The Executive MBA Program with a specialization in Strategy and Leadership is specifically designed for executives and top managers of various companies. It covers all major topics relevant to the successful leadership and management of the organizations. The aim of the Program is to equip professionals with relevant business knowledge and tools in order to improve their own and company’s performance, identify weaknesses and increase efficiency.
The Executive MBA Program with a specialization in Strategy and Leadership is specifically designed for executives and top managers of various companies. It covers all major topics relevant to the successful leadership and management of the organizations. The aim of the Program is to equip professionals with relevant business knowledge and tools in order to improve their own and company’s performance, identify weaknesses and increase efficiency.
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Problem Set 2.pdfProblem Set 2 ECO105 Industrial Organiz.docxwkyra78
Problem Set 2.pdf
Problem Set 2
ECO105 Industrial Organization and Firm Strategy
Professor Michael Noel
University of California San Diego
------
1. A single-product monopolist sells output to two geographically separated markets. Arbitrage is not
possible. The inverse demand curve in market 1 is given by p1 = 8 - q1 and in market 2, it is p2 = 4 -
q2. Note: if you get stuck in one part, move on to the next.)
a. The monopolist currently produces the output at a single plant (called plant "A") with total cost
function C(qA) = 0.5qA
2. Hence qA = q1 + q2 is the total output of the firm (which we can also
call Q). Find the quantities sold in each market, q1 and q2, and total output Q. Find the profits of
the firm. (Hint: this is the basic third degree price discriminating problem. Make sure to
substitute qA out of the problem using the constraint, so that the problem is all in terms of the
two “free” variables, q1 and q2.)
b. (From an old exam.) The monopolist is considering adding a second plant, plant "B". The total
cost function for plant "B" is C(qB) = qB + 0.25qB
2. Hence, if the monopolist purchases the new
plant, her total production is qA + qB = Q, where qA is produced in plant A and qB is produced in
plant B. She then sells Q = q1 + q2 in output, where q1 is sold in market 1 and q2 is sold in market
2. Find the output sold in each market, q1 and q2, the amount of good produced at each plant, qA
and qB, and the total output, Q. Find the profits of the firm in this case. How much is the firm
willing to pay to purchase plant B? (Hint: Do NOT assume that a single plant is matched solely
with a single market! You only know that the total produced equals to the total sold, so q1 + q2 =
qA + qB ( = Q). There are now four quantities to find, q1, q2, qA, qB, but only three of them are
“free variables”, i.e. can be independently chosen. So for example, if you know q1, q2 and qA, it
necessarily determines what qB must be. So set up your profit function initially in terms of all
four quantities and but then use the constraint q1 + q2 = qA + qB to substitute out one of the four.
Which three quantities you keep in the equation is up to you. Then solve for three first order
conditions.)
c. (Challenging.) Assume a new law prohibits price discrimination and requires the monopolist to
charge the same price in both markets. Repeat part a. under this assumption, i.e. only plant A. Has
welfare increased, decreased or remained unchanged relative to part a.? Warning: check to see if
both markets are being served in equilibrium! (You will need to “add” up the two demand curves
– add the q’s, not the p’s! A diagram will help. Watch out for the kinks, it may be that only one
group will be served and it may be that both will be served. At the end it may help to plot your
numerical answer on your graph and make sure it makes sense. For example, if you find both
groups are served, you should be on the segment of the ...
Group Assignment - 0213Group Assignment T116BUS102 Introduct.docxwhittemorelucilla
Group Assignment - 0213
Group Assignment T116
BUS102 Introduction to Microeconomics
Questions, Notes & Guideline for Group Assignment
Due 5.00pm, Tuesday 10 May 2016
Topic
· Three Problem-Solving Questions that require written answers
1. General information
1.1 This group assignment is worth 25 per cent of total assessment and is to be submitted by 5.00pm, Tuesday 10 May 2016.
· There are 3 questions and answer all 3 questions. Each question is worth 20 marks, consisting total of 60 marks all together. Then the marks will be converted to a total of 25 mark scale to be uploaded in Moodle for 25 per cent of your total course assessment.
· A hard copy of the assignment must be submitted to KOI Librarian in Kent street campus by 5.00pm, Tuesday 10 May 2016. You must keep the receipt after the submission for your own record. You are also required to upload an electronic copy of the assignment in Moodle Turnitin by 5.00pm, Tuesday 10 May 2016.
· Late submission will attract loss of 5 marks out of 25 marks (20 per cent), and the assignment submitted after 7.00pm Thursday 12 May 2016 will not be accepted and marked zero.
1.2 This assignment is a group assignment and each group must form a group of four (4) people.Less than four or more than four-people assignment will not be accepted, unless permission is granted by lecturer (Dr Yeon Kim) for special circumstances.
1.3 Names and ID numbers of students in the group must be clearly printed on the Assignment Cover Sheet. A member, who has not contributed to the discussion and assignment, must be marked as “Not contributed” in a bracket following the student’s name and ID.
1.4 You must follow an appropriate format explained below. Not following appropriate format will cause a loss of some marks.
· All written answers must be clearly typed and printed. Hand-written answers will NOT be accepted.
· All assignment questions and sub-questions must be typed in order at the heading.
· Separate each main question by different page. For example, if Question 1 (a) (b) (c) and (d) are answered on pages 1-2, then start Question 2 on page 3, etc.
· You must analyse, explain and show how and why you draw your answers. Providing just answers without explanation will not receive full marks.
· You must also draw and include appropriate and relevant graphs and tables together in your explanation. Draw them using Microsoft Power Point/Word/Excel, NOT hand-drawn.
1.5 Copying the assignment contents from other group assignment is a serious violation of copy right. It will be penalized and attract a VERY heavy loss of marks – “Fail”.
· Please remember that it is not difficult to identify the contents that are copied from other group(s). Write the answers in your own English words.
· Please make sure that nobody in your team shows your assignment to other group(s). Both who show the assignment and who copy the assignment will lose their marks heavily and fail in the assessment.
1.6 Each group must have a coordinator ...
Article Critique Is genetic testing right for you and your f.docxfredharris32
Article Critique
Is genetic testing right for you and your family?
Recent advancements within scientific research have spurred controversy over the topic of genetic
testing, especially with newborns. Although scientists can now identify certain DNA markers that reveal
an increased propensity for various diseases and disorders, numerous moral dilemmas quickly emerge.
How will predicting future events impact the present? Would knowing that your child is most likely
going to develop Alzheimer’s disease change the way that you raise him or her? Should someone help
you understand the implications if you are told that your child is most likely going to be autistic? What
impact will these “potential” results have on your child’s healthcare? Could genetic testing force your
child to be plagued with unnecessary stigmas?
