The demand function for corn takes the form: Qdcorn = 5 – 2Pcorn + 4Ppotatoes – 0.25Pbutter +0.0003M (1) Where Qdcorn

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The demand function for corn takes the form:
Qdcorn = 5 – 2Pcorn + 4Ppotatoes – 0.25Pbutter +0.0003M
(1)
Where Qdcorn is the amount of corn demanded per year in billions of
bushels; Pcorn is the price of corn per bushel; Ppotatoes is the
price of potatoes; Pbutter is the price of butter; and M is
consumers’ average annual income.
Suppose that potatoes cost $0.50 per kg; butter costs $4 per kg,
and income is $30,000
a) What is the implied demand function?
b) At what price of corn will consumers demand 8 billion bushels
per year?
c) How does your answer change if the price of potatoes rises from
$0.50 to $1 per kg?
The supply function for corn takes the form:
Qscorn = 9 + 5Pcorn - 4Pfuel – 1.25Psoybeans
(2)
Where Qscorn is the amount of corn supplied, Pfuel is the price of
fuel, and Psoybeans is the price of soybeans.
d) Assuming that Pfuel = $1.25 per litre and Psoybeans = $8 a
bushel, what is the implied supply function?
e) Write the inverse demand and the inverse supply curve for
corn.
Use the demand and supply functions from Problem 1;
a) Solve for the equilibrium price and quantity for corn and
represent the market situation graphically.
b) Find the total revenue, the total cost, the profit, and the
consumer surplus. What do you observe?
c) Suppose both the price of fuel and income rise, what is the
impact on the market? Who wins and who loses? Why?
d) Suppose the price of fuel increases to $1.50 and income
increases to $40,000, what is impact on the market equilibrium? Who
should be happy or sad? Why?
e) Calculate the point elasticity of demand when the price of corn
is $5 and interpret the result.
f) Calculate the arc elasticity when the price of corn changes from
$3 to $5, and from $3 to $2. Interpret the results.
g) Calculate all other relevant elasticities assuming a decrease in
each variable by 50% from its current level and interpret the
results