MANAGERIAL ECONOMICS (BSP 1703) FORMULA SUMMARY NOTES UNIVERSITY OF SINGAPORE

MANAGERIAL ECONOMICS (BSP 1703)
FORMULA SUMMARY NOTES UNIVERSITY OF
SINGAPORE

, BSP1703 Mathematical Calculations

Chapter 1: Introduction
Δ𝐵 𝑑𝐵 Δ𝐶 𝑑𝐶
MB= = MC= = Marginalist Principal achieved when MB=MC
Δ𝑄 𝑑𝑄 Δ𝑄 𝑑𝑄



Chapter 2: Demand and Supply
Demand Supply
Linear demand function: f(p) = Qd = A – B(Px) Linear supply function: Qs = A + B(Px)
s
i.e., Qxd = 10 – 2Px i.e. Qx = 10 + 2Px
Inverse demand function: px as function of Qd Inverse supply function: px as function of Qs
➔ y = mx + c ➔ Px = - 5 + 0.5Qxs
➔ 2Px = 10 – Qxd ➔ Px = 5 – 0.5Qxd

Profit Max Q, Q*: DD=SS 1/ (Gradient of Linear Line
Δ𝑄/𝑄 𝑃 Δ𝑄 𝑑𝑄/𝑄 𝑃 𝑑𝑄 aka m aka slope)
PED: = =
Δ𝑃/𝑃 𝑄 Δ𝑃 𝑑P/𝑃 𝑄 𝑑𝑃

𝑑𝑄𝑠/𝑄𝑠 𝑃 𝑑𝑄𝑠
PES: =
𝑑P/𝑃 𝑄𝑠 𝑑𝑃

𝑑𝑄𝑥/𝑄𝑥
CED: =
𝑑Py/𝑃𝑦

𝑑𝑄𝑑/𝑄𝑑 𝑌 𝑑𝑄𝑑
YED: =
𝑑Y/𝑌 𝑄𝑑 𝑑𝑌




Chapter 3: Consumer Theory
U = U(X) where U is consumer specific and Δ𝑈 𝑑U
MUX = =
assume that U(x) functions are ordinal
(variable/subjective) in scale

Slope of IC = Budget Line
Δ𝑌 𝑀𝑈𝑥 P𝑥 𝑑𝑦 Δ𝑈 𝑑U
MRS = − = = = . 𝑤ℎ𝑒𝑟𝑒 𝑀𝑈𝑥 = = MRS of F for C=3 (give up 3 units of c to obtain 1 add. unit of F)
Δ𝑋 𝑀𝑈𝑦 P𝑦 𝑑𝑥 Δ𝑋 𝑑X

Budget Constraints; can buy PxX + PYY ≤ I
Slope of Budget Line
𝑰 𝑷𝑿
Budget Line: PxX + PYY = I OR 𝒀 = − 𝑿
𝑷𝒀 𝑷𝒀

Optimal Consumption Bundle:
𝑀𝑈𝑥 P𝑥 𝑀𝑈𝑥 𝑀𝑈𝑦
= → =
𝑀𝑈𝑦 P𝑦 P𝑥 P𝑦
Horizontal Summation:
Each identical firm has DD eqn: Q = -2P + 10
Mkt DD Eqn for 100 identical firms: Q1 + Q2 +……Q100 = Qmkt
100Q = 100 (−2P + 10) Qmkt=-200P+1000 P = −0.005Qmarket +5