Read the article by Pollack (2010) and write a two-page critique examining why so much controversy
surrounds genetic testing today. Do you agree or disagree with the author’s stance on this topic?
Tips for writing your Article Critique:
Introduction – This is meant to give a concise overview of the article being discussed and is usually one
paragraph in length.
Summary – This contains the summary of the article that gives the general argument(s) and overview of
the featured author.
Critique – In this portion of the paper, you should provide a critique/opinion of the article. You should
state whether you agree or disagree with the issues that were posed. Furthermore, you should also
discuss why you agree or disagree with the author’s viewpoint(s). Do not forget to discuss the
importance of this article to the field of psychology.
Conclusion – This summarizes your final thoughts for the featured topic.
Note: Do not forget to double space your response and use Times New Roman 12 pt. font. This written
assignment should have a cover page, two full pages of content in which you organize the four sections
of the article critique based on the guidelines as listed above, and a references page. You are required to
utilize the textbook, assigned article, and one additional source to support your stance on this topic. All
three sources should be included on your references page. You should also have accompanying in-text
citations for each source that you have used throughout your response. Follow APA format.
ECO 520 Case Study One: Production and Cost Guidelines and Rubric
Overview
This course includes two case studies. These exercises are designed to actively involve you in microeconomic reasoning and decision making and
to help you apply the concepts covered in the course to complex real-world situations. The case studies provide practice reading and
interpreting both quantitative and qualitative analysis. You will then use your analysis to make decisions and predictions. These exercises
provide practice communicating reasoning in a professional manner.
Prompt
Case Study One: Production and C ...
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
Problem Set 2.pdfProblem Set 2 ECO105 Industrial Organiz.docxwkyra78
Problem Set 2.pdf
Problem Set 2
ECO105 Industrial Organization and Firm Strategy
Professor Michael Noel
University of California San Diego
------
1. A single-product monopolist sells output to two geographically separated markets. Arbitrage is not
possible. The inverse demand curve in market 1 is given by p1 = 8 - q1 and in market 2, it is p2 = 4 -
q2. Note: if you get stuck in one part, move on to the next.)
a. The monopolist currently produces the output at a single plant (called plant "A") with total cost
function C(qA) = 0.5qA
2. Hence qA = q1 + q2 is the total output of the firm (which we can also
call Q). Find the quantities sold in each market, q1 and q2, and total output Q. Find the profits of
the firm. (Hint: this is the basic third degree price discriminating problem. Make sure to
substitute qA out of the problem using the constraint, so that the problem is all in terms of the
two “free” variables, q1 and q2.)
b. (From an old exam.) The monopolist is considering adding a second plant, plant "B". The total
cost function for plant "B" is C(qB) = qB + 0.25qB
2. Hence, if the monopolist purchases the new
plant, her total production is qA + qB = Q, where qA is produced in plant A and qB is produced in
plant B. She then sells Q = q1 + q2 in output, where q1 is sold in market 1 and q2 is sold in market
2. Find the output sold in each market, q1 and q2, the amount of good produced at each plant, qA
and qB, and the total output, Q. Find the profits of the firm in this case. How much is the firm
willing to pay to purchase plant B? (Hint: Do NOT assume that a single plant is matched solely
with a single market! You only know that the total produced equals to the total sold, so q1 + q2 =
qA + qB ( = Q). There are now four quantities to find, q1, q2, qA, qB, but only three of them are
“free variables”, i.e. can be independently chosen. So for example, if you know q1, q2 and qA, it
necessarily determines what qB must be. So set up your profit function initially in terms of all
four quantities and but then use the constraint q1 + q2 = qA + qB to substitute out one of the four.
Which three quantities you keep in the equation is up to you. Then solve for three first order
conditions.)
c. (Challenging.) Assume a new law prohibits price discrimination and requires the monopolist to
charge the same price in both markets. Repeat part a. under this assumption, i.e. only plant A. Has
welfare increased, decreased or remained unchanged relative to part a.? Warning: check to see if
both markets are being served in equilibrium! (You will need to “add” up the two demand curves
– add the q’s, not the p’s! A diagram will help. Watch out for the kinks, it may be that only one
group will be served and it may be that both will be served. At the end it may help to plot your
numerical answer on your graph and make sure it makes sense. For example, if you find both
groups are served, you should be on the segment of the ...
Group Assignment - 0213Group Assignment T116BUS102 Introduct.docxwhittemorelucilla
Group Assignment - 0213
Group Assignment T116
BUS102 Introduction to Microeconomics
Questions, Notes & Guideline for Group Assignment
Due 5.00pm, Tuesday 10 May 2016
Topic
· Three Problem-Solving Questions that require written answers
1. General information
1.1 This group assignment is worth 25 per cent of total assessment and is to be submitted by 5.00pm, Tuesday 10 May 2016.
· There are 3 questions and answer all 3 questions. Each question is worth 20 marks, consisting total of 60 marks all together. Then the marks will be converted to a total of 25 mark scale to be uploaded in Moodle for 25 per cent of your total course assessment.
· A hard copy of the assignment must be submitted to KOI Librarian in Kent street campus by 5.00pm, Tuesday 10 May 2016. You must keep the receipt after the submission for your own record. You are also required to upload an electronic copy of the assignment in Moodle Turnitin by 5.00pm, Tuesday 10 May 2016.
· Late submission will attract loss of 5 marks out of 25 marks (20 per cent), and the assignment submitted after 7.00pm Thursday 12 May 2016 will not be accepted and marked zero.
1.2 This assignment is a group assignment and each group must form a group of four (4) people.Less than four or more than four-people assignment will not be accepted, unless permission is granted by lecturer (Dr Yeon Kim) for special circumstances.
1.3 Names and ID numbers of students in the group must be clearly printed on the Assignment Cover Sheet. A member, who has not contributed to the discussion and assignment, must be marked as “Not contributed” in a bracket following the student’s name and ID.
1.4 You must follow an appropriate format explained below. Not following appropriate format will cause a loss of some marks.
· All written answers must be clearly typed and printed. Hand-written answers will NOT be accepted.
· All assignment questions and sub-questions must be typed in order at the heading.
· Separate each main question by different page. For example, if Question 1 (a) (b) (c) and (d) are answered on pages 1-2, then start Question 2 on page 3, etc.
· You must analyse, explain and show how and why you draw your answers. Providing just answers without explanation will not receive full marks.
· You must also draw and include appropriate and relevant graphs and tables together in your explanation. Draw them using Microsoft Power Point/Word/Excel, NOT hand-drawn.
