Supply and Demand Question

ECON 281 Assignment 1 – Determine if the following statements
Subject: Economics    / General Economics
Assignment 1 – ECON 281 B1
office at the 8th floor of Tory or hand it in in class. This is an individual assignment, group
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PART I: True, False, Uncertain
Determine if the following statements are true, false or uncertain. Argue with math, graphs,
definitions and logical reasoning. Points will only be awarded to your explanation. Question 1.[10pt] Assumptions 2 and 3 about rationality (Transitivity and Non-Satiation)
guarantee that indifference curves cannot intersect.
Question 2.[10pt] When prices of two goods increase proportional to income, the optimal
choice will be to consume less of either good. 1

PART II: Calculation Questions 1 Supply and Demand Question 1.[12pt] Your demand for chocolate is given by Qd = 50 ? a1 ? P , where a is your
craving for chocolate. For now assume a = 1. Your room mate has a stack of chocolate
which she doesn’t like to share, but she will sell it to you according to the supply function
Qs = D + 5 ? P . Assume for now that D = ?10. Think of P as the number of times you
have to do the dishes per week.
a) Sketch the supply and demand curve, label the axes and intercepts
b) Make an example of what D could represent in terms of the scenario. What does the
negative value of D imply?
c) Calculate equilibrium quantity and price
d) Show graphically and analytically what happens when your craving for chocolate increases from 1 to 4.
Question 2. [18pt] Consider the following demand curve:
P = 15 ? 1 d
Q + 4Py2 +
5 where Q is quantity demanded, P is the good’s own price, Py is the price of another good,
and I is income. a) Price Elasticity (Assume Py = 12 , I = 100)
i) Sketch the curve in the appropriate graph for price elasticity; label axes and
ii) What is the slope (?Q/?P ) of this function?
2 iii) At a price of P = 9, what is the price elasticity? What kind of good is this demand
for (and why)?
b) Income Elasticity (Assume Py = 12 )
i) Sketch the curve in the appropriate graph for income elasticity; label axes and
ii) What is the slope (?Q/?I) of this function?
iii) At a price of p = 4 and I = 100, what is the income elasticity? What kind of
good is this demand for (and why)?
c) Cross-Price Elasticity (Assume I = 100)
i) Sketch the curve in the appropriate graph for price elasticity; label axes and
ii) What is the slope (?Q/?Py ) of this function?
iii) At a price of p = 2 and py = 2 ,what is the cross price elasticity? What is the
relation between the two goods (and why)? 2 Preferences Question 3.[24pt] Suppose you can spend your monthly income on two specific goods X
and Y. For each of the following cases a) to c), answer the following questions:
i) Sketch some indifference curves in the appropriate graph. Tip: Start by connecting
bundles that yield the same level of utility.
ii) Derive the utility function if possible.
iii) What kind of preferences are the indifference curves derived from? Are they rational?
Why, why not?
iv) State a unique example of what good X and Y could be in this case. 3 a) You like to consume 3 units of X together with 1 unit of Y. More of both goods gives
you additional utility but only at this ratio. A basket containing 3 units of X and 2
units of Y does not yield any more utility than a basked of 3 units of X and 1 unit of
Y. Neither good gives you any utility alone.
b) You like good X, but you do not like good Y. So for every additional Y you consume,
you have to be compensated with 2 additional units of X to be as well off as before.
You are indifferent between consuming bundle (X,Y) and bundle (X+2,Y+1).
c) You like both good X and Y, but good X is always more important. You always prefer
baskets containing more X to baskets containing fewer X, regardless of how much Y
they contain. But if two baskets contain the same number of X, you prefer the basket
with the most Y. 3 Consumer Choice Question 4.[14pt] A consumer has the following utility function and budget constraint:
1 1 U (x, y) = x 2 ? y 2
w = px x + py y,
where w is the consumer’s wage and px and py are the prices of good x and y, respectively.
Assume w = 25, px = 1, py = 5
a) Draw the budget line and sketch the indifference curves. Do you expect an interior
solution? Why?
b) Solve for the optimal consumption bundle.
c) Now assume the government introduces a 10% wage tax (0.10 ? w has to be paid to the
government and will never be seen again). Show graphically and analytically how this
changes your answer. 4 Question 5.[12pt] Consider the following internet plan. The first 2 gigabyte of data download cost a lump sum of $50, every additional 0.1 gigabyte costs an additional $1 dollar. But
if you go over 3 gigabyte you will have to pay 5$ per 0.1 gigabyte. Your monthly budget is
a) Draw the budget line (to scale) as a choice between gigabyte download bandwidth on
the x-axis and a composite good (money or “everything else”) on the y-axis. What is
the maximum amount of bandwidth you can afford?
b) Draw a second plan where you have to pay $60 for unlimited internet.
c) Show and explain with the help of sketching different kinds of indifference curves which
plan would be preferred under which circumstances. How much bandwidth would be
consumed in these cases? 5