Econ 301 Intermediate Microeconomics
Exam 1 formula sheet
1. Consumer surplus: let P C denote the price the consumers pay, QC denote the quantity of the
good they purchase, and P (QD ) denote the inverse demand curve. Then:
QC
Z
P (QD ) − P C dQ
CS =
0
2. Producer surplus: let P P denote the price the producers receive, QP denote the quantity of
the good they sell, and P (QS ) denote the inverse demand curve. Then:
Z
QP
P P − P (QS )dQ
PS =
0
3.
N P V = (B0 − C0 ) +
B1 − C1
B2 − C2
BT − CT
+
+ ... +
2
1+r
(1 + r)
(1 + r)T
4. Suppose you want to optimize (maximize or minimize) the function f (X, Y ) subject to the
constraint g(X, Y ) = C. Then set up the Lagrangian:
L(X, Y, λ) = f (X, Y ) + λ(C − g(X, Y ))
Next, find the following derivatives and set them to zero:
∂L
=0
∂X
∂L
=0
∂Y
∂L
= 0.
∂λ
This is 3 equations in 3 unknowns – simply solve for X and Y .
5. Suppose you want to optimize (maximize or minimize) the function f (X). Then set
∂f
=0
∂X
and solve for X.
1