we know from the text that â€Å"the logic of marginal analysis in general and the markup rule (equation 3. 13) show that optimal price and quantity depend on marginal cost (MC). Fixed Costs have no effect on the choice of optimal price and quantity. † Therefore for this problem we do not consider the $100 fixed costs detailed. As such P = Ep/(1+Ep)MC = P = (-1. 5)/(1-1. 5)10 = $30