1.5 Copying the assignment contents from other group assignment is a serious violation of copy right. It will be penalized and attract a VERY heavy loss of marks – “Fail”.
· Please remember that it is not difficult to identify the contents that are copied from other group(s). Write the answers in your own English words.
· Please make sure that nobody in your team shows your assignment to other group(s). Both who show the assignment and who copy the assignment will lose their marks heavily and fail in the assessment.
1.6 Each group must have a coordinator ...
Article Critique Is genetic testing right for you and your f.docxfredharris32
Article Critique
Is genetic testing right for you and your family?
Recent advancements within scientific research have spurred controversy over the topic of genetic
testing, especially with newborns. Although scientists can now identify certain DNA markers that reveal
an increased propensity for various diseases and disorders, numerous moral dilemmas quickly emerge.
How will predicting future events impact the present? Would knowing that your child is most likely
going to develop Alzheimer’s disease change the way that you raise him or her? Should someone help
you understand the implications if you are told that your child is most likely going to be autistic? What
impact will these “potential” results have on your child’s healthcare? Could genetic testing force your
child to be plagued with unnecessary stigmas?
Read the article by Pollack (2010) and write a two-page critique examining why so much controversy
surrounds genetic testing today. Do you agree or disagree with the author’s stance on this topic?
Tips for writing your Article Critique:
Introduction – This is meant to give a concise overview of the article being discussed and is usually one
paragraph in length.
Summary – This contains the summary of the article that gives the general argument(s) and overview of
the featured author.
Critique – In this portion of the paper, you should provide a critique/opinion of the article. You should
state whether you agree or disagree with the issues that were posed. Furthermore, you should also
discuss why you agree or disagree with the author’s viewpoint(s). Do not forget to discuss the
importance of this article to the field of psychology.
Conclusion – This summarizes your final thoughts for the featured topic.
Note: Do not forget to double space your response and use Times New Roman 12 pt. font. This written
assignment should have a cover page, two full pages of content in which you organize the four sections
of the article critique based on the guidelines as listed above, and a references page. You are required to
utilize the textbook, assigned article, and one additional source to support your stance on this topic. All
three sources should be included on your references page. You should also have accompanying in-text
citations for each source that you have used throughout your response. Follow APA format.
ECO 520 Case Study One: Production and Cost Guidelines and Rubric
Overview
This course includes two case studies. These exercises are designed to actively involve you in microeconomic reasoning and decision making and
to help you apply the concepts covered in the course to complex real-world situations. The case studies provide practice reading and
interpreting both quantitative and qualitative analysis. You will then use your analysis to make decisions and predictions. These exercises
provide practice communicating reasoning in a professional manner.
Prompt
Case Study One: Production and C ...
Enterprise Excellence is Inclusive Excellence.pdfKaiNexus
Enterprise excellence and inclusive excellence are closely linked, and real-world challenges have shown that both are essential to the success of any organization. To achieve enterprise excellence, organizations must focus on improving their operations and processes while creating an inclusive environment that engages everyone. In this interactive session, the facilitator will highlight commonly established business practices and how they limit our ability to engage everyone every day. More importantly, though, participants will likely gain increased awareness of what we can do differently to maximize enterprise excellence through deliberate inclusion.
What is Enterprise Excellence?
Enterprise Excellence is a holistic approach that's aimed at achieving world-class performance across all aspects of the organization.
What might I learn?
A way to engage all in creating Inclusive Excellence. Lessons from the US military and their parallels to the story of Harry Potter. How belt systems and CI teams can destroy inclusive practices. How leadership language invites people to the party. There are three things leaders can do to engage everyone every day: maximizing psychological safety to create environments where folks learn, contribute, and challenge the status quo.
Who might benefit? Anyone and everyone leading folks from the shop floor to top floor.
Dr. William Harvey is a seasoned Operations Leader with extensive experience in chemical processing, manufacturing, and operations management. At Michelman, he currently oversees multiple sites, leading teams in strategic planning and coaching/practicing continuous improvement. William is set to start his eighth year of teaching at the University of Cincinnati where he teaches marketing, finance, and management. William holds various certifications in change management, quality, leadership, operational excellence, team building, and DiSC, among others.
Improving profitability for small businessBen Wann
In this comprehensive presentation, we will explore strategies and practical tips for enhancing profitability in small businesses. Tailored to meet the unique challenges faced by small enterprises, this session covers various aspects that directly impact the bottom line. Attendees will learn how to optimize operational efficiency, manage expenses, and increase revenue through innovative marketing and customer engagement techniques.
Event Report - SAP Sapphire 2024 Orlando - lots of innovation and old challengesHolger Mueller
Holger Mueller of Constellation Research shares his key takeaways from SAP's Sapphire confernece, held in Orlando, June 3rd till 5th 2024, in the Orange Convention Center.
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3.0 Project 2_ Developing My Brand Identity Kit.pptxtanyjahb
A personal brand exploration presentation summarizes an individual's unique qualities and goals, covering strengths, values, passions, and target audience. It helps individuals understand what makes them stand out, their desired image, and how they aim to achieve it.
[Note: This is a partial preview. To download this presentation, visit:
https://www.oeconsulting.com.sg/training-presentations]
Sustainability has become an increasingly critical topic as the world recognizes the need to protect our planet and its resources for future generations. Sustainability means meeting our current needs without compromising the ability of future generations to meet theirs. It involves long-term planning and consideration of the consequences of our actions. The goal is to create strategies that ensure the long-term viability of People, Planet, and Profit.
Leading companies such as Nike, Toyota, and Siemens are prioritizing sustainable innovation in their business models, setting an example for others to follow. In this Sustainability training presentation, you will learn key concepts, principles, and practices of sustainability applicable across industries. This training aims to create awareness and educate employees, senior executives, consultants, and other key stakeholders, including investors, policymakers, and supply chain partners, on the importance and implementation of sustainability.
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1. Develop a comprehensive understanding of the fundamental principles and concepts that form the foundation of sustainability within corporate environments.
2. Explore the sustainability implementation model, focusing on effective measures and reporting strategies to track and communicate sustainability efforts.
3. Identify and define best practices and critical success factors essential for achieving sustainability goals within organizations.
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1. Introduction and Key Concepts of Sustainability
2. Principles and Practices of Sustainability
3. Measures and Reporting in Sustainability
4. Sustainability Implementation & Best Practices
To download the complete presentation, visit: https://www.oeconsulting.com.sg/training-presentations
Putting the SPARK into Virtual Training.pptxCynthia Clay
This 60-minute webinar, sponsored by Adobe, was delivered for the Training Mag Network. It explored the five elements of SPARK: Storytelling, Purpose, Action, Relationships, and Kudos. Knowing how to tell a well-structured story is key to building long-term memory. Stating a clear purpose that doesn't take away from the discovery learning process is critical. Ensuring that people move from theory to practical application is imperative. Creating strong social learning is the key to commitment and engagement. Validating and affirming participants' comments is the way to create a positive learning environment.
