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