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
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
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 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 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 3 Solutions
1. Tara snacks on peanuts and twinkies. Her preferences on peanuts (x) and twinkies (y) can be
represented by the utility function U(x,y) = 2lnx + 2lny where peanuts are measured in pounds and
twinkies in boxes.
a) If the price of pea
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 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
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
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
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
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
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 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
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
UsingtheLagrangiantosolvetheUtilityMaximizationProblem
BasicProblemistomaximizeU(x,y)subjecttotheconstraintPxx+Pyy=I.TheLagrangianisthefunction:
L x, y , U ( x, y ) Px x Py y I
TheLagrangianmethodistomaximizethisnewfunctionofthreevariables.Thisisanuncons
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
Columbia University
Intermediate Microeconomics
Homework 1 Suggested Solutions
1. For each of 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 th
Recitation Solutions Week 3
Intermediate Microeconomics
1. Every week, Victoria has a fixed budget of I dollars to spend on gasoline
(x) and burritos (y). Victorias preferences for these goods can be
represented by the utility function U (x, y) = ln x + l
Homework Assignment 4
1. Suppose there are only two goods, cheese and lottery tickets. Cheese is a normal good and
lottery tickets are inferior. Use income and substitution effects to analyze the effects of the
following government cheese programs on Simo
Homework 5
1. There are 8760 hours in a (non-) leap year. Assume that a typical upper middle income worker
earns $80 per hour and has no other source of income. The worker can use his income to purchase
a consumption good priced at $1 per unit.
a) Illustr
Homework 1
Microeconomics
1. For each of 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 substituti
Homework 6
DO NOT HAND IN
1. Marta has a monthly income of $10,000. Unfortunately, there is a chance that she will have an
accident that will result in costs of $5904. Thus leaving her an income of only $4096. Marta is a
high risk individual and the proba
Homework 3
Intermediate Microeconomics
1. In 2000 Morris drinks pints of juice (x) and gallons of milk (y). His preferences on juice (x)
and milk (y) can be represented by the utility function u(x,y) = xy2.
a) Suppose that Px = $1, Py = $1 and I = $6. Fin
Recitation 2
Question 1
Mary has to choose between different combinations of goods X and Y. Her preferences over
those goods are represented by the utility function u(x, y) = x1/3 y 2/3 and her income is M
dollars. Lets call the prices of goods X and Y as
Columbia University
Intermediate Microeconomics
Homework 4 Suggested Solutions
1. Suppose there are only two goods, cheese and lottery tickets. Cheese is a normal good and
lottery tickets are inferior. Use income and substitution effects to analyze the ef
Intermediate Microeconomics:
Homework 3 Solutions
1. In 2000 Morris drinks pints of juice (x) and gallons of milk (y). His
preferences on juice (x) and milk (y) can be represented by the utility
function u(x, y) = xy 2 .
(a) Suppose that Px = $1, Py = $1,