Economics 2020b / HBS 4011 / HKS API-112
Practice Problems for Lectures 1 to 2
Spring 2011
LECTURE 1: PRODUCER THEORY
1.1. Returns to Scale
Consider the following production technology functions. For each, identify whether the
firm has increasing returns
3.4 Price Discrimination with Two Types of Consumers
(a) A competitive market will set the same price for men and women with price equal to
marginal cost = 4. Soving for the quantities for men and women that correspond to this
price, we have qm = 30 pm =
j1.3 Production with Start-Up Costs
(a) The firm solves max (x) = p y(x) wx
Differentiating the profit function with respect to x gives the first-order condition for an
interior solution is
d / dx
=
p y(x) w = 0.
Here y(x) = 1/x for x > 1, y(x) = 0 for x
Economics 2020b / API 112 / HBS 4011
Spring 2011
Problem Set #9
Due Wednesday, April 20, 2011
1. MWG question 14.B.4
For part b, the hint should read vL and vH and not v1 and v2. For part d, the goal is to show that the
second-best level of effort can be
Economics 2020b / HBS 4011 / Kennedy School API-112
Final Examination
Spring 2010
Instructions: You have 180 minutes to complete the following examination. The exam
has five questions, each with multiple parts. Answer all parts of all questions in the exa
Economics 2020b / API-112 / HBS 4011
Spring 2010
Midterm Examination
March 10, 2010
This exam contains three questions for a total of 90 points. Each question has three parts
worth 10 points for a total of 30 points per question. Please complete all three
Section Notes 1
Wonbin Kang
January 27, 2009
Agenda
1. Prot Maximization Problem (PMP)
2. Cost Minimization Problem (CMP)
3. Example of CMP (2003 Final Exam Problem 3)
4. Firm Technology, Cost Function, and Supply
1
PMP
If you've been reading MWG, you'll
Economics 2020b / HBS 4011 / HKS API-112
Practice Problems with Solutions for Lectures 1 to 2
Spring 2011
1.1. Returns to Scale
(a) Consider a change in scale from (x1, x2) to (x1, x2) for a constant > 1.
f(x1, x2)
= min [A(x1) , B(x2)]
= [Ax1, Bx2]
= f(x
Economics 2020b / HBS 4011 / HKS API-112
Solutions to Practice Problems for Lectures 19 and 20
Spring 2010
19.1 Supervision and Contracting
(a) The firm solves
min wS , wF pL wS 1 pL wF
s.t :
pL v wS 1 pL v wF u0
pL v wS 1 pL v wF pH v wS 1 pH v wF g eH
Practice Problem 5.3
Part (a)
At p = 7, Q = 28. In turn, each rm produces q1 = q2 = 14. Prot for each
rm at this price/quantity vector is equal to:
i (pi = 7) = p qi C(qi ) = 7 14
1
142 = 0.
2
We need to check that this is an equilibrium. Consider a dev
Economics 2020b / HBS 4011 / HKS API-112
Solutions to Practice Problems on Lectures 9 to 13
Spring 2011
9.1 Cobb Douglas and Exchange Equilibrium (Problem 1 on Problem Set 4)
9.2 Exchange Equilibrium with Specialized Consumers
(a) Person 1s endowment conv
Economics 2020b / HBS 4011 / HKS API-112
Practice Problems for Lectures 19 and 20
Spring 2010
19.1 Supervision and Contracting
A firm hires a scientist to develop a new product. The scientist chooses between two
levels of effort, high effort (eh) or low e
API-109
Spring 2011
Practice Problems for Lecture 13
13.1 Tragedy of the Commons: (MWG 11.D.5. Note: MWG does not specify f(0) = 0).
Lake Ec can be freely accessed by fishermen. The cost of sending a boat out on the lake
is r > 0. When b boats are sent ou
LECTURE 9: EXCHANGE EQUILIBRIUM
9.1. Exchange Equilibrium and Boundary Solutions
(a) MWG, problem 15.B.9.
(b) Consider a consumer with the Cobb-Douglas utility function, u(x, y) = xa y1-a.
Show that for any consumption bundle (x, y), there is a wealth lev