Econ 201: Assignment #1
Fall 2022
Josh Boitnott
Instructions:
• Show your work if you want partial marks. Wrong answers with no work shown
will receive a mark of 0.
• I encourage you to work with others; however, you must submit your own version
of the assignment. Further to that, I request that you not publicly post solutions
for others to copy.
• The answers need to be submitted through Crowdmark and are due by Oct. 14th
at 11:59 pm. You will need to submit/upload your solutions through Crowdmark
with the link initial link to the submission sent via e-mail by Crowdmark.
• Please make sure to submit your answers in the co
ect position; we should be
able to read your answers without having to rotate them. Finally, when capturing
the image of your work, please make sure to have sufficient lighting and clarity of
the images.
1. (14 marks) Suppose the market for laser pointers consists of 2 types of people: profes-
sors and cat lovers. The professors have an individual demand of qProf = 13−
1
5
P and
the cat lovers have an individual demand of qCat = 20−
1
2
P .
(a) (4 marks) If there are 30 consumers with a demand of qProf and 8 consumers with
a demand of qCat, then what is the (inverse) market demand curve P (Q
D) (for all
38 people)? Illustrate it in a graph.
(b) (4 marks) Suppose the (inverse) market supply curve is P =
1
15
QS, what is the
market equili
ium outcome? (Hint: Both groups buy laser pointers and you
quantity should be somewhere between 250 and 400.) What is the consumer and
producer surplus in this case? (Reminder: Your consumer surplus will be ugly
to calculate since the demand curve is discontinuous).
(c) (6 marks) The government has become concerned about long term environmental
harm from improper disposal of the laser pointers. To alleviate some of the
urden, the government decides to impose a $7.50 excise tax on each laser pointe
sold. What is the new equili
ium? How much has the government raised in tax
evenue? How big is the dead weight loss? What is the tax incidence for the
consumers?
2. (18 marks) Suppose you are told that a consumer has the following utility function:
U(qx, qy) = e
(qy) ×
√
2qx − 1. Their income is Y , the price of good x is Px, and the
price of good y is Py.
(a) (3 marks) Show that the Marginal Rate of Substitution is the same for U(qx, qy)
as the positive monotonic transformation W = ln(U(qx, qy)). What type of utility
function is W (qx, qy)?
(b) (4 marks) Find q∗x, the demand for good x, and q
∗
y , the demand for good y. Hint :
e sure to include information about where the function works.
(c) (7 marks) Suppose you are given Px = $2 and Py = $18, provide a sketch of of
the income-consumption curve for Y = {20, 25, 30, 35, 40, 45}. Be sure to label
the points for each income and clearly indicate what is happening (i.e. values of
qx and qy co
esponding to each Y ).
(d) (4 marks) Find the cross price elasticity of demand for q∗x and q
∗
y. Does this tell
you anything about the relationship between the two goods?
3. (17 marks) This question is designed to examine how we can utilize our basic theory
without having an explicit indifference curve. Suppose Lia has an income of Y =
$500 and only consumes two good: memory sticks (to store free economics papers she
downloads from the li
ary) and hardcover novels (which she refuses to check out from
the li
ary). Furthermore, let the price of memory sticks be PS = $25 and the price of
hardcover novels be PN = $20.
(a) (5 marks) Create a graph of Lia’s behaviour with the assumption that her utility
is consistent with our normal assumptions (e.g. ∂U/∂qi > 0 and ∂
2U/∂q2i < 0 fo
i = {S,N}) assuming Lia’s preferences would result in her purchasing 10 novels.
What is the budget line? What is her real income in terms of memory sticks?
(b) (4 marks) Before Lia makes any purchases, the place she purchases books from
offers the following deal: any additional books purchased after the first 10 will
get a 25% discount. Use a revealed preferences argument to explain how we know
Lia will be better off. Would this be true for all utility functions? Explain why
or why not.
(c) (5 marks) Another seller of books makes the following offer: get a 25% discount on
orders of the first 10 books. Create a graph of the new budget constraint. Explain
how this would adjust Lia’s bundle with a reference to income and substitution
effects (you do not have to give a specific bundle). Assume that both goods are
normal.
(d) (3 marks) Could Lia be indifferent between the discount option in part (b) and
(c)? Explain why or why not.
4. (15 marks) Read the Chapter “Homer Economicus or Homer Sapiens?” by Jodi Beggs1.
The chapter focuses on the idea of behavioural economics in the TV show The Simp-
sons. This question asks you to consider how our simple model of behaviour (i.e.
U(qx, qy) subject to Y = Pxqx + Pyqy) compares with both the world of Homer Simp-
son and the real world. To answer this question and receive full marks, your response
should be approximately two paragraphs (and no more than three). The main question
to answer is “How does our simple model fail to capture some important behavioural
aspects demonstrated in the television show the simpsons?”
The focus should address the following three ideas/concepts: i) how does the assump-
tion the people live one period limit the model, ii) how does our assumption that
utility is ordinal limit modeling issues of altruism, and iii) how does our model neglect
elements such as keeping up with the Joneses2?
Hint : even though your answer needs to be written in sentences, it might be
helpful to think about utility as Ui(A, qi, qj) = W (A, qi) + V (qj) where A is all
other goods than q, qi is consumption choice of good q for person i, and qj is:
consumption choice of good q in the future, consumption choice of good q by
others, or average consumption choice of good q.
1This has been added to the Homepage in Canvas
2Thorstein Veblen discussed the issues of “keeping up with the Joneses” as a way to describe people
maintaining a level of visible consumption that was similar to or at least as much as their neighbours. This
is where the title for the TV show Keeping Up with the Kardashians comes from, though not sure which
individuals are their neighbours.