In the Adani-Hindenburg case, what is SEBI investigating.pptxAdani case
Adani SEBI investigation revealed that the latter had sought information from five foreign jurisdictions concerning the holdings of the firm’s foreign portfolio investors (FPIs) in relation to the alleged violations of the MPS Regulations. Nevertheless, the economic interest of the twelve FPIs based in tax haven jurisdictions still needs to be determined. The Adani Group firms classed these FPIs as public shareholders. According to Hindenburg, FPIs were used to get around regulatory standards.
The world of search engine optimization (SEO) is buzzing with discussions after Google confirmed that around 2,500 leaked internal documents related to its Search feature are indeed authentic. The revelation has sparked significant concerns within the SEO community. The leaked documents were initially reported by SEO experts Rand Fishkin and Mike King, igniting widespread analysis and discourse. For More Info:- https://news.arihantwebtech.com/search-disrupted-googles-leaked-documents-rock-the-seo-world/
Company Valuation webinar series - Tuesday, 4 June 2024FelixPerez547899
This session provided an update as to the latest valuation data in the UK and then delved into a discussion on the upcoming election and the impacts on valuation. We finished, as always with a Q&A
LA HUG - Video Testimonials with Chynna Morgan - June 2024Lital Barkan
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answerstohomework3summer2013.docx
1. 1
Economics 101
Summer 2013
Answers to Homework #3
Due Tuesday, June 11, 2013
Directions: The homework will be collected in a box before the lecture. Please place your name, TA
name and section number on top of the homework (legibly). Make sure you write your name as it appears
on your ID so that you can receive the correct grade. Late homework will not be accepted so make plans
ahead of time. Please showyour work. Good luck!
Please realize that you are essentially creating “your brand” when you submit this homework. Do
you want your homework to convey that you are competent, careful, professional? Or, do you want
to convey the image that you are careless, sloppy, and less than professional. For the rest of your
life you will be creating your brand: please think about what you are saying about yourself when
you do any work for someone else!
1. This problem consists of two separate problems using the price elasticity of demand
concept.
a. Suppose that you know that the market demand curve for a product is given by
the equation P = 100 – 2Q. Furthermore you know that initially 40 units are
demanded in this market when it is in equilibrium. Then, some event causes the
equilibrium to change so that only 35 units are demanded in this market. From
this information you are asked to calculate the price elasticity of demand using the
arc elasticity concept. Finally you are asked to identify whether demand is elastic,
unit elastic, or inelastic when quantity changes from 40 units to 35 units.
b. Suppose you know that the price elasticity of demand for good X has a value of 2.
Suppose that the price in the market is initially $10 and the quantity demanded is
100 units. If price in this market decreases by 10%, what will be the percentage
change in the quantity demanded given the above information?
Answer:
a. To answer this question you will want to find the price associated with the
quantity demanded of 40 units: P = 100 – 2Q = 100 – 2(40) = $20 per unit. You
will also want to find the price associated with the quantity demanded of 35 units:
2. 2
P = 100 – 2Q = 100 – 2(35) = $30. Now, we have a (Q1, P1) and a (Q2, P2) that
we can use in our arc elasticity formula for price elasticity of demand.
Price elasticity of demand = │[(Q2 – Q1)/Q2 + Q1)]/[(P2 – P1)/(P2 + P1)] │
Price elasticity of demand = │[(35 – 40)/(35 + 40)]/[(30 – 20)/(30 + 20)]
Price elasticity of demand = 1/3 and since this value is less than one we can
conclude that the demand curve is inelastic between
b. From the information we know that the price elasticity of demand =2; we also
know that the price elasticity of demand = the absolute value of [(% change in the
quantity demanded of good X)/(% change in the price of good X)]. Thus, 2 = the
absolute value of [(the % change in the quantity demanded of good X)/-10%]. Or,
the % change in the quantity demanded of good X is 20%. The quantity
demanded of good X will increase by 20% (the quantity demanded will now be
120 units) since the price of the good is inversely related to the quantity
demanded of the good.
2. Suppose the market demand and supply of widgets is given by the following equations:
Market Demand for Widgets: P = 100- Q
Market Supply of Widgets: P = 3Q + 20
where P is the price per unit and Q is the quantity demanded.
a. What is the equilibrium price and equilibrium quantity of widgets?
b. Describe what happened to the supply curve due to this change in production
costs. What is the equation for the new supply curve?
Suppose that production costs increase in the market for widgets such that at every
quantity the cost has now increased by $20.
c. Given the change in production costs described above, calculate the new
equilibrium price and equilibrium quantity in the market for widgets.
d. Intuitively what do you think happened to total expenditure in this market given
the increase in production costs? Explain your answer.
e. Calculate total expenditure in the market for widgets initially and total
expenditure in the market for widgets after the increase in production costs.
f. Does your answer in (e) support or confirm your answer in (d)?
g. Calculate the value of the price elasticity of demand between these two points of
equilibrium using the arc elasticity of demand formula.
Answer:
a. 100 – Q = 3Q + 20
4Q = 80
3. 3
Qe = 20
Pe = 100 – 20 = $80 per unit
b. The new supply curve will shift to the left but be parallel to the initial supply
curve: the two curves will have the same slope. Thus, the new supply curve will
be P = b’ + 3Q. We also know that the supply curve has shifted vertically up by
20 units since costs have risen at each quantity by $20. Thus, the new y-intercept
of the supply curve will be equal to the initial y-intercept plus 20: the new supply
curve will be P = 40 + 3Q.
c. 3Q = 40 = 100 – Q
4Q = 60
Qe’ = 15
Pe’ = 100 – 15 = $85 per unit
d. Total expenditure should decrease since the price is increasing in the elastic
region of the demand curve. We know we are in the elastic region of the demand
curve for any price greater than $50 since (50, $50) is the midpoint of the demand
curve.
e. Total expenditure initially = ($80 per unit)(20 units) = $1600
Total expenditure after change in production costs = ($85 per unit)(15 units) =
$1275
f. Yes, provided in (d) you predicted that total expenditure would fall.
g. Price Elasticity of Demand = │{[(Q2 – Q1)/(Q2 + Q1)]/[(P2 – P1)/(P2 + P1)]}│
Price Elasticity of Demand = {[(15 – 20)/35]/[(85 – 80)/165]} = [(1/7)/(5/165)] ≈
4.7
3. Suppose the market for doughnuts has five consumers and each consumer’s demand for
doughnuts can be described by the equation Pd = 5 – Qd where Pd is the price per
doughnut and Qd is the quantity of doughnuts demanded.
a. What is the market demand curve for doughnuts?
