Barnard College
BC 3035
Spring 2014
Problem Set 2
1. Utility function: U = f(x, y)
Budget constraint: 100 = 4x + 5y
a) Graph the budget constraint, labeling all relevant items.
For each bundle given below, is the bundle feasible for this budget constraint

Barnard College
BC 3035
Spring 2015
Problem Set 5 - Solution
1. We have used Cobb-Douglas utility functions, U = Ax y , all semester.
a) Find the demand functions, x = f(Px) and y = g(Py), of a Cobb-Douglas utility function.
Hint: A demand function shows

Barnard College
BC 3035
Spring 2015
Problem Set 8 - Solution
California Dreaming?
Since the union lowered labor costs, life has been good at Macrohards Vulcanite
production plant in California. Their current situation is:
Total Cost: TC = VC + FC = 75Q 4Q

Barnard College
BC 3035
Spring 2015
Problem Set 9
Ms. Ann Goes to Washington
Hillary is considering a run for national office and wants to assemble a core group of
advisors. She is considering Marissa, Anns boss, as her economic advisor, so she
asks Maris

Barnard College
BC 3035
Spring 2015
Problem Set 6 - Solution
1. Ann, Through the Looking-Glass
Ann has taken a job at Macrohard, a start-up tech company in Seattle. She is on the
production team developing a new product, code-named Looking-Glass. This is

Barnard College
BC 3035
Spring 2015
Problem Set 10
A Funny Thing Happened on the Way to the Forum
Marissa and Ann are with the mover and shakers at the Davos World Economic Forum.
Ann is talking with Sheryl, an old friend of Marissas.
Sheryls firm manufac

Barnard College
BC 3035
Spring 2015
Problem Set 7 - Solution
1. Anns Great Expectations
Ann has been promoted to a management position. She is part of the team sent to
review the operation of a Macrohard facility in California, which produces Vulcanite.
T

Barnard College
BC 3035
Spring 2015
Problem Set 9 - Solution
Ms. Ann Goes to Washington
Hillary is considering a run for national office and wants to assemble a core group of
advisors. She is considering Marissa, Anns boss, as her economic advisor, so she

Barnard College
BC 3035
Spring 2015
Problem Set 10 - Solution
A Funny Thing Happened on the Way to the Forum
Marissa and Ann are with the mover and shakers at the Davos World Economic Forum.
Ann is talking with Sheryl, an old friend of Marissas.
Sheryls f

Barnard College
BC 3035
Spring 2015
Problem Set 11
The Player
This is Anns toughest assignment yet: figuring out how to manage this product.
Macrohard maintains a monopoly in the holographic TV market because of its patent,
but it is about to expire.
The

Barnard College
BC 3035
Spring 2015
Problem Set 8
California Dreaming?
Since the union lowered labor costs, life has been good at Macrohards Vulcanite
production plant in California. Their current situation is:
Total Cost: TC = VC + FC = 75Q 4Q2 + 0.1Q3 +

Barnard College
BC 3035
Spring 2015
Problem Set 3 - Solution
1. Ann is Sleepless in Seattle from drinking coffee at cafs all over the city. At one
caf, Ann and her Friends, Monica and Phoebe, discuss how they spend their caf
budget on coffee and muffins.

Barnard College
BC 3035
Spring 2015
Problem Set 1
1. Find the first and second derivatives.
a) U = 10x 0.5
b) U = 4 + x 2 + 3 x
c) U = 7 x 5
2. Do the functions in problem 1 display the properties normally expected from a utility
function? Assume x > 0.
3

Barnard College
BC 3035
Spring 2015
Problem Set 3
1. Ann is Sleepless in Seattle from drinking coffee at cafs all over the city. At one
caf, Ann and her Friends, Monica and Phoebe, discuss how they spend their caf
budget on coffee and muffins.
a) Monicas

Barnard College
BC 3035
Spring 2015
Problem Set 4
1. A tax grows in Seattle.
a) Beth, Seattles city finance commissioner, needs to raise additional tax revenue.
She knows the price of X (Px) is about to drop, so she wants to introduce an income
surcharge

Barnard College
BC 3035
Spring 2015
Problem Set 2 - Solution
1. Utility function: U = f(x, y)
Budget constraint: 100 = 4x + 5y
a) Graph the budget constraint, labeling all relevant items.
y
25
20
15
10
5
0
0
5
10
15
20
25
30
x

Barnard College
BC 3035
Spring 2015
Problem Set 5
1. We have used Cobb-Douglas utility functions, U = Ax y , all semester.
a) Find the demand functions, x = f(Px) and y = g(Py), of a Cobb-Douglas utility function.
Hint: A demand function shows the optimal

Barnard College
BC 3035
Spring 2015
Problem Set 1 - Solution
1. Find the first and second derivatives.
a) U = 10x 0.5
dU
5
U' =
= (10)(0.5)x (0.51) = 5x 0.5 = 0.5
dx
x
2
d U
2.5
2.5
U' = 2 = (5)(0.5)x (0.51) = 2.5x 1.5 = 1.5 =
x x
dx
x
b) U = 4 + x 2 + 3

Barnard College
BC 3035
Spring 2015
Problem Set 6
1. Ann, Through the Looking-Glass
Ann has taken a job at Macrohard, a start-up tech company in Seattle. She is on the
production team developing a new product, code-named Looking-Glass. This is a
personal

Barnard College
BC 3035
Spring 2015
Problem Set 4 - Solution
1. A tax grows in Seattle.
a) Beth, Seattles city finance commissioner, needs to raise additional tax revenue.
She knows the price of X (Px) is about to drop, so she wants to introduce an income

Barnard College
BC 3035
Spring 2015
Problem Set 7
1. Anns Great Expectations
Ann has been promoted to a management position. She is part of the team sent to
review the operation of a Macrohard facility in California, which produces Vulcanite.
The price of

Barnard College
BC 3035
Spring 2015
Problem Set 11 - Solution
The Player
This is Anns toughest assignment yet: figuring out how to manage this product.
Macrohard maintains a monopoly in the holographic TV market because of its patent,
but it is about to e