Free Essay

# Sollution

Submitted By faizfantasy
Words 1129
Pages 5
Microeconomics–Midterm Solution.

August 21, 2009

1. The elasticity of demand is given by E d =

percentage change in quantity demanded percentage change in price

.

(a) The elasticity of demand for roasted coﬀee is given by d ERC = 75−70 70 10.35−10.48 10.35

= −5.68681.
∆Q ∆P

The linear demand curve can be written as Q = A − BP where B = Hence, the linear demand curve is Q = 473.077 − 36.4615P . (b) The elasticity of demand for instant coﬀee is given by d EIC = 820−850 820 4.11−3.76 3.76

=

75−70 10.35−10.48

=

−38.4615. Using (Q, P ) = (75, 10.35) or (Q, P ) = (70, 10.48), we obtain A = 473.077.

= −0.393031.

(c) Roasted coﬀee is more elastic since it is a luxury item, as can be seen from the high price. 2. Let soft drinks be S and burgers be B. (a) The indiﬀerence curves are L-shaped with the corner of the L lying on the line S = 3B. (b) The consumption ratio is
S B

= 3.

(c) The budget constraint is 10B + 5S = 100. (d) We have two equations in two variables: equations, we obtain B = 4 and S = 12. 3. (a) Natasha is risk averse since her utility function is concave. (b) The expected income of the new job is 0.6 × 50 + 0.4 × 27 = 40.8. The expected utility from the new job is √ √ 0.6 10 × 50 + 0.4 10 × 27 = 19.9891.
S B

= 3 and 10B + 5S = 100. Solving the two

1

The utility from the existing job is oﬀers a higher expected income.

10 ∗ 40 = 20. Since the utility from the existing

job is higher, she should not take up the new job oﬀer despite the fact that the new job (c) The amount that Natasha would be willing to pay is the risk premium. To ﬁnd the risk premium, we ﬁrst ﬁnd the certainty equivalent of the risky income bundle. From (b), we know that the expected utility from the risky job is 19.9891. The certainty equivalent of the risky income bundle is that income level that obtained with certainty gives aa utility equal to utility of the risky income bundle. So, we want I such that √ 10I = 19.9891. Solving this equation, we obtain I = 39.9563 as the certainty equivalent. The risk premium is the expected income of the risky bundle minus the certainty equivalent, or 40.8 − 39.9563 = 0.8437. 4. (a) The expected income from investment A is
2 3

× 400 + 1 100 = 300 > 200. The utility 3

obtained from the investment is min{FS , FH } = min{400, 100} = 100. On the other hand, the utility from the guaranteed income is min{FS , FH } = min{200, 200} = 200. Since the utility obtained from the new investment is lower, the individual will not invest in A. (b) The utility from the new investment B is min{FS , FH } = min{100, 400} = 100 which is less than the utility of 200 obtained from the guaranteed income of 200. Hence, it does not make sense for the investor to invest in B either. (c) Now the consumer invests 100 in both projects. In the sunny state, he obtains a net return of 200 from Investment A and a net return of −100 from Investment B. Hence, his aggregate net return is 100. Hence, FS = 300 (the existing income of 200 plus the net return of 100). In the stormy state, the net return from B is 200 and from A is −100. Hence, aggregate net return is 100 and FH = 200 + 100 = 300. Hence, utility is min{FS , FH } = min{300, 300} = 300. So, with hedging, the investor obtains a guaranteed income, and hence, a utility of 300 which is higher than the existing utility of 200. 5. (a) Since the capital stock is ﬁxed at 9, the short run production function is q = F (L) = √ 2 2 3 L. Hence, L = q9 . So, the cost of labour is wL = 4000 q9 . The cost of capital is rK = 10000 × 9 = 90000. Hence, the short run cost function is C(q) = rK + wL 4000 2 = 90000 + q . 9 The average cost is AC(q) =
90000 4000 q + 9 q.

The marginal cost is M C(q) =

dC(q) dq

=

8000 9 q.

2

(b) In order to make 20 motors, the ﬁrm should design a new production facility using the cost minimizing capita-labour combination. This is obtained by equating the M RT SLK to the input price ratio w r

=

4 10 .