Suppose the market demand and market supply curves for coffee are given by the
following equations where Pc is the price per cup of coffee and Qc is the quantity of cups
of coffee:
Market Demand for Coffee: Pc = 5 – (1/20)Qc
Market Supply of Coffe: Pc = 1 + (1/60)Qc
b. Suppose you know that the price of doughnuts is fixed at $1 per doughnut. How
many doughnuts will be demanded in the market given this information?
c. What is the equilibrium price and equilibrium of coffee given the above
information?
4. 4
Suppose the quantity of coffee supplied at every price decreases by 20 units.
Furthermore you are told that the cross-price elasticity of doughnuts for coffee has a
value of -1.0.
d. What is the new supply equation for coffee given the above information?
e. Calculate the new equilibrium price and quantity in the coffee market.
f. Using the simple percentage change formula (the standard mathematical
definition of percentage change), what is the percentage change in the price of
coffee given your answers in (c) and (e)?
g. Using the simple percentage change formula (the standard mathematical
definition of percentage change), what is the percentage change in the quantity
demanded of coffee given your answer in (c) and (e)?
h. Calculate the price elasticity of demand for coffee using two different methods: a)
use the simple percentage change formula to get an estimate of the price elasticity
of demand; and b) use the arc elasticity formula to get a numerical value of the
price elasticity of demand.
i. Given your values in (g), is demand for coffee inelastic or elastic over this range
of prices? Explain your answer.
j. Calculate the percentage change in the quantity of doughnuts demanded given this
change in the supply of coffee. What will be the new quantity demanded of
doughnuts?
Answer:
a. Pd = 5 – (1/5)Qd
To see this think about drawing one consumer’s demand curve and then from that
graph think about what the y-intercept and the x-intercept would be if there were
five consumers with identical individual demand curves.
b. P = 5 – (1/5)Qd
1 = 5 – (1/5)Qd
Qd = 20 doughnuts
c. 5 – (1/20)Qc = 1 + (1/60)Qc
4 = (1/20)Qc + (1/60)Qc
4 = (1/15)Qc
Qc = 60
Pc = 1 + (1/60)(60) = $2 per cup of coffee
d. The supply curve will have the same slope but a different y-intercept than the
original supply curve. The new supply equation will be Pc = b + (1/60)Qc. You
need a point on the new supply curve so that you can use the coordinates of this
point to find the new supply curve’s y-intercept. So, originally when Pc = $2 per
cup, 60 units were supplied; now when Pc = $2 per cup, only 40 units are
5. 5
supplied-we can therefore use the coordinates (40, $2) in our equation in order to
find the y-intercept. Thus, 2 = b + (1/60)(40) or b = 4/3. The new supply equation
is Pc = 4/3 + (1/60)Qc.
e. 4/3 + (1/60)Qc = 5 – (1/20)Qc
(1/60 + 1/20)Qc = 5 – 4/3
(1/15)Qc = 11/3
Qc = 55 cups of coffee
Pc = 5 – (1/20)Qc = 5 – (1/20)(55) = $2.25 per cup of coffee
f. Percentage change in the price of coffee = [(2.25 – 2)/2](100%) = 12.5%
g. Percentage change in the quantity demanded of coffee = [(55 – 60)/60](100%) =
-8.3%
h.
a. Price elasticity of demand for coffee = │(% change in the quantity
demanded of coffee)/(% change in the price of coffee)│ = 8.3%/12.5% =
.664
b. Price elasticity of demand for coffee = │{[(Q2 – Q1)/(Q2 + Q1)]/[(P2 –
P1)/(P2 + P1)]}│= (5/115)/(.25/4.25) ≈.74
i. Demand is inelastic since the absolute value of the price elasticity of demand is
less than one.
j. Cross-price elasticity of doughnuts for coffee = ( % change in quantity demanded
of doughnuts)/(% change in the price of coffee)
-1.0 = (% change in quantity demanded of doughnuts)/12.5%
-12.5% = % change in the quantity demanded of doughnuts
Quantity of doughnuts initially = 20 doughnuts
Quantity of doughnuts now = (1 - .125)(20 doughnuts) = 17.5 doughnuts
4. Suppose you are told that the price elasticity of demand for soft drinks is 2.0; the cross
price elasticity of demand of soft drinks for iced tea is 1.5; the cross price elasticity of
demand of soft drinks for popcorn is -2.0; and the income elasticity of demand for soft
drinks is 1.2. Use this information to answer the following question.
a. Describe verbally the relationship between soft drinks and popcorn. In your
statement describe how you know these two goods have this relationship.
b. Describe verbally the relationship between soft drinks and iced tea. In your
statement describe how you know these two goods have this relationship.
c. Are soft drinks a normal or an inferior good given the above information? Explain
your answer fully.
Answer:
6. 6
a. Soft drinks and popcorn are complements since the cross-price elasticity of
demand between these two goods is negative. The negative sign tells us that when
the price of popcorn increases this price increase results in a decrease in the
quantity of soft drinks demanded. Two goods are complements if an increase
(decrease) in the price of one results in a decrease (increase) in the quantity
demanded of the other.
b. Soft drinks and iced tea are substitutes since the cross-price elasticity of demand
between these two goods is positive. The positive sign tells us that when the price
of iced tea increases this price increase results in an increase in the quantity of
soft drinks demanded. Two goods are substitutes if an increase (decrease) in the
price of one results in an increase (decrease) in the quantity demanded of the
other.
c. Soft drinks are a normal good in this example since the income elasticity of
demand is a positive number. When the price of soft drinks increases (decreases)
this price increase results in an increase (decrease) in the quantity demanded of
soft drinks. A good is a normal good if the quantity demanded of the good
increases when income increases.
5. In Xenia the typical consumer purchases 10 pounds of potatoes, 2 pounds of coffee, and 5
bags of apples. Use this market basket and the following data for this question. (Hint: you
will want to use a calculator or Excel for this question.)
Year Price of Potatoes Per
Pound
Price of Coffee Per
Pound
Price of a Bag of
Apples
Cost of Market
Basket
1 $1 $2 X $34
2 $1 Y $3 $27
3 $2 $2 $4 Z
4 $3 $3 A $61
a. Fill in the missing cells in the above table.
b. Given the above data construct the CPI index for Xenia using year 1 as your base
year and a 100 point scale. Carry out calculations to two places past the decimal.
