Homework 9
1. The demand for copper in Canada is perfectly elastic at the world price of copper ($3.40 per pound). If
the Canadian government places a $.10 per pound tax on copper mining companies in Canada then what
is the effect of this tax on the price
Homework1Solutions
1. For each of the following utility functions graph the indifference curves through the
bundles (2,3) and (2,4). Find one other bundle on each indifference curve. For each of
them find the formula for the marginal rate of substitution
Recitation 11
1. The US domestic supply of bauxite and domestic demand for bauxite are given by:
QUSS = .5P and QUSD = 400 - 2.5P. Price is measured in dollars per ton and quantity is measured in
millions of tons per year.
a) Given the domestic supply and
1. A typical cheese shop has a daily cost curve given by C (Q) 0.2Q 2 5Q 500 where quantity is
measured in pounds sold per day. The cheese market is a perfectly competitive market.
a)
What is the typical cheese shops MC curve? What is its AC curve? What i
Homework Assignment 10
1. Sheila and Bruce are taking a bike trip. Sheila brought 20 bags of raisins (x) and 10 bags of
granola (y). Sheila's utility function is US(x,y) = 2lnxS + 4lnyS. Bruce brought 10 bags of raisins
and 20 bags of granola. Bruce's uti
Homework Assignment 4
1. Cecilia can work 160 hours in a month. She has the opportunity to work for $10 per hour. With the
income that she earns from working she purchases cans of beans at a price of $1 per can. She has no other
income.
a) Putting hours o
Homework 7 Solutions
1. Suppose there are two firms that supply pencils. The first firm has a marginal cost function of MC1 = Q1
and the second firm has a marginal cost function of MC2 = (1/4)Q2 + 3. If these are the only two firms in the
industry then wh
Homework 6
Do Not Hand In
1. A firm produces a soft drink using two ingredients, sugar (S) and bubbly water (B) in fixed
proportions: 6 tablespoons of sugar per 12 oz of bubbly water.
c) What is the production function?
d) Does this production function ex
Homework Assignment 11
1. To successfully price discriminate a firm must separate customers with more elastic demands
who are charged less, from customers with inelastic demands, who are charged more. Explain
how the following practices can be used to sep
Sketch of the derivation of the Slutsky Equation
The consumers utility maximization problem is:
Max U(x,y) subject to Pxx + Pyy = I
The solution to this problem is found by solving the two equations in the two unknowns:
Tangency: MRS = (U/x)/(U/y) = Px/Py
Recitation 5
Intermediate Microeconomics
1. Suppose that Simon has $100. He can invest any fraction of his money in real state (a risky asset).
If housing prices are up then he will receive a return of $2 on every dollar invested (for a total of $3).
If h
Part II Question 1 ( 32 points) Do ONE question in Part II
Suppose that we can represent Pauline's preferences for cans of pop (the x-good) and pizza slices (ygood) with the utility function u(x,y)= min[4x,5y] . The Marshallian demand functions associated
Recitation 2
Exercise 1:
Martin is shopping for school supplies. He needs to purchase pens which cost $1 per
package and notebooks which cost $1.5 each. He has $9 to spend on school supplies.
a) Putting pens on the x-axis and notebooks on the y-axis illus
Intermediate Microeconomics-Recitation 1
1. Draw indifference curves to represent the following types of preferences and indicate the
direction of increasing satisfaction:
a. I like both peanut butter and jelly, and I always get the same additional satisf
W3211 Slides #1
Introduction and Mathematical Review
Jonathan Vogel
Columbia University
Spring 2017
Introduction
Two main themes in economics
1. Individual behavior
I
Assumptions:
1. Agents face well defined problems
I
agents have choice variables
I
agent
Q1) Jagdish is a farmer who has the option of planting either only corn or only millet (his acreage is too
small to divide between crops). Regardless of which crop he chooses the yield from his farm (and hence
his income) will depend on the weather, in pa
Estimating the Effect of a Tariff in a Small Open Economy
$ per unit
$ per unit
QS
A = Consumer Surplus
B= Domestic Producer Surplus
P*
Imports = QD-QS
A
PW
B
PW
Imports
QS(PW)
QD
QD(PW)
Imports
units
Recitation 7 Intermediate Microeconomics
1. Bobs Basil Farm uses both premium organic manure (x) and compost (y) to fertilize the basil
plants. The production function of Bobs is given by where both manure (x) and compost are
measured in cubic yards and Q
Walras Law
Statement of Walras Law for the 2-person, 2-good exchange economy: If the market
for one good clears then the market for the second good clears.
Demonstration of Walras Law for the specific example of Bruce and Sheila from class
Pxxs + Pyys = 1
Lecture 3:
Utility Maximization
Key Terms
Budget Constraint
Optimization Principle
Agents choose to allocate their fixed
income in such a way as to maximize their
utility.
Well show: To maximize utility, given a fixed amount of
income, an individual wi
Lecture 4:
Demand Functions
Income and Substitution Effects
Key Terms
Demand Functions
Normal good
Inferior good
Income effect
Substitution effect
Giffen good
Price, income, and cross-price elasticities
Elastic, Inelastic, and unit-elastic goods
Consumer
Lecture 5:
Information and Uncertainty
Key Terms in Lecture
Expected value
Fair game
St. Petersburg Paradox
Expected utility
Certainty equivalent
Utility of the expected value
Attitudes towards risk
Risk neutral
Risk averse
Risk inclined
Insurance
Ri
W3211
Professor Vogel
Recitation for week of January 30 - Math review
If this is too long to finish in recitation, then do these at home.
1. The objective function is
f ( x, y) = ln x + ln y,
and the constraint is
px + qy = I,
where , , p, q > 0 are posit
Bruce
Px/Py = 15/18
A
10
5
55/6
35/6
B
US = 605/6
US = 100
UB = 245/6
UB = 40
Sheila
10
11
A = endowment: MRSS = 1 and MRSB = 5/8. B = General Equilibrium allocation: MRSS = 15/18 = MRSB
Intermediate Micro
Recitation 4
In the state of New Francia a typical worker earns a wage of $10 per hour. She can work up to 20
hours per week tax free, that is, she can earn $200 per week before she must pay taxes on her
earnings. For every dollar that
1
Part I Question 1 (25 points) Do All Questions in Part I
Mark must decide how to allocate his 24-hour day between non-wage activities, leisure,
and wage activities, labor. For every hour of labor that he supplies he is paid by his
employer $w. Mark can
Name_
Suppose that the monthly market demand curve for roses in Kearney is
QD(P) = 1120 10P. Price (P) is measured in dollars per plant and quantity (Q) is
measured in plants per month. The total cost curve of a typical rose grower is
C(Q) = 0.01Q2 + 8Q +