M RT SLK =

0.5L−0.5 K 0.5 K M PL = = . 0.5 K −0.5 M PK 0.5L L

The ﬁrm also needs to produce an output of 20. So, F (L, K) = 20. We therefore have two equations. M RT SLK w r F (L, K) = 20. =

Using the calculated M RT S, and the values of w and r, we solve the two equations to obtain (L = 31.6228, K = 12.6491). This is the cost minimizing capital-labour combination. Hence, in designing the new production facility, the ﬁrm needs to increase its capital stock from 9 to 12.6491. 6. (a) The average cost function is AC(Q) = increasing returns to scale. (b) The marginal cost is M C(Q) = dC(Q) dQ C(Q) Q

=

10 . Q0.5

Clearly, this is a decreasing function

of Q. As Q increases, AC(Q) falls. This implies that the industry is characterized by =
5 . Q0.5

A price taking ﬁrm would maximize proﬁt

by equating price with marginal cost. Hence, P = M C(Q) which implies 2= 5 , Q0.5

or Q = 6.25. This is the proﬁt maximizing quantity. (c) Proﬁt is given by Π(Q) = (P − AC(Q))Q. At Q = 6.25, AC(Q) = 4. Hence, Π(6.25) = (2 − 4)6.25 = −12.5. Hence, the maximum possible proﬁt for the ﬁrm is a loss of 12.5. This implies that ﬁrms will inevitably sustain losses in the long run if they behave as price takers. Since no ﬁrm can sustain losses in the long run, they cannot continue to behave as price takers in the long run. So, a perfectly competitive structure is not possible in this industry. (Note: This part is not required for the answer. What is going on is that M C(Q) < AC(Q) at all Q. This is the characteristic of all industries with increasing returns to scale. So, P = M C(Q) implies that P < AC(Q). Hence, the ﬁrm will suﬀer losses at all Q. This loss in minimized at Q = 6.25.)

3

### Similar Documents

#### Optimization 7th Edition Sollution

...MATHEMATICAL PROGRAMMING - INDR. 363 (1) 2011 FALL Class Meeting Location ENG Z27 Class Meeting Times TH B3,TU B3 Instructor Office Hours Office Location Office Phone Email Web Address Number of Credits ETC Credit Prerequisites Language ONUR KAYA W 14:00-16:00 ENG 206 1583 okaya@ku.edu.tr 3 6 INDR. 262 English Assistant TA/RA/Lab Assistant Name AYLİN LELİZAR POLAT GÜLÇİN ERMİŞ Email aypolat@ku.edu.tr gulermis@ku.edu.tr Office Hours Office Location Course Description Introduction to modeling with integer variables and integer programming; network models, dynamic programming; convexity and nonlinear optimization; applications of various optimization methods in manufacturing, product design, communications networks, transportation, supply chain, and financial systems. Course Objectives The course is designed to teach the concepts of optimization models and solution methods that include integer variables and nonlinear constraints. Network models, integer, dynamic and nonlinear programming will be introduced to the students. Students will be exposed to applications of various optimization methods in manufacturing, product design, communications networks, transportation, supply chain, and financial systems. Several different types of algorithms will also be presented to solve these problems. The course also aims to teach how to use computer programs such as Matlab and GAMS to solve mathematical models. Learning Outcomes Students are expected to......

Words: 768 - Pages: 4

Free Essay

#### Government Can

...Gather 'round! I'm here to give you anything you like! You want free college, money, mortages?! Whatever you like! You have come to the right place! Why? I'll tell you why!) Who can take your money? (Who can take your money?) With a twinkle in their eye? (With a twinkle in their eye?) Take it all away and Give it to some other guy [Chorus] The Government (the Government) The Government can! (The Government can!) Who can tax the Sun rise? (Who can tax the Sun rise?) Who can tax the trees? (Who can tax the trees?) Let you run a business and Collect up all the fees [Chorus] The Government can 'cause They mix it up with lies and Make it all taste good! (Make it all taste good!) The Government takes Everything we make To pay for all of their "sollutions" Healthcare, Climate Change, Pollution [- From: http://www.elyrics.net/read/t/tim-hawkinslyrics/the-government-can-lyrics.html -] (Throw away the Constitution) Who can give a bailout? (Who can give a bailout?) Tell us to behave? (Tell us to behave?) Make the Founding Fathers Roll over in their graves [Chorus] The Government takes Everything we make They're power hungry And malicious The economics are fictitious Soon we'll have to eat our dishes Mmm! Delicious! Who can be a failure? (Who can be a failure?) In so many ways? (In so many ways?) Instead of getting fired, HEY! We'll give ourselves a raise! [Chorus] The Government can 'cause They mix it up with lies and Make it all taste good! (Make it all taste good!) And your......

Words: 307 - Pages: 2

Free Essay

#### Toyota Tqm

...Toyota Motor Corporation, Ltd. I. Viewpoint The viewpoint of the CEO of Toyota will be applied. II. Time Context Present Year III. Objectives Toyota Motor Corporation’s objective is to identify ways to keep up and adapt with the foreign business cultures to successively expand by at least 10% before 2020. IV. Statement of the problem Minor Problems: • Strategies to adapt with foreign cultures and anticipate its possible negative effects • While adapting to foreign cultures, Toyota’s products should maintain its products’ quality • Adaptation with the business environment Major Problem: • Problems in expansion due to issues in foreign culture adaptation V. Areas of Consideration | |Finance |Marketing |Production/Operation | |Strengths |Brand reputation valued at billions |Innovative culture |Industry leader in production and | | |of dollars |Strong brand portfolio |sales | | |Strong financial performance |Highly targeted marketing |“Toyota Production System” | | | |Diversified product range |Has 40......