Show how you got these values and then enter your answers in the following
table. (Hint: you will want to use a calculator on this problem.)
Year CPI with base year year 1
7. 7
c. Now, recalculate the CPI using year 4 as your base year. Put your new CPI index
numbers in the following table.
Year CPI with base year year 4
d. Joe lives and works in Xenia. He knows his nominal income per year over these
four years and wants to calculate his real income. He asks you to help him out.
Here is the data he provides you with for your analysis.
Year Nominal Income
1 $50,000
2 $50,000
3 $56,000
4 $60,000
He asks you to calculate his real income in year 1 dollars and his real income in
year 4 dollars. He wants you to put your findings in the following table and also
explain how you calculated his real income.
Year Nominal
Income
CPI:
BY
year 1
Real Income (BY:
Year 1)
CPI:
BY
year 4
Real Income (BY:
Year 4)
1 $50,000
2 $50,000
8. 8
3 $56,000
4 $60,000
e. Consulting your answer in (d), calculate the ratio of real income in year 1 to real
income in year 4 using year 1 as the base year. Then calculate the ratio of real
income in year 1 to real income in year 4 using year 4 as the base year. Compare
your answers.
f. Calculate the general rate of inflation per year for Xenia based on the CPI. Enter
your findings in the table below.
Year Rate of Inflation
1 ----
2
3
4
g. What does it mean if, when you calculate the annual rate of inflation, yet get a
negative rate of inflation? Is a negative rate of inflation a good or bad outcome?
Explain your answer fully.
h. Given your analysis has Joe’s nominal income kept up with the general rate of
change in prices in Xenia over these four years? Explain your answer. If your
answer is no, then calculate what his nominal income would need to equal in year
4 for his purchasing power in year 4 to be equal to his purchasing power in year 1.
Answer:
a. Cost of market basket in year 1 = (10)(1) + (2)(2) + (5)X = 34, this implies that X
= $4
Cost of market basket in year 2 = (10)(1) + (2)Y + (5)(3) = 27, this implies that Y
= $1
Cost of market basket in year 3 = (10)(2) + (2)(2) + (5)(4) = z, this implies that Z
= $44
Cost of market basket in year 4 = (10)(3) + (2)(3) + (5)A, this implies that A = $5
Year Price of Potatoes Per
Pound
Price of Coffee Per
Pound
Price of a Bag of
Apples
Cost of Market
Basket
1 $1 $2 $4 $34
9. 9
2 $1 $1 $3 $27
3 $2 $2 $4 $44
4 $3 $3 $5 $61
b. To find the CPI for year n, use the following formula:
CPI year n = [(Cost of market basket in year n)/(Cost of market basket in base
year)]*(scale factor)
Year CPI with base year year 1
1 100
2 79.41
3 129.41
4 179.41
c. There are two equivalent ways to do this calculation:
Year CPI with base year year 4
1 (100/179.41)(100) = 55.74 or (34/61)(100) = 55.74
2 (79.41/179.41)(100) = 44.26 or (27/61)(100) = 44.26
3 (129.41/179.41)(100) = 72.13 or (44/61)(100) = 72.13
4 (179.41/179.41)(100) = 100 or (61/61)(100) = 100
d.
Year Nominal
Income
CPI:
BY
year 1
Real Income (BY:
Year 1)
CPI:
BY
year 4
Real Income (BY:
Year 4)
1 $50,000 100 $50,000 55.74 $89,702
2 $50,000 79.41 $62,964 44.26 $112,969
3 $56,000 129.41 $43,272 72.13 $77,638
4 $60,000 179.41 $33,443 100 $60,000
10. 10
To find these answers use the formula:
Real income = [(Nominal Income)/(Inflation index)]*(Scale Factor)
Where the inflation index is the relevant CPI and the scale factor equals 100 since
the CPI is measured on a 100 point scale in this example.
e. With the base year Year 1:
(Real income in year 1)/(Real income in year 4) = $50,000/$33,443 = 1.5
With the base year Year 4:
(Real income in year 1)/(Real income in year 4) = $89,702/$60,000 = 1.5
The two ratios are the same: the choice of base year does not affect the ratio of
real prices.
f. Inflation rate = [(CPI current year – CPI previous year)/(CPI previous
year)](100%)
Year Rate of Inflation
1 ----
2 -20.59%
3 62.96%
4 38.64%
g. This tells you that the general price level is falling: that is, there is deflation in the
overall economy. A negative rate of inflation may be good or bad depending upon
your situation: for example, if you lend money to someone and fix the payment in
nominal terms and then there is deflation, you will receive the same nominal
amount of money but this money will have greater purchasing power. You will be
better off while the individual who borrowed the money from you and is now
paying it back will be worse off.
h. No, Joe’s nominal income has not kept up with the rate of inflation over these
four years: we can see that by comparing his real income in year 1 ($50,000) to
his real income in year 4 ($33,443) using year 1 as our base year. Joe’s nominal
income has less purchasing power in year 4 than in year 1.
For Joe to have the same purchasing power in year 4 as in year 1 he would need to
have real income of $50,000 in both years. So,
Real income = [(Nominal income)/(Inflation index)](scale factor)
50,000 = (Nominal income/179.41)(100)
Nominal income = $89,705
11. 11
To maintain the same purchasing power between year 1 and year 4, Joe’s nominal
income must increase from $50,000 in year 1 to $89,705 in year 4.
6. In this problem the goal is to practice drawing budget lines from a given set of
information and then to be able to generalize what you have learned from the exercise.
Each question is independent of the rest of the questions.
a. Mary has income of $120 and she spends all of this income on either shoes (price
of a pair of shoes is $40) or shirts (price of a shirt is $10). Draw Mary’s budget
line, BL1, on a graph with shoes on the horizontal axis and shirts on the vertical
axis. Write an equation for Mary’s BL1. Then, suppose that Mary’s income
doubles: on your graph draw Mary’s BL2 based on this information. Write an
equation for Mary’s BL2. In words describe any similarity between BL1 and
BL2: explain why this similarity exists.
b. Susan has $150 to spend on sandwiches (S) and milk (M). The price of
sandwiches is $5 per sandwich and the price of milk is $2 per carton. Given this
information draw Susan’s budget line, BL1, on a graph with sandwiches on the
horizontal axis and milk on the vertical axis. Suppose the price of sandwiches
increases to $10 while everything else is held constant. Draw this new budget
line, BL2, on your graph. Explain in words the effect of a change in the price of
sandwiches on this budget line. Write equations for both BL1 and BL2.
c. You are given the following graph of Jorge’s budget lines, BL1 and BL2. You
know that Jorge’s income is $500 per day and that he spends all of his income on
either airplane tickets (T) or food (F). From the graph, calculate the price of food
as well as the price of an airplane ticket for BL1. Then, calculate the price of food
as well as the price of an airplane ticket for BL2.
