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Mathematics for Economists Assignment 2

Mathematics for Economists Assignment 2
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Type Essay
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Description/Paper Instructions

Mathematics for Economists Assignment 2

Problem 1

Federal ethanol mandates require billions of gallons of ethanol be produced, purchased, and mixed into gasoline as part of an effort to reduce fossil fuel use and increase energy independence in the U.S. Suppose these ethanol mandates are removed from the market.

  • What would you expect to happen to the equilibrium price and quantity in the market

for ethanol?

  • What would you expect to happen to the equilibrium price and quantity in the market

for corn, which is the predominant source of ethanol production in the U.S.?

  • If you are a corn producer, what steps might you take as a result of the removal of the

ethanol mandates?

  • Consider C&H, the Nation’s Largest Sugar Manufacturer. Sugar competes directly with

high fructose corn syrup, a product made from corn. What steps might C&H take as a

result of the removal of the ethanol mandates?

Problem 2

Saxum Vineyard, in Paso Robles, CA, is one of the more than 8,000 wineries in the United States.  While Saxum produces a number of different kinds of wine, they focus their production on Syrah (also known as Shiraz).  Saxum sells their wines all over the United States.  Suppose you manage a vineyard like Saxum and want to determine how much you should charge for your Syrah.  Suppose the market demand function for Syrah is as follows.

QD = 200 – 38.18PO + 8.35PS – 2Pc + 10Inc + .8TS + .5M21

Where QD is monthly demand for bottle of Syrah (in millions), PO is the price of Syrah in the market, PS is the average price of substitute bottles of wine (other varieties), PC is the average price of a pound of cheese and is used to gauge the price of complimentary goods, Inc is average US income (in thousands), TS is the number of wine trade shows and competitions each year which firms can attend to market their wines, and M21 is the number (in millions) of millennials over the age of 21.

This last variable is included to capture a change in consumer preferences; millennials are drinking wine at a much higher rate than previous generations.

The market for Syrah also has supply, produced by wineries similar to Saxum Vineyard and your winery, which can be stated as follows.

QS = -100 + 22.93PO – 5PPI – 10PS + 8Temp + 1Sup

Where QS is monthly supply of bottles of Syrah (in millions), PO is the price of Syrah in the market, PPI is the Producer Price Index (an index used to gauge changes in the costs of production in the US), PS is the price of substitute wines which could easily be produced instead of Syrah, Temp is the expected temperature during the harvest season for grapes, and Sup is the number of wineries supply Syrah in the market (in thousands).

Using the market supply and demand functions for Syrah given, fill in the template provided with the coefficients for each function.  Using the information below, fill in the values for each of the variables except Price of Syrah.  Then, set up your QD and QS to automatically calculate as you adjust the values for each variable.

Demand:

-Price of Substitutes: $18

-Price of Cheese: $15

-Income: $53,000

-Trade Shows/Competitions: $3

-Millennials = 43 million

Supply

-PPI: 111

-Price of Substitutes: $18

-Temperature: 60

-Number of Suppliers: 8,000

Now that you’ve set up your demand and supply functions, answer the following questions.

  1. a) When the price of Syrah increases by $1, what is the effect on quantity demanded and quantity supplied?
  2. b) How much does a $1 decrease in the price of substitute bottles of wine shift the demand and supply curves?
  3. c) Suppose the price of Syrah is currently $22 per bottle. How many bottles will be demanded and supplied monthly?
  4. d) If the market price of Syrah falls to $16 per bottle, how many bottles will be demanded and supplied monthly?
  5. e) Trying prices in $1 increments between $16 and $22, at what price and quantity does the market equilibrium occur?
  6. f) Suppose the costs of production increase to 123.222. If the price of wine stays at $20 per bottle, what will be supplied in the market and will this create a shortage?
  7. g) With the increase in production costs to 123.222, at what price will the market be in equilibrium again? What will be demanded and supplied at this price?

Mathematics for Economists Assignment 2

MARKET DEMAND MARKET SUPPLY
Coefficients Values Coefficients Values
Intercept Intercept
Price of Syrah Price of Syrah
Price of Substitutes PPI
Price of Cheese Price of Substitutes
Income Temperature
Trade Shows Suppliers
Millennials
QD=  QS=

 

RUBRIC

QUALITY OF RESPONSE NO RESPONSE POOR / UNSATISFACTORY SATISFACTORY GOOD EXCELLENT
Content (worth a maximum of 50% of the total points) Zero points:  Student failed to submit the final paper. 20 points out of 50:  The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. 30 points out of 50:  The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately.  Elements of the required response may also be lacking. 40 points out of 50:  The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples.  The answer is complete. 50 points:  The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples.  No aspects of the required answer are missing.
Use of Sources (worth a maximum of 20% of the total points). Zero points:  Student failed to include citations and/or references. Or the student failed to submit a final paper. 5 out 20 points:  Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. 10 out 20 points:  References to scholarly sources are occasionally given; many statements seem unsubstantiated.  Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. 15 out 20 points:  Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented.  APA 6th Edition is used with only a few minor errors.  There are minor errors in reference and/or citations. And/or there is some use of questionable sources. 20 points:  Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented.  APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment.
Grammar (worth maximum of 20% of total points) Zero points:  Student failed to submit the final paper. 5 points out of 20:  The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors  10 points out 20:  The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors 15 points out of 20:  The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage. 20 points:  The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free.
Structure of the Paper (worth 10% of total points) Zero points:  Student failed to submit the final paper. 3 points out of 10: Student needs to develop better formatting skills. The paper omits significant structural elements required for and APA 6th edition paper. Formatting of the paper has major flaws. The paper does not conform to APA 6th edition requirements whatsoever. 5 points out of 10: Appearance of final paper demonstrates the student’s limited ability to format the paper. There are significant errors in formatting and/or the total omission of major components of an APA 6th edition paper. They can include the omission of the cover page, abstract, and page numbers. Additionally the page has major formatting issues with spacing or paragraph formation. Font size might not conform to size requirements.  The student also significantly writes too large or too short of and paper 7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment. 10 points: Student provides a high-caliber, formatted paper. This includes an APA 6th edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper.
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Mathematics for Economists Assignment 2

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