Words: 1151 - Pages: 5

Free Essay

#### Gleo

...Marketing 4 ontwikkelingen convergentie (samensmelting tussen verschillende branches) INTEGRATIE VAN: * informatie- en communicatiesector mobiele telefoon, dvd * infrastructuren vaste en draadloze netwerken * media- en entertainmentindustrie dagblad “DAG”; Luisterboeken; TV, radio, film en video, games, muziek, dagbladen, tijdschriften en boeken * media- en entertainmentindustrie en de creatieve economie on-line presentatie aanbod digitale informatie; digitaal loket van de overheid/gemeente, digiD, RabobankMobiel, SMS-alertdiensten ------------------------------------------------- KNELPUNTEN: Rechten en Piraterij MESO-OMGEVING Globalisering / internationalisatie: Internationalisering: Met je product naar het buitenland gaan. Samenwerken en -leven met anderstaligen, een buitenlandse afzetmarkt verkennen, of op de hoogte blijven van trends binnen je vakgebied; steeds vaker moeten burgers over de grens kijken. Voor alle leerlingen en studenten is internationalisering van belang, of ze nu buitenNederland de arbeidsmarkt op gaan of hier blijven. De raad is voorstander van een sterkere internationale oriëntatie in het onderwijs.  Globalisering: luchtvervuiling, kredietcrisis, hoe spelen we hier op in? Markt wordt transparanter. Niet beinvloedbare omgevingsfactoren. Orkanen, stormen. Globalisering is een moeilijk te omschrijven begrip. Het is eigenlijk een proces van wereldwijde interactie tussen mensen, bedrijven, regeringen en culturen gedreven door......

Words: 4688 - Pages: 19

Free Essay

#### Internet Consumption and Energy

Words: 4355 - Pages: 18

Free Essay

#### Negotation

...1.0 introduction The Thomas Kilmann Model is simple tool that provides practice scenario of particular methodologies to managing conflict viably. The exploration upheld TKI offers a commonsense approach to launch safe and nonemotional discourse to resolve conflict. That is the reason its perfect for utilization in such a variety of diverse situations. It can additionally enhance organizational profit by helping individuals pick up knowledge into their own particular and others' conduct which thus helps them settle on better decisions about conclusions. The TKI is directed in simple to-utilize online and self-scorable configurations. Conflict is an inescapable part of human relationships. Where responsibility to mission and extended periods with negligible assets converge, not-for-profit work environments might be overflowing with conflict trades. Conflict can go out from administering varying viewpoints and clearly inconsistent concerns. Assuming that we can acknowledge it as a regular part of our zealous scene, it might be simpler to work with than in the event that we need (or wish!) conflict to never resurface. 2.0 Introduction of Thomas Kilmann Models. The Thomas-Kilmann Conflict Mode Instrument is intended to evaluate an individual conduct and behavior in certain scenarios. "Conflict Situations" are the scenarios in which the concerns of two individuals seem, by all accounts, to be incongruent. Conflict is a social......

Words: 1809 - Pages: 8

#### Microsof and Nokia Corporation

...Definition of innovation. The term "innovation" comes from the Latin «novatio» -"renewal" or "change", and «in» - "in line, into". If translated literally, «Innovatio» means «in the direction of change". The concept of innovation has a lot of classical definitions. One of them is – innovation is a process of intentional change made to create value by meeting opportunity and seeking advantage (Dr. Bruton A. (2012). Creativity, Innovation and Entrepreneurship. Retrieved October 7, 2012 from http://resources.talcie.org/topics-and-activities/creativity-innovation-and-entrepreneurship). Thus, the innovation means the use of novations in the form of new technologies, products and services, new organization form of production and labor, maintenance and management. That is why, we can say that innovation is possible in all areas of human activity. 7 Interwoven areas of Innovation (Source: http://www.innovarsity.com/products/bec_mc_innovation_systemic.html) Two components of innovation. According to the American Heritage Dictionary (1994), "Innovation is the act of introducing something new". J. Byrd and P.L.Brown, the authors of “The Innovation Equation”, consider that "the act of introducing" is akin to taking a risk and "new" is about creativity. This leads on to what they call the innovation equation: Innovation = Creativity x Risk Taking Creativity is the ability to generate and develop new unconventional ideas, to successfully solve the......