12. 12
Answers:
a. BL1: Y = 12 – 4X
BL2: Y = 24 – 4X
The two budget lines have the same slope: the slope of the budget line is (-Px/Py) and
since neither the price of shoes (Px) or the price of shirts (Py) have changed, the ratio
of these two prices is unchanged. The two budget lines are parallel and this represents
a change in income.
b. When sandwiches get more expensive this results in the budget line pivoting in
along the horizontal axis: for a given amount of income, an increase in the price of
sandwiches implies that the person cannot consume as many sandwiches as they
could initially. BL2 pivots in toward the origin.
BL1: M = 75 – 2.5S
BL2: M = 75 – 5S
13. 13
c. BL1: 500 = PtT + PfF
500 = PtT assuming that F = 0
500 = 5Pt
Pt = $100 per ticket
500 = PfF assuming that T = 0
Pf = $5 per unit of food
BL2: 500 = Pt’T + Pf’F
Since the y-intercept has not changed we know that Pt = Pt’ = $100 per ticket. To find
Pf’, we know 500 = Pf’F and F = 50 when T = 0. So, Pf’ = $10 per unit of food
7. Suppose you are told that Mary’s utility function is given by the equation U = 2XY
where U is the level of utility measured in utils and X and Y refer to good X and good Y
respectively. You are also told that the marginal utility of good X can be expressed as
MUx = 2Y; and the marginal utility of good Y can be expressed as MUy = 2X.
a. In a graph draw three indifference curves illustrating Mary’s utility from
consuming different bundles of X and Y: draw an IC1 representing utility of 20
(U = 20); and IC2 representing utility of 40; and an IC3 representing utility of 80.
Make sure for each IC you identify at least three distinct points that lie on that IC.
You will find it helpful to complete a table like the following for each IC. (In the
14. 14
table I have provided one possible solution and proposed two other numbers to
try.)
U = 2XY = 20
X Y
1 10
2 ?
? 5
b. Suppose you are told that Mary maximizes her utility at 40 utils when she selects
5 units of good X and 4 units of good Y when the price of good X is $4/unit of
good X and the price of good Y is $5/unit of good Y. Prove that Mary is
maximizing her utility given the information provided. Verbally as well as
mathematically identify what must be true for Mary to be maximizing her utility.
c. Given the above information, calculate Mary’s income. Show how you found
your answer.
d. Draw a graph illustrating Mary’s IC and her budget line as well as her utility
maximizing bundle given the above information.
Answer:
a. Here are some possible (X, Y) combinations that yield utility of 20, 40, and 80
based on U = 2XY.
U = 2XY = 20
X Y
U = 2XY = 40
X Y
U = 2XY = 80
X Y
1 10 1 20 1 40
2 5 2 10 2 20
4 2.5 4 5 10 4
5 2 10 2 20 2
10 1 20 1 40 1
15. 15
b. In order to maximize utility it must be the case that the addition to total utility from
good X of spending one more dollar on good X must be equal to the addition to total
utility from good Y of spending one more dollar on good Y. If this condition is not
met, than the individual could rearrange their spending and increase their total utility.
Mathematically this implies that (MYx/Px) = (MUy/Py). We can rearrange this
equation to (MUx/MUy) = (Px/Py). Or, in absolute value terms, the slope of the
budget line (-Px/Py) is equal to the slope of the indifference curve (MUx/MUy) when
the individual maximizes his utility. This is our definition of the utility maximization
rule for a consumer.
So, now let’s look at plugging in the information we’ve been given:
MUx = 2Y
MUy = 2X
Px = $4/unit of good X
Py = $5/unit of good Y
So, 2Y/2X = 4/5 or Y = (4/5)X
But, we also know that the combination (X, Y) = (5, 4) maximizes Mary’s utility. So,
16. 16
4 = (4/5)(5) is a true statement.
c. I = PxX + PyY
I = ($4/unit of good X)(5 units of good X) + ($5/unit of good Y)(4 units of good Y)
I = $40
d.
8. Use the graph below to answer this question.
17. 17
You are told that Wei’s income is $100 and he spends all of this income on either good X
or good Y. BL1 is his initial budget line.
a. Given BL1 and the above information, what is the price of good X and the price of
good Y?
b. The graph also depicts Wei’s BL2. What is a likely explanation for why Wei’s budget
line changed from BL1 to BL2? Be specific in your answer.
c. Suppose you are told that Wei consumes 3 units of good X and 4 units of good Y when
he maximizes his utility subject to his income and the prices of good X and good Y he
faces with BL1. When Wei’s budget line is BL2, he maximizes his utility by consuming
8 units of good X. Given this information, how many units of good Y does he consume if
he faces BL2 and he is maximizing his utility?
d. If we constrain Wei to have the same utility as he had when he faced BL1, but assume
he is now facing the new prices of BL2, will this new BL (in class this was “BL3”)
relative to BL2 reflect an increase or a decrease in income? Explain your answer.
e. Suppose you are told that on BL3 Wei maximizes his utility when he consumes the
bundle (X, Y) = (5, 2). From the given information calculate Wei’s income and
substitution effect. (Hint: you may find it helpful to draw a graph before answering this
question.)
f. Given the above information, what is Wei’s adjusted income for BL3?
Answer:
a. If Wei spends all of his income on good X, he can afford 5 units. So, Income/(5 units)
= $100/(5 units of good X) = $20 per unit of good X. The price of good X is $20 per unit
of good X. Similarly, if Wei spends all of his income on good Y he can afford 10 units:
18. 18
so Income/(10 units of good Y) = $100/(10 units of good Y) = $10 per unit of good Y.
The price of good Y is $10 per unit of good Y.
b. BL1 and BL2 have different slopes but the same y-intercept. This implies that the price
of good X has changed while income and the price of good Y have remained constant.
The price of good X has decreased since Wei can now afford more of good X: the price
of good X is now $10 per unit of good X.
c. We can write the equation for Wei’s BL2 as Y = 10 – X. If X = 8 units, then Wei must
be consuming Y = 10 – 8 = 2 units of good Y.
d. When the price of good X decreases Wei’s budget line changes from BL1 to BL2:
although Wei’s nominal income has not changed his real purchasing power has increased
when the price of good X decreases. Thus, when we construct BL3 this must reflect a
decrease in Wei’s income (an imagined decrease) from that represented in BL2.
e. The substitution effect is 2 units of good X and the income effect is 3 units of good X.
