ECON 300 C AU 2020: Quiz 1
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35 minutes maximum for 2 question(s) for a total of 25 points. There are 2 page(s). You will have 5
minutes after the quiz concludes where you must submit your scanned quiz on Canvas, or through email.
To ask a question, send me a private message in chat and I will respond so as to not disturb other students.
If clarifications or corrections need to be made, they will be on a word document on my shared screen.
Write your answer clearly and show all of your work.
Problem 1.
The market for tomatoes is perfectly competitive with demand and supply given by the functions
log(Q) =
2
1
log(Y ) − log(P )
2
3
(Demand)
log(Q) =
1
1
log(P ) − log(R)
3
2
(Supply)
where Y > 0 is the income level of consumers and R > 0 is the amount spent on rent for the land needed
to grow tomatoes. The logarithms are natural logarithms, i.e. base e.
a. (8 points.) Find the equilibrium price P ∗ and quantity Q∗ in terms of Y and R. Make sure your
final answer does not include a logarithm.
b. (4 points.)For the following questions on the equilibrium, use partial derivatives to support your answers. If you could not solve for the equilibrium, use the supply and demand function and graphs to
support your answers.
Hint: For both, you may find a partial derivative that depends on both Y and R so it is not constant
like most of the exercises you have done. However, do keep in mind that R and Y are always positive
so use this to make your conclusions.
– Using the equilibrium from part a, after an increase in Y does equilibrium price increase or
decrease? Does equilibrium quantity increase or decrease?
– Using the equilibrium from part a, after an increase in R does equilibrium price increase or
decrease? Does equilibrium quantity increase or decrease?
For parts c and d, suppose that consumers own the land and rent it to firms. Assume their only source of
income is the rent collected from renting out their land so Y = R.
c. (3 points.) Substitute Y = R into the supply and demand functions. Just by looking at these functions with R in place of Y , how does an increase in R affect the supply and demand curves? Hint:
think of shifts; you may find drawing a simple graph helpful.
ECON 300 C AU 2020: Quiz 1
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d. (2 points.) Substitute Y = R into the equilibrium price and quantity from part a if you found it. If
you have not found it, solve for equilibrium price and quantity with R in place of Y .
If there is an increase in R, does equilibrium price increase or decrease? Does equilibrium quantity
increase or decrease?
Problem 2.
Consider the demand function for some good
Q = D(P, Y ) =
Y
.
3P
a. (2 points.) Show that this demand is price unit-elastic/unitary for all P and Y .
b. (2 points.) Calculate the income elasticity of demand. Be sure to simplify it all the way.
c. (2 point.) After a 1% decrease in the consumer’s income, how much does quantity demanded change
in percentage terms?
d. (2 points.) Is this good a normal good or inferior good?