Case Study: Chapter 2
Please address the following case study relating to supply and demand in a fictitious national market for chicken eggs. This case study relates to Chapter 2 of the textbook and the lecture on Demand, Supply, and Market Equilibrium.
Note: The lecture is decomposed into four sections that correspond to a section of the case study and related pages of the book. The lecture section and book pages are indicated with each section of the case study.
Please submit your work as a single Word document. When I request calculations, you can write them by hand and incorporate a photograph into the document or you can type up the calculations in the document. Similarly, you can create any tables by hand, in Word, or other ways, but your tables should be clear. The document should be approximately 2-4 pages (counting each side of the paper as a page) in length. Please indicate in some way which part of the document responds to each question. The assignment will be graded based on correctness, effort, and presentation.
Section 1. Demand: Pages 38-52
Your analysts present you with the general demand function:
???????? = 7.6 0.5???? 1.2???? + 1.5???????????????????????????? + 0.1???????????????????????????????????? + 0.2???????? + 2????
where ???????? is the quantity demanded, ???? is the price, ???? is average consumer income (in $10,000s), ???????????????????????????? is the price of breakfast cereal (which here is considered a substitute for eggs), ???????????????????????????????????? is the Egg Health Index (a measure of consumer perception of the healthiness of eggs, ???????? is the expected price of eggs next month, and ???? is the number of hundred millions of consumers in the market.
Currently, average consumer income is $50,000 (so 5 $10,000s), the price of breakfast cereal is $3, the Egg Health Index is 60, consumers expect the price of eggs to be $2.50 next month, and there are 300,000,000 consumers (so 3 hundred millions).
a. Use these values of the factors affecting demand to find the direct demand function.
b. Create a demand schedule by finding the quantity demanded when the price is $1.00, $1.50, $2.00, $2.50, $3.00, and $3.50.
c. Use algebra to convert the direct demand function into an inverse demand function (show a line or two of work).
d. Graph the inverse demand function (you can sketch freehand or use Excel but be sure to label the axes and either the scale or a couple points on the curve).
Section 2. Supply: Pages 52-61
Your analysts present you with the general supply function:
???????? = 4.5 + 1.6???? 2???????????????????????? 1???????????????????????????? + 0.03???????????????????????????????????????????? 0.5???????? + 0.4????
where ???????? is quantity supplied, ???? is the price, ???????????????????????? is the price of grain (an important feedstuff for chicken), ???????????????????????????? is the price of chicken breast (which here is treated as a substitute use of chickens), ???????????????????????????????????????????? is the annual rate at which your chickens lay their eggs (which is treated as technology), ???????? is the expected price of eggs next month, and ???? is the number of major firms in the egg industry.
Currently, the price of grain is $4, the price of chicken breast is $3, your chickens lay 300 eggs per year, you expect the price of eggs next month to be $3, and there are 18 major firms in the egg industry.
a. Use these values of the factors affecting supply to find the direct supply function.
b. Create a supply schedule by finding the quantity supplied when the price is $1.00, $1.50, $2.00, $2.50, $3.00, and $3.50.
c. Use algebra to convert the direct supply function into an inverse supply function (show a line or two of work).
d. Graph the inverse supply function (you can sketch freehand or use Excel but be sure to label the axes and either the scale or a couple points on the curve).
Section 3. Market Equilibrium and the Value of Market Exchange: Pages 61-67
a. Use the direct demand and supply functions for eggs that you found in your answer to Module 1 to solve for the equilibrium price and quantity of eggs sold. Then put the demand and supply schedules together and show that this is the equilibrium. Finally put both the demand curve and the supply curve on the same graph to show the equilibrium graphically.
b. Use your graph of the market equilibrium to find the vertices of the triangle representing consumer surplus. Calculate the value of consumer surplus in this market.
c. Use your graph of the market equilibrium to find the vertices of the triangle representing Producer surplus. Calculate the value of Producer surplus in this market.
Section 4. Changes in Market Equilibrium: Pages 68-76
Qualitative analysis
a. A study in the New England Journal of Medicine is being published that is very critical of the cholesterol associated with eggs. You believe this will negatively impact consumer preferences for eggs (e.g. it will decrease the Egg Health Index). What effect do you expect this to have on the equilibrium price and quantity of eggs?
b. Now assume instead that it is the end of Winter and both consumers and firms expect that prices will rise next month due to Spring holidays such as Easter. Though both consumers and firms expect prices to rise, they may believe prices will rise by different amounts. What effect do you expect this to have on the equilibrium price and quantity of eggs?
Quantitative analysis
a. Industry-wide modifications to chicken feeding practices have been very successful at increasing egg production and the average number of eggs laid per chicken jumps from 300 to 370. What are the new equilibrium price and quantity?
b. Now assume instead that favorable growing conditions in the Midwest drive down the price of grains which are used to feed chickens and also in breakfast cereal. The price of grain used to feed chickens falls from $4 to $3.55 and the price of cereal falls from $3 to $2.20. What are the new equilibrium price and quantity?