The graph below illustrates this.
f. On BL3 we know the price of good X is $10 and the price of good Y is $10. Wei
maximizes his utility by consuming the bundle (X, Y) = (5, 2) and we can calculate that
he would need income = ($10 per unit of good X)(5 units of good X) + ($10 per unit of
good Y)(2 units of good Y) = $70.
9. Mario’s Widgets produces widgets and his production function for these widgets is given
by the equation:
W = 2K.5L.5
19. 19
where W is widgets, K is capital, and L is labor. Mario’s Widgets uses only capital and
labor to produce the widgets. In the short run, Mario’s Widgets capital is equal to 4 units.
Mario’s Widgets pays $10 per unit of capital and $20 per unit of labor. Use this
information to answer this set of questions. Hint: you will find it helpful to use Excel to
do this set of questions.
a. In the short run, what is the fixed cost associated with widget production?
b. For the short run, write an equation for Mario’s Widgets variable cost of widget
production.
c. For the short run, write an equation for Mario’s Widgets total cost of production.
d. Complete the following table given the above information. All calculations should be
rounded to two places past the decimal. (Hint: this is where you will want to start using
Excel.)
L K W MPL VC FC TC AVC AFC ATC MC
0
1
4
9
16
25
36
49
64
81
100
Answer:
a. FC = PkK = ($10 per unit of K)(4 units of K) = $40
b. VC = PlL = ($20 per unit of L)(units of L) = 20L
c. TC = FC + VC = 40 + 20L
d.
L K W MPL VC FC TC AVC AFC ATC MC
20. 20
0 4 0 0 40 40
1 4 4 4.00 20 40 60 5 10.00 15.00 5
4 4 8 1.33 80 40 120 10 5.00 15.00 15
9 4 12 0.80 180 40 220 15 3.33 18.33 25
16 4 16 0.57 320 40 360 20 2.50 22.50 35
25 4 20 0.44 500 40 540 25 2.00 27.00 45
36 4 24 0.36 720 40 760 30 1.67 31.67 55
49 4 28 0.31 980 40 1020 35 1.43 36.43 65
64 4 32 0.27 1280 40 1320 40 1.25 41.25 75
81 4 36 0.24 1620 40 1660 45 1.11 46.11 85
100 4 40 0.21 2000 40 2040 50 1.00 51.00 95
10. Consider a production function for a firm:
Q = 2K1/2L1/2
where Q is output, K is capital, and L is labor. Suppose initially K is equal to 25 units and
L is equal to 16 units. You also know that the price of K, Pk, is $10 per unit of K and the
price of L, Pl, is $4 per unit of L.
a. Given the above information, what is the value of output?
b. What is the total cost of producing the output you calculated in (a)?
c. What is the average total cost of producing this level of output?
d. Suppose the amount of labor increases to 32 units and the amount of capital increases
to 50 units. Given this information, what level of output can the firm now produce? (Hint:
you can do this without a calculator – and, then you can check your answer with a
calculator!)
e. Given the information in (d), what is the total cost for the firm of producing this level
of output?
f. Given the information in (d) and (f), calculate the firm’s average total cost of producing
this new level of output.
g. Given your answer to the above set of questions, what can you conclude about returns
to scale for this firm?
21. 21
Answer:
a. Q = 2K1/2L1/2
Q = 2(25)1/2(16)1/2
Q = (2)(5)(4)
Q = 40 units of output
b. TC = PlL + PkK
TC = ($4 per unit of L)(16 units of L) + ($10 per unit of K)(25 units of K)
TC = $314
c. ATC = TC/Q
ATC = $314/(40 units of output)
ATC = $7.85 per unit of output
d. Q’ = 2K1/2L1/2
Q’ = 2(50)1/2(32)1/2
Q’ = 2(2)1/2(25)1/2 (2)1/2(16)1/2
Q’ = 2(2)(5)(4)
Q’ = 80 units of output
e. TC’ = PlL + PkK
TC’ = ($4 per unit of L)(32 units of L) + ($10 per unit of K)(50 units of K)
TC’ = $128 + $500
TC’ = $628
f. ATC’ = TC’/Q’
ATC’ = $628/(80 units of output)
ATC’ = $7.85 per unit of output
g. When the amount of labor and capital is increased proportionately (in this example
these inputs were doubled) output doubles, total cost doubles, and average total cost
remains constant. This implies this firm has constant returns to scale.
11. Consider a production function for a firm:
Q = 2KL1/2
where Q is output, K is capital, and L is labor. Suppose initially K is equal to 25 units and
L is equal to 16 units. You also know that the price of K, Pk, is $10 per unit of K and the
price of L, Pl, is $4 per unit of L.
a. Given the above information, what is the value of output?
b. What is the total cost of producing the output you calculated in (a)?
c. What is the average total cost of producing this level of output? Round your answer to
the nearest hundredth.
22. 22
d. Suppose the amount of labor increases to 32 units and the amount of capital increases
to 50 units. Given this information, what level of output can the firm now produce? (Hint:
you can do this without a calculator – and, then you can check your answer with a
calculator!)
e. Given the information in (d), what is the total cost for the firm of producing this level
of output?
f. Given the information in (d) and (f), calculate the firm’s average total cost of producing
this new level of output.
g. Given your answer to the above set of questions, what can you conclude about returns
to scale for this firm over the range of output you have considered?
Answer:
a. Q = 2KL1/2
Q = 2(25)(16)1/2
Q = 50(4)
Q = 200 units of output
b. TC = PlL + PkK
TC = ($4 per unit of L)(16 units of L) + ($10 per unit of K)(25 units of K)
TC = $314
c. ATC = TC/Q
ATC = $314/(200 units of output)
ATC = $1.57 per unit of output
d. Q’ = 2KL1/2
Q’ = 2(50)(32)1/2
Q’ = 100(4)(2)1/2
Q’ = 100(4)(1.42)
Q’ = 568 units of output
e. TC’ = PlL + PkK
TC’ = ($4 per unit of L)(32 units of L) + ($10 per unit of K)(50 units of K)
TC’ = $628
f. ATC’ = TC’/Q’
ATC’ = $628/(568 units of output)
ATC’ = $1.11 per unit of output
g. When the amount of L and K is increased proportionately (in this example, these
inputs were doubled) output increased by more than double (it increased by a factor
greater than 2), total cost doubled (it increased by a factor of 2), and average total cost
declined. This implies that as output expanded from 200 units to 568 units, the firm’s cost
per unit declined: this firm has increasing returns to scale over this range of output.