Words: 1708 - Pages: 7

#### 3hrc

...3HRC Assessment 1.1 My organisation are an innovative and trusted developer, manufacturer and supplier of speciality procedural packs and vascular access devices for use across a range of clinical departments. As a proudly indepedent Company, our responsiveness and agility, combined with strong partnership and collaboration ethos, make us a supplier of choice to health organisations the world over. Our Company goal is “a commitment to excellence” Our Company vision is “to be the best” Whilst this is a simple phrase it is far from simple to make happen. We are well on our way to being the best in our chosen healthcare specialities. Our Company values strengthen our on-going relations with customers, partners and each other. Adoption of these values is essential to support the business objectives and inspire us to achieve business and personal goals. Our core values of Respect, Excellence, Success, Entreprenurial, Customer and Teamwork form the acronym RESPECT. My Company doesn’t currently have a mission statement although their mission for the future is for continued expansion both in the UK and throughout the world. 1.2 My Company has a vast range of products in the following clinical areas, Radiology, Renal, Cardiology, Oncology, Critical care, Diagnostic imaging, Anaesthetics, General surgery, Accident and emergency, Nephrology, Nutrition, Ophthalmology, Orthopaedics, Pharmacy and urology. The product groups are, soft tissue biopsy needles,......

Words: 2684 - Pages: 11

Free Essay

#### Issue

...The speaker claims that the responsibility for protecting the environment ultimately belongs to each individual rather than government. The issue involves various aspects of environmental protection and government regulations. In my view, while it is true that ordinary people are ultimately responsible for protecting the environment, the government is also obliged to join the efforts, for the reason that only government has the necessary regulatory power and financial support to coordinate such efforts. I concede that individuals are ultimately responsible for the environmental protection. After all, government, by nature, is only a regulatory body that consists of ordinary people. Futhermore, the financial support gained by governments are from tax-payers and the regulatory power is also endowed by the people to some degree. For example, the government's decision to foster environmental protection is effective only when it is supported by tax money. Therefore, individuals are the ones that are responsible for protecting the environment. However, even though individuals have the duty to proctect environment, it is no excuse for government to escape such duties. First, only government possesses the regulatory power to enforce environmental protection laws. The central reason why the efforts have been less than successful in some places is that they are always in conflict with the interests of certain groups of people. As a result, measures have to be taken in a forceful......

Words: 2704 - Pages: 11

#### Sustainability, Consumption and Waste

...SUSTAINABILITY CONSUMPTION AND WASTE; Marketing to Change Societal Impact through Education for Lifestyle Change By George L. Gonzales SUB 6520 Sustainable Marketing Alliant International University Marshall Goldsmith School of Management Dr. Ute Jamrozy "A society grows great when old men plant trees whose shade they know they shall never sit in." - Greek Proverb     Marketing to Change Societal Impact through Education for Lifestyle Change I will attempt to describe the amount of material waste in relation to economic consumption, and through educational marketing implicate the societal impact of current consumption lifestyles, leaving one conclusion - to change consumption patterns. Awareness-building, as a behavioral change mechanism that questions individual self awareness of how an individual’s thinking and activities affect the climate, natural environment and social well-being. Increasing knowledge and understanding on global warming and ecological degradation and social and political distress should influence people to take a positive position on sustainability issues and take action. Doppelt, (2008). The action must come from the stakeholders at risk; the citizen-consumer, industry and government. Awareness-building is a proactive behavioral change mechanism that can be manifested with an organized marketing effort. In problem solving, “a basic level of understanding of the problem and......

Words: 3026 - Pages: 13

#### Fujitsu Limited

...Executive Summary The aim of this formal business report is to analyse a number of aspects of business management using a successful existing company. This report is based on a one of the world’s leading Information and Communication technologies company-Fujitsu LTD. The report includes a brief introduction of Fujitsu, to get more familiar with the company, its approach and activities. The report also includes an environmental analysis (SWOT), to see what are the strengths and weaknesses of Fujitsu LTD., and what opportunities and threats is the company facing. The research investigates 3 organisational goals that are planned to be reached in future and cascades the through the various business departments and levels-finance, marketing, human resources and operations. In this report we examine three different plans that Fujitsu has implemented over the past five years. From the research we observed that Fujitsu uses its own management philosophy, called Fujitsu way and we examined this approach through various points. In the report we reviewed how conceptual, human and technical skills are used in Fujitsu. We also considered how staff should be motivated in Fujitsu in order to reach the overall organizational goals. We conducted our research using various resources, such as ITB Library, Business Sources Premium and Emerald databases, Company’s website and Internet. Table of Contents Executive Summary i Table of Figures iv Table of......

Words: 4878 - Pages: 20