Mathematics for Economists Assignment 2
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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.
- a) When the price of Syrah increases by $1, what is the effect on quantity demanded and quantity supplied?
- b) How much does a $1 decrease in the price of substitute bottles of wine shift the demand and supply curves?
- c) Suppose the price of Syrah is currently $22 per bottle. How many bottles will be demanded and supplied monthly?
- d) If the market price of Syrah falls to $16 per bottle, how many bottles will be demanded and supplied monthly?
- e) Trying prices in $1 increments between $16 and $22, at what price and quantity does the market equilibrium occur?
- 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?
- 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=
Mathematics for Economists Assignment 2
RUBRIC
Excellent Quality
95-100%
Introduction 45-41 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Literature Support
91-84 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Methodology
58-53 points
Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.
Average Score
50-85%
40-38 points
More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.
83-76 points
Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.
52-49 points
Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.
Poor Quality
0-45%
37-1 points
The background and/or significance are missing. No search history information is provided.
75-1 points
Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.
48-1 points
There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met
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Mathematics for Economists Assignment 2