AMS/ECON 11B
Quiz 8 Solutions
March 11, 2013
1. (8 pts) Use the method of Lagrange multipliers to nd the maximum value of the
function.
0.3 0.5
f (x, y ) = 25x y
subject to the constraint
10x + 15y = 800.
You may assume that the critical value you nd yiel
AMS/ECON 11B
Quiz 7 Solutions
March 6, 2013
1. (6 pts) Find the critical point(s) of the function
2
3
2
f (x, y ) = x + 2xy + y + 2y + x + 3
First, dierentiate: fx = 2x + 2y + 1 and fy = 2x + 3y 2 + 4y .
Next, solve the pair of equations fx = 0 and fy = 0
AMS/ECON 11B
Quiz 5Solutions
February 20, 2013
The demand function for a certain rm is given by
20ps Y 1/2
,
q=
1.5p + 20
where q is the monthly demand for the rms product, p is the price of the rms
product, ps is the average price of a substitute and Y i
AMS/ECON 11B
Quiz 4 Solutions
February 6, 2013
1. (6 pts) Find the Consumers and Producers surplus at equilibrium for the market
60
with supply equation p = 5 + 0.2q and demand equation p =
.
1 + 0.2q
First: Find the point of market equilibrium. . .
60
=
AMS/ECON 11B Quiz 8 Solutions
November 25, 2013
1. (6 pts) Find the critical point(s) and critical value(s) of the function
3
2
2
f (x, y ) = x x 4xy + 2y + 4x 4y + 5.
First order conditions:
fx = 3x2 2x 4y + 4 = 0 =
3x2 2x (4x + 4) + 4 = 0 = 3x2 6x = 0
f
AMS/ECON 11B Quiz 6 Solutions
November 13, 2013
1. A rms production function is given by Q = 24K 2/3 L1/2 , where Q is monthly
output, measured in 100s of units, and K and L are monthly capital and labor inputs,
both measured in $1000s. Current input leve
AMS/ECON 11B
Quiz 5 Solutions
November 6, 2013
Find the indicated partial derivatives of the given functions. Clean up your answers.
(a) (4 pts) f (x, y, z ) = 3x2 yz 3 2x3 y 5z + 1;
fx = 6xyz 3 6x2 y
fz = 9x2 yz 2 5.
uv 2 + 2u2
(b) (2 pts) w =
;
u + 3v
w
AMS/ECON 11B
Quiz 7 Take Home
November 20, 2013
1. Find the critical points and critical values of the functions below.
(a) f (x, y ) = x2 + 2xy + 2y 2 3x + 4y + 1
(b) w = u3 + u2 4uv + 2v 2 + 4u + 4v + 3
(c) g (x, y, z ) = 10x3/4 y 2/5 10xz 5yz + 460z
2.
AMS/ECON 11B
Quiz 4 Solutions October 25, 2013
1. (10 pts) Compute the Producers and Consumers surplus at equilibrium for the
market with supply and demand curves
p = 50
Demand:
Supply:
p=5+
12
q
10
1
q
4
I. Find the point of market equilibrium:
1
12
5 +
AMS/ECON 11B
Fall 2013
Midterm Exam Solutions
(1) Compute the following denite and indenite integrals.
5
a. (3 pts)
0
4x
dx = 4
3x + 1
2(3x 2) 3x + 1
27
5
=
0
8 13 4 8 (2) 1
432
=
= 16
27
27
27
Comment: Use formula #12 from the list of integration formula
AMS/ECON 11B
Fall 2013
Midterm Exam Solutions
(1) Compute the following denite and indenite integrals.
6
a. (3 pts)
0
2(12t 2)(4t + 1)3/2
2t 4t + 1 dt = 2
240
6
=
0
1
8752
(70 125 (2) 1) =
145.867
60
60
Comment: Use formula #11 from the list of integrat