Economics 100B Exercise Set B
Prof. Galperti
Spring 2015
1
Group CP Consumer and Producer Theory
1. For each of the following, say whether the production technology satises (i) Diminishing
MRTS, (ii) Diminishing Marginal Product in each input, and (iii) C

Produc'on Func'on
The produc'on func'on species the maximum amount of an output that
can be produced from a par'cular combina'on of inputs.
q = f(L,K)
where q units of output are produced using L units of

Homework 4 Solutions
Problem 5.1.4. Let = cfw_m + n 2 | m, n Z.
R
(a) Show that m + n 2 is a unit in R if and only if m2 2n2 = 1.
(b) Show that 1 + 2 has innite order in R .
(c) Show that 1 and 1 are the only units that have nite order in R .
Proof. (a) D

Homework 5 Solutions
Problem 5.3.20. In the ring Z[i] of Gaussian integers let p be the ideal generated by a prime number. Show
that Z[i]/ p has p2 elements, and has characteristic p.
Proof. Dene a map : Zp [x] Z[i]/ p where (f (x) = f (i) + p . One can v

Homework 6 Solutions
Problem 6.1.3. Suppose that u is algebraic over the eld K, and that a K. Show that u + a is algebraic over
K, nd its minimal polynomial over K, and show that the degree of u + a over K is equal to the degree of u over
K.
Proof. Let f

Homework 7 Solutions
Problem 6.3.3. In this exercise we outline how to construct a regular pentagon. Let = cos(2/5)+i sin(2/5).
(a) Show that is a primitive fth root of unity.
(b) Show that ( + 1 )2 + ( +1 ) 1 = 0.
(c) Show that + 1 = (1 + 5)/2.
(d) Show

Intermediate Microeconomics Part II:
Firms, Competitive Markets, and Welfare
Simone Galperti
April 2015 version
Section 0. (Page 1)
You studied a model of consumer preferences and behavior in the rst part
of the Intermediate Microeconomics course. In this

Economics 100B, Spring 2015, Practice Exercises on Optimal
Supply
Suppose that the cost function of a rm is c(q) = 4q 3 + 2q + 27.
(a) Calculate the short-run supply of the rm.
1
space
2
space
3
(b) How much does the rm supply when the price p = 17? Is th

Economics 100B, Spring 2015, Midterm Practice Exercises
1
1
Exercise 1: Consider the production technology f (L, K) = L 3 K 3 . Use the Lagrangian approach to compute the long-run cost function of the rm.
1
space
2
1
1
Exercise 2: Consider the production

Economics 100b Final Examination (B)
Prof. Galperti, Winter 2014
1 2 3 4 5
8 12 20 12 15
6 Total
18
85
Your name:
Last two digits of your student ID:
If you signed the Buckley
Waiver, please circle this:
WAIVER
You have two hours and 45 minutes to complet

Economics 100B Midterm Examination 2
Prof. Simone Galperti, Spring 2015
You have 80 minutes to complete this examination. You may not use any notes, calculators, cellphones,
or books during the examination. Write your answers in pen, including all necessa

Economics 100B: Microeconomics, Part B
Spring 2015, Professor Simone Galperti
This is the second of three courses in the core microeconomics sequence. It builds on the material presented
in Economics 100A. The principal themes of the course will be the th

Economics 100B Problem Set 1 Solutions
Prof. Galperti
Spring 2015
1
Group CP Consumer and Producer Theory
1. For each of the following, say whether the production technology satises (i) Diminishing
MRTS, (ii) Diminishing Marginal Product in each input, an

Economics 100B Problem Set 4 Solutions
Prof. Galperti
Spring 2015
1
Group CP Consumer and Producer Theory
17. Suppose a rms cost function is c(q) = q 2 + 100. Compute the average cost, marginal
cost, and average variable cost functions. Also compute the q

Economics 100B Syllabus
Intermediate Microeconomics:
Production, Costs, Supply and Competitive Markets
UCSD Fall 2014, Tang, Section A00
Times and Places
Lectures:
MWF 10-10:50a Pepper Canyon 106
Discussion Sections (attend any one of four):
Tuesdays 6-6:

Homework 3 Solutions
Problem 1. Suppose F is a eld and f is a polynomial with coecients in F . Let a be the leading coecient of
f . Prove that there exists an integer m and irreducible monic polynomials p1 , . . . , pm such that f = ap1 pm .
Proof. Suppos

Economics 100B Midterm Examination 2
Prof. Simone Galperti, Spring 2015
You have 80 minutes to complete this examination. You may not use any notes, calculators, cellphones,
or books during the examination. Write your answers in pen, including all necessa

Costs
Costs
Total Cost = Fixed Cost + Variable Cost
We have been examining produc3on func3ons
Produc3on func3ons dene ecient produc-on (that is, the maximum
that can be produced from a given set of inputs)
There

Compe(ve Firms
Firms sell iden%cal products
Firms freely enter and exit the market
Implica(on: Firms are price takers
where is prot, R is total revenue, and C is total cost.
If rm raises prices from market pr

Econ 100B: Tang
Practice Problem Set 1: Theory of Production (Ch. 6) Key
1) Assume that to produce almonds you need almond trees (T) and honeybees
(B). Say to make one truckload (q) of almonds you need 5 hives of honeybees to
pollinate 1 line of your almo

Econ 100B, Midterm 1
LAST NAME: _
Tuesday, April 22, 2008
FIRST NAME: _
STUDENT ID: _
SIGNATURE: _
You have one hour and twenty minutes for the exam. Show all
work. We reserve the right to deduct points from answers that
are hard to read. There are a tota

Econ 100B, Midterm 1
LAST NAME: _
Tuesday, April 22, 2008
FIRST NAME: _
STUDENT ID: _
SIGNATURE: _
You have one hour and twenty minutes for the exam. Show all
work. We reserve the right to deduct points from answers that
are hard to read. There are a tota

Practice Midterm 1B
1
1
1) Specialty tea is made according to the production function: q = 4 K 4 L2 .
Suppose that capital at the tea factory is fixed at K=1. Find values of w and r that
would result in the short-run total cost function for tea C (q) = q

Econ 100B: Tang
Practice Problem Set 1: Theory of Production (Ch. 6)
1) Assume that to produce almonds you need almond trees (T) and honeybees
(B). Say to make one truckload (q) of almonds you need 5 hives of honeybees to
pollinate 1 line of your almond t